%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEO479+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n003.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 : Wed Aug 30 22:51:32 EDT 2023

% Result   : Theorem 8.13s 8.34s
% Output   : Proof 8.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.02/1.09  % Problem    : GEO479+1 : TPTP v8.1.2. Released v7.0.0.
% 1.02/1.10  % Command    : do_cvc5 %s %d
% 1.11/1.31  % Computer : n003.cluster.edu
% 1.11/1.31  % Model    : x86_64 x86_64
% 1.11/1.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.11/1.31  % Memory   : 8042.1875MB
% 1.11/1.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 1.11/1.31  % CPULimit   : 300
% 1.11/1.31  % WCLimit    : 300
% 1.11/1.31  % DateTime   : Tue Aug 29 20:41:57 EDT 2023
% 1.11/1.31  % CPUTime    : 
% 2.24/2.43  %----Proving TF0_NAR, FOF, or CNF
% 8.13/8.34  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Do1LsXLTw3/cvc5---1.0.5_27635.p...
% 8.13/8.34  ------- get file name : TPTP file name is GEO479+1
% 8.13/8.34  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27635.smt2...
% 8.13/8.34  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 8.13/8.34  % SZS status Theorem for GEO479+1
% 8.13/8.34  % SZS output start Proof for GEO479+1
% 8.13/8.34  (
% 8.13/8.34  (let ((_let_1 (not (forall ((Q143335 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143335))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.bool) P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (=> (and (forall ((G0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143335))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.s (tptp.fun _let_2 tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) _let_5)) _let_3)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143335))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2)))))))) (= (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) _let_6)) _let_3)))) (tptp.s tptp.bool (tptp.i _let_4 _let_3))))))))))))))) (let ((_let_2 (forall ((N $$unsorted) (P0 $$unsorted)) (=> (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.s (tptp.fun _let_2 tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) _let_5)) _let_3)))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2)))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.bool) P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.image) (tptp.s _let_5 F0))) _let_3)))) (tptp.s tptp.bool (tptp.i _let_4 _let_3)))))))))))))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.univ))) (let ((_let_5 (tptp.cart tptp.real tptp.n10))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.s _let_6 tptp.univ))) (let ((_let_8 (tptp.fun _let_5 tptp.real))) (let ((_let_9 (tptp.fun _let_6 _let_3))) (let ((_let_10 (tptp.fun tptp.real _let_5))) (let ((_let_11 (tptp.fun _let_3 _let_6))) (let ((_let_12 (tptp.s tptp.num tptp.u_0))) (let ((_let_13 (tptp.fun tptp.num tptp.num))) (let ((_let_14 (tptp.s _let_13 tptp.bit1))) (let ((_let_15 (tptp.s tptp.num (tptp.i _let_14 _let_12)))) (let ((_let_16 (tptp.s _let_13 tptp.numeral))) (let ((_let_17 (tptp.s tptp.num (tptp.i _let_16 _let_15)))) (let ((_let_18 (tptp.fun tptp.num tptp.bool))) (let ((_let_19 (tptp.s _let_18 tptp.p0))) (let ((_let_20 (tptp.p (tptp.s tptp.bool (tptp.i _let_19 _let_17))))) (let ((_let_21 (tptp.s tptp.num (tptp.i _let_16 (tptp.s tptp.num (tptp.i _let_14 _let_15)))))) (let ((_let_22 (tptp.cart tptp.real tptp.n3))) (let ((_let_23 (tptp.s _let_22 tptp.y))) (let ((_let_24 (tptp.fun tptp.num tptp.real))) (let ((_let_25 (tptp.s (tptp.fun _let_22 _let_24) tptp.d_))) (let ((_let_26 (tptp.s _let_24 (tptp.i _let_25 _let_23)))) (let ((_let_27 (tptp.s _let_22 tptp.x))) (let ((_let_28 (tptp.s _let_24 (tptp.i _let_25 _let_27)))) (let ((_let_29 (tptp.fun tptp.real tptp.real))) (let ((_let_30 (tptp.fun tptp.real _let_29))) (let ((_let_31 (tptp.s _let_30 tptp.realu_mul))) (let ((_let_32 (tptp.s _let_13 tptp.bit0))) (let ((_let_33 (tptp.s tptp.num (tptp.i _let_16 (tptp.s tptp.num (tptp.i _let_32 _let_15)))))) (let ((_let_34 (tptp.s _let_30 tptp.realu_add))) (let ((_let_35 (tptp.fun _let_22 tptp.real))) (let ((_let_36 (tptp.cart tptp.real tptp.n20))) (let ((_let_37 (tptp.s _let_36 tptp.y))) (let ((_let_38 (tptp.s (tptp.fun _let_36 _let_24) tptp.d_))) (let ((_let_39 (tptp.s _let_24 (tptp.i _let_38 _let_37)))) (let ((_let_40 (tptp.s _let_36 tptp.x))) (let ((_let_41 (tptp.s _let_24 (tptp.i _let_38 _let_40)))) (let ((_let_42 (tptp.fun _let_36 tptp.real))) (let ((_let_43 (tptp.s _let_5 tptp.y))) (let ((_let_44 (tptp.s (tptp.fun _let_5 _let_24) tptp.d_))) (let ((_let_45 (tptp.s _let_5 tptp.x))) (let ((_let_46 (tptp.s _let_13 tptp.suc))) (let ((_let_47 (tptp.s _let_24 tptp.f))) (let ((_let_48 (tptp.fun tptp.num _let_18))) (let ((_let_49 (tptp.fun _let_24 tptp.real))) (let ((_let_50 (tptp.s _let_18 tptp.univ))) (let ((_let_51 (tptp.s tptp.num (tptp.i _let_16 _let_12)))) (let ((_let_52 (tptp.s _let_24 tptp.realu_ofu_num))) (let ((_let_53 (tptp.s tptp.real (tptp.i _let_52 _let_17)))) (let ((_let_54 (tptp.s _let_29 tptp.sqrt))) (let ((_let_55 (tptp.s tptp.real (tptp.i _let_52 _let_51)))) (let ((_let_56 (tptp.fun _let_24 tptp.bool))) (let ((_let_57 (tptp.fun _let_3 tptp.bool))) (let ((_let_58 (tptp.fun _let_18 tptp.bool))) (let ((_let_59 (tptp.fun _let_58 tptp.bool))) (let ((_let_60 (tptp.prod tptp.num tptp.num))) (let ((_let_61 (tptp.fun _let_60 tptp.bool))) (let ((_let_62 (tptp.fun _let_18 _let_61))) (let ((_let_63 (tptp.fun tptp.n3 tptp.bool))) (let ((_let_64 (tptp.s _let_63 tptp.univ))) (let ((_let_65 (tptp.fun tptp.n20 tptp.bool))) (let ((_let_66 (tptp.s _let_65 tptp.univ))) (let ((_let_67 (tptp.fun tptp.n10 tptp.bool))) (let ((_let_68 (tptp.s _let_67 tptp.univ))) (let ((_let_69 (tptp.s (tptp.fun _let_30 tptp.bool) tptp.monoidal))) (let ((_let_70 (tptp.s (tptp.fun _let_30 tptp.real) tptp.neutral))) (let ((_let_71 (tptp.fun tptp.num _let_13))) (let ((_let_72 (tptp.s _let_71 tptp.t_))) (let ((_let_73 (tptp.s (tptp.fun _let_71 tptp.bool) tptp.monoidal))) (let ((_let_74 (tptp.s _let_71 tptp.p_))) (let ((_let_75 (tptp.s (tptp.fun _let_71 tptp.num) tptp.neutral))) (let ((_let_76 (tptp.fun (tptp.list tptp.char) tptp.bool))) (let ((_let_77 (tptp.fun tptp.bool tptp.bool))) (let ((_let_78 (tptp.s _let_77 tptp.univ))) (let ((_let_79 (tptp.fun tptp.num tptp.int))) (let ((_let_80 (tptp.s _let_79 tptp.intu_ofu_num))) (let ((_let_81 (tptp.s tptp.int (tptp.i _let_80 _let_17)))) (let ((_let_82 (tptp.s tptp.int tptp.x))) (let ((_let_83 (tptp.s tptp.int (tptp.i _let_80 _let_51)))) (let ((_let_84 (tptp.fun tptp.int tptp.int))) (let ((_let_85 (tptp.s tptp.int tptp.p1))) (let ((_let_86 (tptp.s tptp.int tptp.m))) (let ((_let_87 (tptp.fun tptp.int _let_84))) (let ((_let_88 (tptp.s _let_87 tptp.intu_mul))) (let ((_let_89 (tptp.s _let_84 (tptp.i _let_88 _let_86)))) (let ((_let_90 (tptp.s tptp.int tptp.n))) (let ((_let_91 (tptp.s _let_84 (tptp.i _let_88 _let_90)))) (let ((_let_92 (tptp.s tptp.int (tptp.i _let_89 (tptp.s tptp.int (tptp.i _let_91 _let_85)))))) (let ((_let_93 (tptp.s tptp.int (tptp.i _let_89 _let_90)))) (let ((_let_94 (tptp.s tptp.int tptp.y))) (let ((_let_95 (tptp.s _let_87 tptp.intu_min))) (let ((_let_96 (tptp.s _let_84 (tptp.i _let_95 _let_82)))) (let ((_let_97 (tptp.s tptp.int (tptp.i _let_96 _let_94)))) (let ((_let_98 (tptp.s tptp.int tptp.z))) (let ((_let_99 (tptp.s _let_84 (tptp.i _let_95 _let_94)))) (let ((_let_100 (tptp.s tptp.int (tptp.i _let_96 (tptp.s tptp.int (tptp.i _let_99 _let_98)))))) (let ((_let_101 (tptp.s _let_87 tptp.intu_max))) (let ((_let_102 (tptp.s _let_84 (tptp.i _let_101 _let_82)))) (let ((_let_103 (tptp.s tptp.int (tptp.i _let_102 _let_94)))) (let ((_let_104 (tptp.s _let_84 (tptp.i _let_101 _let_94)))) (let ((_let_105 (tptp.s tptp.int (tptp.i _let_102 (tptp.s tptp.int (tptp.i _let_104 _let_98)))))) (let ((_let_106 (tptp.fun tptp.int tptp.bool))) (let ((_let_107 (tptp.fun tptp.int _let_106))) (let ((_let_108 (tptp.s _let_87 tptp.intu_add))) (let ((_let_109 (tptp.s _let_84 (tptp.i _let_108 _let_86)))) (let ((_let_110 (tptp.s _let_84 (tptp.i _let_108 _let_90)))) (let ((_let_111 (tptp.s tptp.int (tptp.i _let_109 (tptp.s tptp.int (tptp.i _let_110 _let_85)))))) (let ((_let_112 (tptp.s tptp.int (tptp.i _let_109 _let_90)))) (let ((_let_113 (tptp.s _let_84 tptp.intu_abs))) (let ((_let_114 (tptp.s tptp.real tptp.r0))) (let ((_let_115 (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real))) (let ((_let_116 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_117 (tptp.s _let_3 tptp.integer))) (let ((_let_118 (tptp.s tptp.int tptp.a0))) (let ((_let_119 (tptp.s tptp.real tptp.x))) (let ((_let_120 (tptp.s tptp.real tptp.y1))) (let ((_let_121 (tptp.s tptp.real tptp.x2))) (let ((_let_122 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 _let_121)) _let_120)))) (let ((_let_123 (tptp.s tptp.real tptp.y2))) (let ((_let_124 (tptp.s tptp.real tptp.x1))) (let ((_let_125 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 _let_124)) _let_123)))) (let ((_let_126 (tptp.s _let_30 tptp.realu_div))) (let ((_let_127 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_126 _let_121)) _let_123)))) (let ((_let_128 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_126 _let_124)) _let_120)))) (let ((_let_129 (tptp.fun tptp.real _let_3))) (let ((_let_130 (tptp.s _let_3 (tptp.i (tptp.s _let_129 tptp.realu_lt) _let_55)))) (let ((_let_131 (and (tptp.p (tptp.s tptp.bool (tptp.i _let_130 _let_120))) (tptp.p (tptp.s tptp.bool (tptp.i _let_130 _let_123)))))) (let ((_let_132 (tptp.s _let_129 tptp.realu_le))) (let ((_let_133 (tptp.s _let_29 tptp.realu_inv))) (let ((_let_134 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i _let_133 _let_120)))) (tptp.s tptp.real (tptp.i _let_133 _let_123)))))) (let ((_let_135 (tptp.s _let_30 tptp.realu_sub))) (let ((_let_136 (= (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_34 _let_128)) _let_127)) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_34 _let_125)) _let_122)))) _let_134))))) (let ((_let_137 (tptp.s tptp.real tptp.c))) (let ((_let_138 (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real tptp.a0))))) (let ((_let_139 (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real tptp.b0))))) (let ((_let_140 (tptp.s tptp.real (tptp.i _let_52 _let_33)))) (let ((_let_141 (tptp.s tptp.real tptp.y))) (let ((_let_142 (tptp.s _let_30 tptp.realu_min))) (let ((_let_143 (tptp.s _let_29 (tptp.i _let_142 _let_119)))) (let ((_let_144 (tptp.s tptp.real (tptp.i _let_143 _let_141)))) (let ((_let_145 (tptp.s tptp.real tptp.z))) (let ((_let_146 (tptp.s _let_29 (tptp.i _let_142 _let_141)))) (let ((_let_147 (tptp.s tptp.real (tptp.i _let_143 (tptp.s tptp.real (tptp.i _let_146 _let_145)))))) (let ((_let_148 (tptp.s _let_30 tptp.realu_max))) (let ((_let_149 (tptp.s _let_29 (tptp.i _let_148 _let_119)))) (let ((_let_150 (tptp.s tptp.real (tptp.i _let_149 _let_141)))) (let ((_let_151 (tptp.s _let_29 (tptp.i _let_148 _let_141)))) (let ((_let_152 (tptp.s tptp.real (tptp.i _let_149 (tptp.s tptp.real (tptp.i _let_151 _let_145)))))) (let ((_let_153 (tptp.s _let_29 tptp.realu_abs))) (let ((_let_154 (tptp.s tptp.real tptp.p1))) (let ((_let_155 (tptp.s tptp.real tptp.m))) (let ((_let_156 (tptp.s _let_29 (tptp.i _let_31 _let_155)))) (let ((_let_157 (tptp.s tptp.real tptp.n))) (let ((_let_158 (tptp.s _let_29 (tptp.i _let_31 _let_157)))) (let ((_let_159 (tptp.s tptp.real (tptp.i _let_156 (tptp.s tptp.real (tptp.i _let_158 _let_154)))))) (let ((_let_160 (tptp.s tptp.real (tptp.i _let_156 _let_157)))) (let ((_let_161 (tptp.s _let_29 tptp.realu_neg))) (let ((_let_162 (tptp.s _let_29 (tptp.i _let_34 _let_155)))) (let ((_let_163 (tptp.s _let_29 (tptp.i _let_34 _let_157)))) (let ((_let_164 (tptp.s tptp.real (tptp.i _let_162 (tptp.s tptp.real (tptp.i _let_163 _let_154)))))) (let ((_let_165 (tptp.s tptp.real (tptp.i _let_162 _let_157)))) (let ((_let_166 (tptp.prod tptp.hreal tptp.hreal))) 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_let_198 _let_195)))))) (let ((_let_201 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_202 (tptp.s _let_201 tptp.naddu_inv))) (let ((_let_203 (tptp.s tptp.nadd tptp.y))) (let ((_let_204 (tptp.s tptp.hreal (tptp.i _let_199 (tptp.s _let_196 (tptp.i _let_198 _let_203)))))) (let ((_let_205 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_206 (tptp.fun tptp.nadd _let_201))) (let ((_let_207 (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num))) (let ((_let_208 (tptp.s tptp.nadd (tptp.i _let_207 _let_51)))) (let ((_let_209 (tptp.s _let_13 tptp.r0))) (let ((_let_210 (tptp.s (tptp.fun _let_13 tptp.nadd) tptp.mku_nadd))) (let ((_let_211 (tptp.s (tptp.fun tptp.nadd _let_13) tptp.destu_nadd))) (let ((_let_212 (tptp.s tptp.nadd tptp.a0))) (let ((_let_213 (tptp.fun tptp.num _let_60))) (let ((_let_214 (tptp.s _let_71 tptp.m_))) (let ((_let_215 (tptp.s tptp.bool tptp.f0))) (let ((_let_216 (tptp.s _let_48 tptp.l_))) (let ((_let_217 (tptp.s tptp.bool tptp.t))) (let ((_let_218 (tptp.s _let_18 tptp.odd))) (let ((_let_219 (tptp.s _let_18 tptp.even))) (let ((_let_220 (tptp.s _let_13 tptp.pre))) (let ((_let_221 (tptp.s tptp.num tptp.n))) (let ((_let_222 (tptp.s _let_71 tptp.div))) (let ((_let_223 (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_48 tptp.p0) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_222 _let_179)) _let_221)))) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_71 tptp.mod) _let_179)) _let_221))))))) (let ((_let_224 (tptp.s tptp.num tptp.b0))) (let ((_let_225 (tptp.s tptp.num tptp.a0))) (let ((_let_226 (tptp.p (tptp.s tptp.bool (tptp.i _let_19 (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_214 _let_225)) _let_224))))))) (let ((_let_227 (tptp.p (tptp.s tptp.bool (tptp.i _let_19 (tptp.s tptp.num (tptp.i _let_220 _let_221))))))) (let ((_let_228 (tptp.s tptp.num tptp.d))) (let ((_let_229 (tptp.s tptp.num tptp.c))) (let ((_let_230 (tptp.s tptp.num tptp.p1))) (let ((_let_231 (tptp.s _let_13 (tptp.i _let_72 _let_179)))) (let ((_let_232 (tptp.s _let_13 (tptp.i _let_72 _let_221)))) (let ((_let_233 (tptp.s tptp.num (tptp.i _let_231 (tptp.s tptp.num (tptp.i _let_232 _let_230)))))) (let ((_let_234 (tptp.s tptp.num (tptp.i _let_231 _let_221)))) (let ((_let_235 (tptp.s _let_13 (tptp.i _let_74 _let_179)))) (let ((_let_236 (tptp.s _let_13 (tptp.i _let_74 _let_221)))) (let ((_let_237 (tptp.s tptp.num (tptp.i _let_235 (tptp.s tptp.num (tptp.i _let_236 _let_230)))))) (let ((_let_238 (tptp.s tptp.num (tptp.i _let_235 _let_221)))) (let ((_let_239 (tptp.p _let_217))) (let ((_let_240 (tptp.s tptp.ind0 tptp.indu_0))) (let ((_let_241 (tptp.s tptp.bool tptp.d0))) (let ((_let_242 (tptp.s tptp.bool tptp.b))) (let ((_let_243 (tptp.s tptp.bool tptp.b0))) (let ((_let_244 (tptp.fun tptp.bool _let_77))) (let ((_let_245 (tptp.s _let_244 (tptp.i (tptp.s (tptp.fun tptp.bool _let_244) tptp.cond) _let_243)))) (let ((_let_246 (tptp.s tptp.bool tptp.c0))) (let ((_let_247 (tptp.s tptp.bool tptp.a))) (let ((_let_248 (tptp.p _let_241))) (let ((_let_249 (tptp.p _let_246))) (let ((_let_250 (=> _let_249 _let_248))) (let ((_let_251 (tptp.p _let_242))) (let ((_let_252 (tptp.p _let_247))) (let ((_let_253 (and (=> _let_252 _let_251) _let_250))) (let ((_let_254 (tptp.s _let_77 tptp.p0))) (let ((_let_255 (tptp.p (tptp.s tptp.bool (tptp.i _let_254 _let_215))))) (let ((_let_256 (tptp.p (tptp.s tptp.bool (tptp.i _let_254 _let_217))))) (let ((_let_257 (=> _let_251 _let_252))) (let ((_let_258 (tptp.s tptp.bool tptp.a0))) (let ((_let_259 (tptp.p _let_258))) (let ((_let_260 (tptp.p _let_243))) (let ((_let_261 (=> _let_259 _let_260))) (let ((_let_262 (= _let_258 _let_243))) (let ((_let_263 (tptp.p _let_215))) (let ((_let_264 (not _let_263))) (let ((_let_265 (tptp.p (tptp.s tptp.bool tptp.r0)))) (let ((_let_266 (tptp.p (tptp.s tptp.bool tptp.p1)))) (let ((_let_267 (tptp.p (tptp.s tptp.bool tptp.q)))) (let ((_let_268 (and _let_266 _let_267))) (let ((_let_269 (=> _let_268 _let_265))) (let ((_let_270 (=> _let_266 (=> _let_267 _let_265)))) (let ((_let_271 (or _let_266 _let_267))) (let ((_let_272 (or _let_266 _let_267 _let_265))) (let ((_let_273 (and _let_266 _let_267 _let_265))) (let ((_let_274 (= _let_217 _let_217))) (let ((_let_275 (forall ((Q143335 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143335))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.bool) P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (or (not (forall ((G0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143335))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.s (tptp.fun _let_2 tptp.bool) P0))) (or (not (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_3)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) _let_5)) _let_3))))))))))))))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6)))) (not (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143335))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (or (not (= (tptp.s _let_1 (tptp.i _let_4 _let_2)) (tptp.s _let_1 (tptp.i _let_4 _let_3)))) (= _let_3 _let_2)))))))) (= (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) _let_6)) _let_3)))) (tptp.s tptp.bool (tptp.i _let_4 _let_3)))))))))))))) (let ((_let_276 (forall ((N $$unsorted) (P0 $$unsorted) (BOUND_VARIABLE_214457 $$unsorted) (BOUND_VARIABLE_214455 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 BOUND_VARIABLE_214457))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.bool) P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_5 BOUND_VARIABLE_214455))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (or (not (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.s (tptp.fun _let_2 tptp.bool) P0))) (or (not (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_3)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) _let_5)) _let_3))))))))))))))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6)))) (not (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) BOUND_VARIABLE_214455))) (or (not (= (tptp.s _let_1 (tptp.i _let_4 _let_2)) (tptp.s _let_1 (tptp.i _let_4 _let_3)))) (= _let_3 _let_2)))))))) (= (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) _let_6)) _let_3)))) (tptp.s tptp.bool (tptp.i _let_4 _let_3)))))))))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (THEORY_LEMMA :args ((= _let_276 _let_275) THEORY_QUANTIFIERS))) :args ((or _let_275 (not _let_276)))) (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args (_let_275 false _let_276)) :args (false false _let_275)) :args (_let_274 _let_274 _let_239 (forall ((X $$unsorted) (XI_ $$unsorted)) (= (and (tptp.p (tptp.s tptp.bool X)) (tptp.p (tptp.s tptp.bool XI_))) (forall ((X0 $$unsorted)) (let ((_let_1 (tptp.s tptp.bool tptp.t))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.bool _let_2) X0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.bool X))) (tptp.s tptp.bool XI_))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_1)) _let_1))))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool X)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool XI_)))) (= (=> _let_1 _let_2) (= (and _let_1 _let_2) _let_1))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.e_) (tptp.s _let_1 X)))) (forall ((X0 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) X) (tptp.s A X0))) (tptp.s tptp.bool tptp.t)))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.q_) (tptp.s _let_1 X)))) (forall ((Q0 $$unsorted)) (=> (forall ((X0 $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) X) (tptp.s A X0)))) (tptp.p (tptp.s tptp.bool Q0)))) (tptp.p (tptp.s tptp.bool Q0))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (= (or (tptp.p (tptp.s tptp.bool X)) (tptp.p (tptp.s tptp.bool XI_))) (forall ((R0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool R0)))) (=> (=> (tptp.p (tptp.s tptp.bool X)) _let_1) (=> (=> (tptp.p (tptp.s tptp.bool XI_)) _let_1) _let_1)))))) (= _let_263 (forall ((P0 $$unsorted)) (tptp.p (tptp.s tptp.bool P0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool X)))) (= (not _let_1) (=> _let_1 (tptp.p (tptp.s tptp.bool tptp.f0)))))) _let_239 (= (tptp.s tptp.bool tptp.u_falsityu_) _let_215) (= _let_270 _let_269) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (= _let_1 _let_1))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (= (= _let_1 _let_1) (tptp.p (tptp.s tptp.bool tptp.t))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (=> (= _let_1 _let_2) (= _let_2 _let_1))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (= (= _let_1 _let_2) (= _let_2 _let_1))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s A Y))) (=> (and (= _let_2 _let_3) (= _let_3 _let_1)) (= _let_2 _let_1)))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A Y))))) (= _let_1 _let_1))) (forall ((B $$unsorted) (A $$unsorted) (T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.s A T1))) (= _let_1 _let_1))) (forall ((T1 $$unsorted) (T2 $$unsorted) (T3 $$unsorted)) (let ((_let_1 (and (tptp.p (tptp.s tptp.bool T1)) (tptp.p (tptp.s tptp.bool T2)) (tptp.p (tptp.s tptp.bool T3))))) (= _let_1 _let_1))) (forall ((T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T1)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool T2)))) (= (and _let_1 _let_2) (and _let_2 _let_1))))) (= _let_268 (and _let_267 _let_266)) (= _let_273 _let_273) (= _let_273 (and _let_267 _let_266 _let_265)) (= (and _let_266 _let_266) _let_266) (= (and _let_266 _let_266 _let_267) _let_268) (forall ((T1 $$unsorted) (T2 $$unsorted) (T3 $$unsorted)) (let ((_let_1 (or (tptp.p (tptp.s tptp.bool T1)) (tptp.p (tptp.s tptp.bool T2)) (tptp.p (tptp.s tptp.bool T3))))) (= _let_1 _let_1))) (forall ((T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T1)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool T2)))) (= (or _let_1 _let_2) (or _let_2 _let_1))))) (= _let_271 (or _let_267 _let_266)) (= _let_272 _let_272) (= _let_272 (or _let_267 _let_266 _let_265)) (= (or _let_266 _let_266) _let_266) (= (or _let_266 _let_266 _let_267) _let_271) (= _let_269 _let_270) (= _let_269 (=> _let_267 (=> _let_266 _let_265))) (forall ((P0 $$unsorted) (Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool R0)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool P0)))) (let ((_let_3 (tptp.p (tptp.s tptp.bool Q0)))) (= (and _let_2 (or _let_3 _let_1)) (or (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((P0 $$unsorted) (Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool R0)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool Q0)))) (let ((_let_3 (tptp.p (tptp.s tptp.bool P0)))) (= (and (or _let_3 _let_2) _let_1) (or (and _let_3 _let_1) (and _let_2 _let_1))))))) (forall ((A $$unsorted) (T0 $$unsorted)) (= (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool T0))) (tptp.p (tptp.s tptp.bool T0)))) (forall ((A $$unsorted) (T0 $$unsorted)) (= (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool T0))) (tptp.p (tptp.s tptp.bool T0)))) (=> _let_262 _let_261) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.s tptp.bool T0))) (let ((_let_2 (tptp.p _let_1))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.s tptp.bool tptp.f0))) (let ((_let_5 (tptp.s tptp.bool tptp.t))) (and (= (= _let_5 _let_1) _let_2) (= (= _let_1 _let_5) _let_2) (= (= _let_4 _let_1) _let_3) (= (= _let_1 _let_4) _let_3)))))))) _let_264 (= _let_264 _let_239) (= (not _let_239) _let_263) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T0)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool tptp.f0)))) (let ((_let_3 (tptp.p (tptp.s tptp.bool tptp.t)))) (and (= (and _let_3 _let_1) _let_1) (= (and _let_1 _let_3) _let_1) (= (and _let_2 _let_1) _let_2) (= (and _let_1 _let_2) _let_2) (= (and _let_1 _let_1) _let_1)))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T0)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool tptp.f0)))) (let ((_let_3 (tptp.p (tptp.s tptp.bool tptp.t)))) (and (= (or _let_3 _let_1) _let_3) (= (or _let_1 _let_3) _let_3) (= (or _let_2 _let_1) _let_1) (= (or _let_1 _let_2) _let_1) (= (or _let_1 _let_1) _let_1)))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T0)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool tptp.f0)))) (let ((_let_3 (tptp.p (tptp.s tptp.bool tptp.t)))) (and (= (=> _let_3 _let_1) _let_1) (= (=> _let_1 _let_3) _let_3) (= (=> _let_2 _let_1) _let_3) (= (=> _let_1 _let_1) _let_3) (= (=> _let_1 _let_2) (not _let_1))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))) (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))) (forall ((A $$unsorted) (A5 $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s A X) (tptp.s A A5)))) (forall ((A $$unsorted) (A5 $$unsorted)) (and (exists ((X $$unsorted)) (= (tptp.s A X) (tptp.s A A5))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s A A5))) (=> (and (= _let_2 _let_3) (= _let_1 _let_3)) (= _let_2 _let_1)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (A5 $$unsorted)) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (and (= (tptp.s A A5) _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A A5)))))) (forall ((A $$unsorted) (P0 $$unsorted) (A5 $$unsorted)) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (and (= _let_1 (tptp.s A A5)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A A5)))))) (forall ((A $$unsorted) (P0 $$unsorted) (A5 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (=> (= _let_1 (tptp.s A A5)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A A5)))))) (forall ((Q1020 $$unsorted) (P0 $$unsorted) (A5 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q1020 X))) (=> (= (tptp.s Q1020 A5) _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q1020 tptp.bool) P0) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q1020 tptp.bool) P0) (tptp.s Q1020 A5)))))) (forall ((A $$unsorted) (B $$unsorted) (P0 $$unsorted)) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y)))))))) (forall ((A $$unsorted) (B $$unsorted) (P0 $$unsorted)) (= (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y)))))) (exists ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1))))))) (and (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (and (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (and (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))) (forall ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (and (tptp.p (tptp.s tptp.bool P0)) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (forall ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1))))))) (or (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (or (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (or (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))) (exists ((X $$unsorted)) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (or (tptp.p (tptp.s tptp.bool P0)) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (exists ((X $$unsorted)) (or (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))) (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (and (tptp.p (tptp.s tptp.bool P0)) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool Q0)))) (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool P0))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))) (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (and (tptp.p (tptp.s tptp.bool P0)) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool P0))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool Q0)))) (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (forall ((X $$unsorted)) (or (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool Q0)))) (or (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool P0))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (or (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool P0))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool Q0)))) (forall ((X $$unsorted)) (or (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (=> (tptp.p (tptp.s tptp.bool P0)) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (forall ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (forall ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (=> (tptp.p (tptp.s tptp.bool P0)) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (=> (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))) (forall ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (forall ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))) (=> (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (forall ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool Q0)))) (=> (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool P0))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (exists ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool Q0)))) (=> (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool P0))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))) (exists ((X $$unsorted)) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))) (= (tptp.s A X) _let_1))))))) (= _let_262 (and _let_261 (=> _let_260 _let_259))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))) (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))) (= _let_1 (tptp.s A X))))))))) (=> _let_253 (=> (and _let_252 _let_249) (and _let_251 _let_248))) (=> _let_253 (=> (or _let_252 _let_249) (or _let_251 _let_248))) (=> (and _let_257 _let_250) (=> (=> _let_252 _let_249) (=> _let_251 _let_248))) (=> _let_257 (=> (not _let_252) (not _let_251))) (forall ((A $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))) (=> (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) tptp.p0) (tptp.s A X))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) tptp.q0) (tptp.s A X)))))))) (forall ((A $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))) (=> (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) tptp.p0) (tptp.s A X))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) tptp.q0) (tptp.s A X)))))))) (forall ((B $$unsorted) (A $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) T0) (tptp.s A X))))) (= _let_1 _let_1))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G0) _let_1)))))) (= (tptp.s _let_1 F0) (tptp.s _let_1 G0))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (= (= (tptp.s _let_1 F0) (tptp.s _let_1 G0)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G0) _let_1))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s A X)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.h_) _let_2))))))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.q_) _let_2)) (tptp.s tptp.bool (tptp.i _let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.h_) _let_2)))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) U_0) _let_1)) _let_2))) (= _let_2 _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) tptp.h_) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) U_0) _let_1)))) _let_1)))))) (forall ((A $$unsorted) (P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))) (= _let_1 (tptp.s A X))))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.h_) (tptp.s _let_1 P0))) (tptp.s A X))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T0)))) (or _let_1 (not _let_1)))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.s tptp.bool T0))) (or (= _let_1 (tptp.s tptp.bool tptp.t)) (= _let_1 (tptp.s tptp.bool tptp.f0))))) (forall ((T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T2)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.p (tptp.s tptp.bool T1)))) (let ((_let_4 (not _let_3))) (and (= (not (and _let_3 _let_1)) (or _let_4 _let_2)) (= (not (or _let_3 _let_1)) (and _let_4 _let_2)))))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T0)))) (= (not (not _let_1)) _let_1))) (forall ((T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T2)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool T1)))) (= (not (=> _let_2 _let_1)) (and _let_2 (not _let_1)))))) (forall ((T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool T1)))) (let ((_let_2 (tptp.p (tptp.s tptp.bool T2)))) (= (=> (not _let_1) (not _let_2)) (=> _let_2 _let_1))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (not (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (forall ((X $$unsorted)) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (exists ((X $$unsorted)) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (not (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (not (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (exists ((X $$unsorted)) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (forall ((X $$unsorted)) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (not (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))))) (= (forall ((B0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.bool tptp.bool) tptp.p0) (tptp.s tptp.bool B0))))) (and _let_256 _let_255)) (= (exists ((B0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.bool tptp.bool) tptp.p0) (tptp.s tptp.bool B0))))) (or _let_256 _let_255)) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (forall ((X $$unsorted)) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))) (or (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (forall ((X $$unsorted)) (or (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (or (tptp.p (tptp.s tptp.bool P0)) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (or (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))) (forall ((X $$unsorted)) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (or (tptp.p (tptp.s tptp.bool P0)) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (forall ((X $$unsorted)) (or (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (=> (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))) (exists ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (exists ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool Q0)))) (=> (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (tptp.p (tptp.s tptp.bool Q0))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (=> (tptp.p (tptp.s tptp.bool P0)) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (exists ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (= (exists ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool P0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))) (=> (tptp.p (tptp.s tptp.bool P0)) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (X0 $$unsorted) (XI_ $$unsorted) (XI_I_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A XI_I_))) (let ((_let_3 (tptp.s tptp.bool X0))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun A _let_5))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) U_0) _let_4)) _let_3)) _let_1)) _let_2))) (and (=> (= _let_3 (tptp.s tptp.bool tptp.t)) (= _let_2 _let_4)) (=> (= _let_3 (tptp.s tptp.bool tptp.f0)) (= _let_2 _let_1)))))))))))) (forall ((X $$unsorted) (X0 $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s tptp.bool X))) (let ((_let_3 (tptp.s A X0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun A A))) (let ((_let_8 (tptp.fun A _let_7))) (= (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) _let_2)) _let_3)) _let_1)) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_4 A) tptp.h_) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) U_0) _let_3)) _let_2)) _let_1)))))))))))))))) (forall ((A $$unsorted) (T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.s A T2))) (let ((_let_2 (tptp.s A T1))) (let ((_let_3 (tptp.fun A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.bool _let_4) tptp.cond))) (and (= (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.bool tptp.t))) _let_2)) _let_1)) _let_2) (= (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.bool tptp.f0))) _let_2)) _let_1)) _let_1)))))))) (forall ((B0 $$unsorted) (T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.s tptp.bool T2))) (let ((_let_2 (tptp.s tptp.bool B0))) (let ((_let_3 (tptp.p _let_2))) (let ((_let_4 (tptp.s tptp.bool T1))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_2)) _let_4)) _let_1))) (and (or (not _let_3) (tptp.p _let_4)) (or _let_3 (tptp.p _let_1))))))))))) (forall ((A $$unsorted) (B0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.s A T0))) (let ((_let_2 (tptp.fun A A))) (let ((_let_3 (tptp.fun A _let_2))) (= (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) (tptp.s tptp.bool B0))) _let_1)) _let_1)) _let_1))))) (forall ((B $$unsorted) (A $$unsorted) (B0 $$unsorted) (F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s (tptp.fun A B) F0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.s tptp.bool B0))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.fun A A))) (let ((_let_8 (tptp.fun A _let_7))) (= (tptp.s B (tptp.i _let_2 (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) _let_4)) _let_3)) _let_1)))) (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_4)) (tptp.s B (tptp.i _let_2 _let_3)))) (tptp.s B (tptp.i _let_2 _let_1)))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (B0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.s tptp.bool B0))) (let ((_let_6 (tptp.fun B B))) (let ((_let_7 (tptp.fun B _let_6))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) _let_5)) _let_4)) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_5)) (tptp.s B (tptp.i _let_4 _let_1)))) (tptp.s B (tptp.i _let_3 _let_1))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (B0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.s tptp.bool B0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun B B))) (let ((_let_9 (tptp.fun B _let_8))) (= (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) _let_5)) (tptp.s B (tptp.i _let_4 _let_1)))) (tptp.s B (tptp.i _let_3 _let_1)))) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_5)) _let_4)) _let_3)) _let_1))))))))))))) (=> _let_253 (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_77 (tptp.i _let_245 _let_247)) _let_246))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_77 (tptp.i _let_245 _let_242)) _let_241))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.y))) (let ((_let_2 (tptp.s (tptp.fun A tptp.bool) tptp.p0))) (let ((_let_3 (tptp.s tptp.bool tptp.c))) (let ((_let_4 (tptp.p _let_3))) (let ((_let_5 (tptp.s A tptp.x))) (let ((_let_6 (tptp.fun A A))) (let ((_let_7 (tptp.fun A _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_3)) _let_5)) _let_1))))) (and (=> _let_4 (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_5)))) (=> (not _let_4) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_1)))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (P0 $$unsorted)) (= (forall ((X $$unsorted)) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y))))))) (exists ((Y $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) P0) _let_1)) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) Y) _let_1))))))))))) (forall ((A $$unsorted) (B $$unsorted) (P0 $$unsorted)) (= (forall ((X $$unsorted)) (and (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y)))))) (forall ((Y $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s B XI_))) (let ((_let_2 (tptp.s B Y))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) P0) (tptp.s A X))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))) (= _let_2 _let_1))))))))) (exists ((F0 $$unsorted)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) P0) _let_2)) _let_1))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) _let_1))))))))) (forall ((A $$unsorted) (B $$unsorted) (P0 $$unsorted)) (= (forall ((X $$unsorted)) (and (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y)))))) (forall ((Y $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s B XI_))) (let ((_let_2 (tptp.s B Y))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) P0) (tptp.s A X))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))) (= _let_2 _let_1))))))))) (and (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) P0) _let_1)) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1))))))))) (forall ((F0 $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.fun A B))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) P0) _let_1)) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) P0) _let_1)) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) XI_) _let_1))))))))) (= (tptp.s _let_1 F0) (tptp.s _let_1 XI_)))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.bool tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_1 (tptp.s tptp.bool tptp.f0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_1 (tptp.s tptp.bool tptp.t))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.bool tptp.bool) P0) (tptp.s tptp.bool X)))))))) (forall ((A $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.bool A) F0))) (and (= (tptp.s A (tptp.i _let_1 (tptp.s tptp.bool tptp.f0))) (tptp.s A A5)) (= (tptp.s A (tptp.i _let_1 (tptp.s tptp.bool tptp.t))) (tptp.s A B0)))))) (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun B C))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A C))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (= (tptp.s C (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.o) _let_5)) _let_3)) _let_1)) (tptp.s C (tptp.i _let_5 (tptp.s B (tptp.i _let_3 _let_1))))))))))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) tptp.i1) _let_1)) _let_1))) (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun B C))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A C))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (= (tptp.s C (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.o) _let_5)) _let_3)) _let_1)) (tptp.s C (tptp.i _let_5 (tptp.s B (tptp.i _let_3 _let_1))))))))))))) (forall ((D $$unsorted) (C $$unsorted) (A $$unsorted) (B $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 H0))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun C D))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun B D))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun A D))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun A C))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_11 _let_9))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_5 _let_13) tptp.o) _let_6)) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.o) _let_4)) _let_2)))) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.o) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.o) _let_6)) _let_4)))) _let_2))))))))))))))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) tptp.i1) _let_1)) _let_1))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A A))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (and (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.o) (tptp.s _let_5 tptp.i1))) _let_2)) _let_2) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.o) _let_2)) (tptp.s _let_3 tptp.i1))) _let_2))))))))) (exists ((B0 $$unsorted)) (tptp.p (tptp.s tptp.bool B0))) (forall ((R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.bool R0))) (= (tptp.p _let_1) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.n10 tptp.bool) tptp.oneu_rep) (tptp.s tptp.n10 (tptp.i (tptp.s (tptp.fun tptp.bool tptp.n10) tptp.oneu_abs) _let_1)))) _let_1)))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.n10 A5))) (= (tptp.s tptp.n10 (tptp.i (tptp.s (tptp.fun tptp.bool tptp.n10) tptp.oneu_abs) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.n10 tptp.bool) tptp.oneu_rep) _let_1)))) _let_1))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.n10 tptp.bool))) (=> (forall ((X $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.n10 tptp.bool) U_0) (tptp.s tptp.n10 X))) (tptp.s tptp.bool tptp.t))) (= (tptp.s tptp.n10 tptp.one) (tptp.s tptp.n10 (tptp.i (tptp.s (tptp.fun _let_1 tptp.n10) tptp.h_) (tptp.s _let_1 U_0))))))) (forall ((V $$unsorted)) (= (tptp.s tptp.n10 V) (tptp.s tptp.n10 tptp.one))) (forall ((A $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.n10))) (= (tptp.s _let_1 F0) (tptp.s _let_1 G0)))) (forall ((P0 $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.n10 tptp.bool) P0) (tptp.s tptp.n10 tptp.one)))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.n10 tptp.bool) P0) (tptp.s tptp.n10 X))))))) (forall ((A $$unsorted) (E0 $$unsorted)) (exists ((FN $$unsorted)) (= (tptp.s A (tptp.i (tptp.s (tptp.fun tptp.n10 A) FN) (tptp.s tptp.n10 tptp.one))) (tptp.s A E0)))) (forall ((A $$unsorted) (E0 $$unsorted)) (and (exists ((FN $$unsorted)) (= (tptp.s A (tptp.i (tptp.s (tptp.fun tptp.n10 A) FN) (tptp.s tptp.n10 tptp.one))) (tptp.s A E0))) (forall ((FN $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.n10 A))) (let ((_let_2 (tptp.s _let_1 XI_))) (let ((_let_3 (tptp.s _let_1 FN))) (let ((_let_4 (tptp.s A E0))) (let ((_let_5 (tptp.s tptp.n10 tptp.one))) (=> (and (= (tptp.s A (tptp.i _let_3 _let_5)) _let_4) (= (tptp.s A (tptp.i _let_2 _let_5)) _let_4)) (= _let_3 _let_2)))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.let) _let_3)) _let_1)) (tptp.s B (tptp.i _let_3 _let_1))))))) (forall ((A $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.s A T0))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) tptp.letu_end) _let_1)) _let_1))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun _let_1 A))) (= (tptp.s A (tptp.i (tptp.s _let_3 tptp.gabs) _let_2)) (tptp.s A (tptp.i (tptp.s _let_3 tptp.h_) _let_2))))))) (forall ((A $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s A B0))) (let ((_let_2 (tptp.s A A5))) (let ((_let_3 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.geq) _let_2)) _let_1))) (= _let_2 _let_1)))))) (forall ((Q4002 $$unsorted) (Q4005 $$unsorted) (X $$unsorted) (XI_ $$unsorted) (X0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s Q4005 X0))) (let ((_let_2 (tptp.fun Q4002 tptp.bool))) (let ((_let_3 (tptp.fun Q4005 _let_2))) (let ((_let_4 (tptp.s _let_3 XI_))) (let ((_let_5 (tptp.s _let_3 X))) (let ((_let_6 (tptp.s tptp.bool V))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (and (= (tptp.p _let_6) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q4002 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q4005 _let_1) X) (tptp.s Q4005 X0))) (tptp.s Q4002 Y))))))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.u_seqpattern) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) _let_6)) (tptp.s _let_2 (tptp.i _let_5 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool XI_))) (let ((_let_2 (tptp.s tptp.bool X))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.u_unguardedu_pattern) _let_2)) _let_1))) (and (tptp.p _let_2) (tptp.p _let_1))))))) (forall ((X $$unsorted) (XI_ $$unsorted) (XI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool XI_I_))) (let ((_let_2 (tptp.s tptp.bool XI_))) (let ((_let_3 (tptp.s tptp.bool X))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.u_guardedu_pattern) _let_3)) _let_2)) _let_1))) (and (tptp.p _let_3) (tptp.p _let_2) (tptp.p _let_1))))))))) (forall ((Q4047 $$unsorted) (Q4051 $$unsorted) (U_0 $$unsorted)) (=> (forall ((Z0 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q4051 tptp.bool) U_0) (tptp.s Q4051 Z0))) (tptp.s tptp.bool tptp.f0))) (forall ((X $$unsorted) (X0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q4051 tptp.bool))) (let ((_let_2 (tptp.s (tptp.fun _let_1 Q4051) tptp.h_))) (let ((_let_3 (tptp.s Q4047 X))) (let ((_let_4 (tptp.fun Q4047 _let_1))) (let ((_let_5 (tptp.s _let_4 X0))) (let ((_let_6 (tptp.s _let_1 (tptp.i _let_5 _let_3)))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.fun Q4051 Q4051))) (let ((_let_9 (tptp.fun Q4051 _let_8))) (let ((_let_10 (tptp.fun _let_4 Q4051))) (and (= (tptp.p _let_7) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.q_) _let_6))) (forall ((X1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q4051 Y))) (let ((_let_2 (tptp.s Q4051 X1))) (let ((_let_3 (tptp.fun Q4051 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q4047 _let_3) X0) (tptp.s Q4047 X))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))) (= _let_2 _let_1))))))))) (= (tptp.s Q4051 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q4047 _let_10) tptp.u_match) _let_3)) _let_5)) (tptp.s Q4051 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) _let_7)) (tptp.s Q4051 (tptp.i _let_2 _let_6)))) (tptp.s Q4051 (tptp.i _let_2 (tptp.s _let_1 U_0))))))))))))))))))))) (forall ((Q4069 $$unsorted) (Q4073 $$unsorted) (U_0 $$unsorted)) (=> (forall ((Z0 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q4073 tptp.bool) U_0) (tptp.s Q4073 Z0))) (tptp.s tptp.bool tptp.f0))) (forall ((X $$unsorted) (X0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q4073 tptp.bool))) (let ((_let_2 (tptp.s (tptp.fun _let_1 Q4073) tptp.h_))) (let ((_let_3 (tptp.s Q4069 X0))) (let ((_let_4 (tptp.fun Q4069 _let_1))) (let ((_let_5 (tptp.s _let_4 X))) (let ((_let_6 (tptp.s _let_1 (tptp.i _let_5 _let_3)))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.fun Q4073 Q4073))) (let ((_let_9 (tptp.fun Q4073 _let_8))) (let ((_let_10 (tptp.fun Q4069 Q4073))) (and (= (tptp.p _let_7) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.q_) _let_6))) (forall ((X1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q4073 Y))) (let ((_let_2 (tptp.s Q4073 X1))) (let ((_let_3 (tptp.fun Q4073 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q4069 _let_3) X) (tptp.s Q4069 X0))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))) (= _let_2 _let_1))))))))) (= (tptp.s Q4073 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.u_function) _let_5)) _let_3)) (tptp.s Q4073 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) _let_7)) (tptp.s Q4073 (tptp.i _let_2 _let_6)))) (tptp.s Q4073 (tptp.i _let_2 (tptp.s _let_1 U_0))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted) (XI_ $$unsorted) (X0 $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s B X0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.s A XI_))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun A _let_5))) (let ((_let_7 (tptp.fun B _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.mku_pair) _let_3)) _let_1)) _let_4)) _let_2))) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((X $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.fun B _let_1))) (= (tptp.s _let_1 X) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.mku_pair) (tptp.s A A5))) (tptp.s B B0)))))))) (forall ((A $$unsorted) (B $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.s _let_1 R0))) (let ((_let_3 (tptp.prod A B))) (= (exists ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.fun B _let_1))) (= (tptp.s _let_1 R0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.mku_pair) (tptp.s A A5))) (tptp.s B B0))))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.repu_prod) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.absu_prod) _let_2)))) _let_2)))))) (forall ((A $$unsorted) (B $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun A (tptp.fun B tptp.bool)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.absu_prod) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.repu_prod) _let_2)))) _let_2))))) (forall ((A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.fun B _let_1))) (let ((_let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.mku_pair) (tptp.s A X))) (tptp.s B Y))))) (let ((_let_4 (tptp.prod A B))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.repu_prod) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.absu_prod) _let_3)))) _let_3)))))) (forall ((A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.prod A B))) (let ((_let_6 (tptp.fun B _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.c_) _let_2)) _let_1)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.absu_prod) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.mku_pair) _let_2)) _let_1)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 P0))) (tptp.s A X)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun B _let_1))) (= (tptp.s _let_1 P0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.c_) (tptp.s A X))) (tptp.s B Y))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun A tptp.bool))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.fst) _let_2)) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_3 A) tptp.h_) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun B tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 P0))) (tptp.s B Y)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun B _let_1))) (= (tptp.s _let_1 P0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.c_) (tptp.s A X))) (tptp.s B Y))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun B tptp.bool))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.snd) _let_2)) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_3 B) tptp.h_) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))) (forall ((A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s B B0))) (let ((_let_2 (tptp.s B Y))) (let ((_let_3 (tptp.s A A5))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.prod A B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.c_))) (= (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_1))) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))) (forall ((A $$unsorted) (B $$unsorted) (P0 $$unsorted)) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun B _let_1))) (= (tptp.s _let_1 P0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.c_) (tptp.s A X))) (tptp.s B Y)))))))) (forall ((B $$unsorted) (A $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A B))) (let ((_let_3 (tptp.fun B _let_2))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) tptp.fst) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) (tptp.s B Y))))) _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.prod A B))) (let ((_let_3 (tptp.fun B _let_2))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun _let_2 B) tptp.snd) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) (tptp.s A X))) _let_1)))) _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun B _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.fst) _let_2)))) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.snd) _let_2)))) _let_2))))) (forall ((Q4341 $$unsorted) (Q4340 $$unsorted) (P0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod Q4341 Q4340))) (let ((_let_2 (tptp.fun Q4340 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4341 _let_2) tptp.c_) (tptp.s Q4341 X))) (tptp.s Q4340 Y))))))))) (forall ((P1 $$unsorted)) (let ((_let_1 (tptp.prod Q4341 Q4340))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 P1)))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted) (PAIRI_ $$unsorted)) (exists ((FN $$unsorted)) (forall ((A01 $$unsorted) (A10 $$unsorted)) (let ((_let_1 (tptp.s B A10))) (let ((_let_2 (tptp.s A A01))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (= (tptp.s C (tptp.i (tptp.s (tptp.fun _let_4 C) FN) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_2)) _let_1)))) (tptp.s C (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) PAIRI_) _let_2)) _let_1))))))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted) (F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.fun _let_3 C))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun B C))) (let ((_let_8 (tptp.fun A _let_7))) (= (tptp.s C (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.curry) _let_6)) _let_2)) _let_1)) (tptp.s C (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1)))))))))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted) (F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.prod A B))) (let ((_let_7 (tptp.fun B _let_6))) (let ((_let_8 (tptp.fun _let_6 C))) (= (tptp.s C (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.uncurry) _let_5)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.c_) _let_2)) _let_1)))) (tptp.s C (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))) (forall ((D $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (F0 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s C Z0))) (let ((_let_2 (tptp.s B Y))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.prod _let_4 C))) (let ((_let_7 (tptp.fun C _let_6))) (let ((_let_8 (tptp.fun _let_6 D))) (let ((_let_9 (tptp.s _let_8 F0))) (let ((_let_10 (tptp.prod B C))) (let ((_let_11 (tptp.fun C _let_10))) (let ((_let_12 (tptp.prod A _let_10))) (let ((_let_13 (tptp.fun _let_10 _let_12))) (let ((_let_14 (tptp.fun _let_12 D))) (= (tptp.s D (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_8 _let_14) tptp.passoc) _let_9)) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun A _let_13) tptp.c_) _let_3)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun B _let_11) tptp.c_) _let_2)) _let_1)))))) (tptp.s D (tptp.i _let_9 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.c_) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_3)) _let_2)))) _let_1)))))))))))))))))))) (forall ((Q4498 $$unsorted) (Q4497 $$unsorted) (P0 $$unsorted)) (= (forall ((P1 $$unsorted)) (let ((_let_1 (tptp.prod Q4498 Q4497))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 P1)))))) (forall ((P1 $$unsorted) (P2 $$unsorted)) (let ((_let_1 (tptp.prod Q4498 Q4497))) (let ((_let_2 (tptp.fun Q4497 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4498 _let_2) tptp.c_) (tptp.s Q4498 P1))) (tptp.s Q4497 P2))))))))))) (forall ((Q4523 $$unsorted) (Q4522 $$unsorted) (P0 $$unsorted)) (= (exists ((P1 $$unsorted)) (let ((_let_1 (tptp.prod Q4523 Q4522))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 P1)))))) (exists ((P1 $$unsorted) (P2 $$unsorted)) (let ((_let_1 (tptp.prod Q4523 Q4522))) (let ((_let_2 (tptp.fun Q4522 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4523 _let_2) tptp.c_) (tptp.s Q4523 P1))) (tptp.s Q4522 P2))))))))))) (forall ((Q4537 $$unsorted) (Q4545 $$unsorted) (Q4544 $$unsorted) (U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4545 Q4544) Q4537))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 T0))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod Q4545 Q4544))) (let ((_let_2 (tptp.fun Q4544 _let_1))) (let ((_let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4545 _let_2) tptp.c_) (tptp.s Q4545 X))) (tptp.s Q4544 Y))))) (let ((_let_4 (tptp.fun _let_1 Q4537))) (let ((_let_5 (tptp.fun Q4537 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q4537 _let_5) tptp.geq) (tptp.s Q4537 (tptp.i (tptp.s _let_4 F0) _let_3)))) (tptp.s Q4537 (tptp.i (tptp.s _let_4 T0) _let_3))))))))))))))) (forall ((T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.prod Q4545 Q4544))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 Q4537))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.s Q4537 (tptp.i _let_4 _let_2)) (tptp.s Q4537 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_5 _let_3) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)))) _let_2))))))))))) (forall ((Q4620 $$unsorted) (Q4624 $$unsorted) (Q4628 $$unsorted) (Q4627 $$unsorted) (Q4604 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (FI_ $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4620 (tptp.prod Q4624 (tptp.prod Q4628 Q4627))) Q4604))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 F0))) (tptp.s _let_1 FI_)))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.prod Q4628 Q4627))) (let ((_let_2 (tptp.fun Q4627 _let_1))) (let ((_let_3 (tptp.prod Q4624 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.prod Q4620 _let_3))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q4620 _let_6) tptp.c_) (tptp.s Q4620 W))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q4624 _let_4) tptp.c_) (tptp.s Q4624 X))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4628 _let_2) tptp.c_) (tptp.s Q4628 Y))) (tptp.s Q4627 Z0))))))))) (let ((_let_8 (tptp.fun _let_5 Q4604))) (let ((_let_9 (tptp.fun Q4604 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q4604 _let_9) tptp.geq) (tptp.s Q4604 (tptp.i (tptp.s _let_8 FI_) _let_7)))) (tptp.s Q4604 (tptp.i (tptp.s _let_8 F0) _let_7))))))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4620 (tptp.prod Q4624 (tptp.prod Q4628 Q4627))) Q4604))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))) _let_2))))))) (forall ((Q4590 $$unsorted) (Q4594 $$unsorted) (Q4593 $$unsorted) (Q4578 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (FI_ $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4590 (tptp.prod Q4594 Q4593)) Q4578))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 F0))) (tptp.s _let_1 FI_)))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.prod Q4594 Q4593))) (let ((_let_2 (tptp.fun Q4593 _let_1))) (let ((_let_3 (tptp.prod Q4590 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q4590 _let_4) tptp.c_) (tptp.s Q4590 X))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4594 _let_2) tptp.c_) (tptp.s Q4594 Y))) (tptp.s Q4593 Z0))))))) (let ((_let_6 (tptp.fun _let_3 Q4578))) (let ((_let_7 (tptp.fun Q4578 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q4578 _let_7) tptp.geq) (tptp.s Q4578 (tptp.i (tptp.s _let_6 FI_) _let_5)))) (tptp.s Q4578 (tptp.i (tptp.s _let_6 F0) _let_5))))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4590 (tptp.prod Q4594 Q4593)) Q4578))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))) _let_2))))))) (forall ((Q4566 $$unsorted) (Q4565 $$unsorted) (Q4558 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (FI_ $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4566 Q4565) Q4558))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 F0))) (tptp.s _let_1 FI_)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod Q4566 Q4565))) (let ((_let_2 (tptp.fun Q4565 _let_1))) (let ((_let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4566 _let_2) tptp.c_) (tptp.s Q4566 X))) (tptp.s Q4565 Y))))) (let ((_let_4 (tptp.fun _let_1 Q4558))) (let ((_let_5 (tptp.fun Q4558 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q4558 _let_5) tptp.geq) (tptp.s Q4558 (tptp.i (tptp.s _let_4 FI_) _let_3)))) (tptp.s Q4558 (tptp.i (tptp.s _let_4 F0) _let_3))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4566 Q4565) Q4558))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))) _let_2))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s B B0))) (let ((_let_2 (tptp.s A A5))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.fun _let_3 C))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun B C))) (let ((_let_8 (tptp.fun A _let_7))) (= (tptp.s C (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_6)) _let_2)) _let_1)) (tptp.s C (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun (tptp.prod A B) C))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun B C))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 U_0) _let_3)) _let_1)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 U_1) _let_3)) _let_1)))))))))) (forall ((P0 $$unsorted)) (= (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B C)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 F0)))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) C))) (let ((_let_2 (tptp.fun A (tptp.fun B C)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) P0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 F0))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s B B0))) (let ((_let_2 (tptp.s A A5))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.fun _let_3 C))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun B C))) (let ((_let_8 (tptp.fun A _let_7))) (= (tptp.s C (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_6)) _let_2)) _let_1)) (tptp.s C (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun (tptp.prod A B) C))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun B C))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 U_0) _let_3)) _let_1)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 U_1) _let_3)) _let_1)))))))))) (forall ((P0 $$unsorted)) (= (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B C)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 F0)))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) C))) (let ((_let_2 (tptp.fun A (tptp.fun B C)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) P0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 F0))))))))))))))) (forall ((Q4732 $$unsorted) (Q4731 $$unsorted) (Q4725 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4732 Q4731) Q4725))) (let ((_let_2 (tptp.fun Q4732 (tptp.fun Q4731 Q4725)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s Q4731 B0))) (let ((_let_2 (tptp.s Q4732 A5))) (let ((_let_3 (tptp.fun Q4731 Q4725))) (let ((_let_4 (tptp.prod Q4732 Q4731))) (let ((_let_5 (tptp.fun Q4731 _let_4))) (let ((_let_6 (tptp.fun Q4725 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q4725 _let_6) tptp.geq) (tptp.s Q4725 (tptp.i (tptp.s (tptp.fun _let_4 Q4725) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q4732 _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s Q4725 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q4732 _let_3) F0) _let_2)) _let_1))))))))))))))))) (forall ((P0 $$unsorted)) (= (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4732 Q4731) Q4725))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 F0)))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q4732 (tptp.fun Q4731 Q4725)))) (let ((_let_2 (tptp.fun (tptp.prod Q4732 Q4731) Q4725))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 F0)))))))))))))))) (forall ((Q4757 $$unsorted) (Q4756 $$unsorted) (Q4750 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4757 Q4756) Q4750))) (let ((_let_2 (tptp.fun Q4757 (tptp.fun Q4756 Q4750)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s Q4756 B0))) (let ((_let_2 (tptp.s Q4757 A5))) (let ((_let_3 (tptp.fun Q4756 Q4750))) (let ((_let_4 (tptp.prod Q4757 Q4756))) (let ((_let_5 (tptp.fun Q4756 _let_4))) (let ((_let_6 (tptp.fun Q4750 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q4750 _let_6) tptp.geq) (tptp.s Q4750 (tptp.i (tptp.s (tptp.fun _let_4 Q4750) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q4757 _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s Q4750 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q4757 _let_3) F0) _let_2)) _let_1))))))))))))))))) (forall ((P0 $$unsorted)) (= (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4757 Q4756) Q4750))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 F0)))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q4757 (tptp.fun Q4756 Q4750)))) (let ((_let_2 (tptp.fun (tptp.prod Q4757 Q4756) Q4750))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 F0)))))))))))))))) (forall ((Q4784 $$unsorted) (Q4783 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4784 Q4783) tptp.bool))) (let ((_let_2 (tptp.fun Q4784 (tptp.fun Q4783 tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q4783 Y))) (let ((_let_2 (tptp.s Q4784 X))) (let ((_let_3 (tptp.fun Q4783 tptp.bool))) (let ((_let_4 (tptp.prod Q4784 Q4783))) (let ((_let_5 (tptp.fun Q4783 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q4784 _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q4784 _let_3) P0) _let_2)) _let_1))))))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun Q4784 (tptp.fun Q4783 tptp.bool)))) (let ((_let_2 (tptp.fun (tptp.prod Q4784 Q4783) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.e_) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 P0)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun Q4783 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q4784 _let_1) P0) (tptp.s Q4784 X))) (tptp.s Q4783 Y))))))))))))) (forall ((Q4820 $$unsorted) (Q4819 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4820 Q4819) tptp.bool))) (let ((_let_2 (tptp.fun Q4820 (tptp.fun Q4819 tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q4819 Y))) (let ((_let_2 (tptp.s Q4820 X))) (let ((_let_3 (tptp.fun Q4819 tptp.bool))) (let ((_let_4 (tptp.prod Q4820 Q4819))) (let ((_let_5 (tptp.fun Q4819 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q4820 _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q4820 _let_3) P0) _let_2)) _let_1))))))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun Q4820 (tptp.fun Q4819 tptp.bool)))) (let ((_let_2 (tptp.fun (tptp.prod Q4820 Q4819) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.q_) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 P0)))))))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun Q4819 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q4820 _let_1) P0) (tptp.s Q4820 X))) (tptp.s Q4819 Y))))))))))))) (forall ((Q4857 $$unsorted) (Q4856 $$unsorted) (Q4855 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4857 (tptp.prod Q4856 Q4855)) tptp.bool))) (let ((_let_2 (tptp.fun Q4857 (tptp.fun Q4856 (tptp.fun Q4855 tptp.bool))))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s Q4855 Z0))) (let ((_let_2 (tptp.s Q4856 Y))) (let ((_let_3 (tptp.s Q4857 X))) (let ((_let_4 (tptp.fun Q4855 tptp.bool))) (let ((_let_5 (tptp.fun Q4856 _let_4))) (let ((_let_6 (tptp.prod Q4856 Q4855))) (let ((_let_7 (tptp.fun Q4855 _let_6))) (let ((_let_8 (tptp.prod Q4857 _let_6))) (let ((_let_9 (tptp.fun _let_6 _let_8))) (let ((_let_10 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) F0) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q4857 _let_9) tptp.c_) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q4856 _let_7) tptp.c_) _let_2)) _let_1)))))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q4857 _let_5) P0) _let_3)) _let_2)) _let_1))))))))))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun Q4857 (tptp.fun Q4856 (tptp.fun Q4855 tptp.bool))))) (let ((_let_2 (tptp.fun (tptp.prod Q4857 (tptp.prod Q4856 Q4855)) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.e_) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 P0)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.fun Q4855 tptp.bool))) (let ((_let_2 (tptp.fun Q4856 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4857 _let_2) P0) (tptp.s Q4857 X))) (tptp.s Q4856 Y))) (tptp.s Q4855 Z0)))))))))))))) (forall ((Q4903 $$unsorted) (Q4902 $$unsorted) (Q4901 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q4903 (tptp.prod Q4902 Q4901)) tptp.bool))) (let ((_let_2 (tptp.fun Q4903 (tptp.fun Q4902 (tptp.fun Q4901 tptp.bool))))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s Q4901 Z0))) (let ((_let_2 (tptp.s Q4902 Y))) (let ((_let_3 (tptp.s Q4903 X))) (let ((_let_4 (tptp.fun Q4901 tptp.bool))) (let ((_let_5 (tptp.fun Q4902 _let_4))) (let ((_let_6 (tptp.prod Q4902 Q4901))) (let ((_let_7 (tptp.fun Q4901 _let_6))) (let ((_let_8 (tptp.prod Q4903 _let_6))) (let ((_let_9 (tptp.fun _let_6 _let_8))) (let ((_let_10 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) F0) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q4903 _let_9) tptp.c_) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q4902 _let_7) tptp.c_) _let_2)) _let_1)))))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q4903 _let_5) P0) _let_3)) _let_2)) _let_1))))))))))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun Q4903 (tptp.fun Q4902 (tptp.fun Q4901 tptp.bool))))) (let ((_let_2 (tptp.fun (tptp.prod Q4903 (tptp.prod Q4902 Q4901)) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.q_) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 P0)))))))) (exists ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.fun Q4901 tptp.bool))) (let ((_let_2 (tptp.fun Q4902 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q4903 _let_2) P0) (tptp.s Q4903 X))) (tptp.s Q4902 Y))) (tptp.s Q4901 Z0)))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.oneu_one) (tptp.s _let_1 F0)))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.s A X2))) (let ((_let_2 (tptp.s A X1))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (=> (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1))) (= _let_2 _let_1))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.onto) (tptp.s _let_1 F0)))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s B Y) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))))))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.ind0 tptp.ind0))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.oneu_one) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.onto) _let_2))))))))) (exists ((F0 $$unsorted) (Z0 $$unsorted)) (and (forall ((X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.s tptp.ind0 X2))) (let ((_let_2 (tptp.s tptp.ind0 X1))) (let ((_let_3 (tptp.s (tptp.fun tptp.ind0 tptp.ind0) F0))) (= (= (tptp.s tptp.ind0 (tptp.i _let_3 _let_2)) (tptp.s tptp.ind0 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((X $$unsorted)) (not (= (tptp.s tptp.ind0 (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.ind0) F0) (tptp.s tptp.ind0 X))) (tptp.s tptp.ind0 Z0)))))) (forall ((X $$unsorted)) (not (= (tptp.s tptp.ind0 (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.ind0) tptp.indu_suc) (tptp.s tptp.ind0 X))) (tptp.s tptp.ind0 tptp.indu_0)))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.s tptp.ind0 X2))) (let ((_let_2 (tptp.s tptp.ind0 X1))) (let ((_let_3 (tptp.s (tptp.fun tptp.ind0 tptp.ind0) tptp.indu_suc))) (= (= (tptp.s tptp.ind0 (tptp.i _let_3 _let_2)) (tptp.s tptp.ind0 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.bool) tptp.numu_rep) _let_240))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.ind0 I0))) (let ((_let_2 (tptp.s (tptp.fun tptp.ind0 tptp.bool) tptp.numu_rep))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.ind0 (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.ind0) tptp.indu_suc) _let_1))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.ind0 A5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.bool) tptp.numu_rep) _let_1))) (or (= _let_1 (tptp.s tptp.ind0 tptp.indu_0)) (exists ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.ind0 I0))) (and (= (tptp.s tptp.ind0 A5) (tptp.s tptp.ind0 (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.ind0) tptp.indu_suc) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.bool) tptp.numu_rep) _let_1)))))))))) (forall ((NUMU_REPI_ $$unsorted)) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.bool) NUMU_REPI_) (tptp.s tptp.ind0 tptp.indu_0)))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.ind0 I0))) (let ((_let_2 (tptp.s (tptp.fun tptp.ind0 tptp.bool) NUMU_REPI_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.ind0 (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.ind0) tptp.indu_suc) _let_1)))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.ind0 A5))) (let ((_let_2 (tptp.fun tptp.ind0 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.numu_rep) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 NUMU_REPI_) _let_1))))))))) (= _let_12 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.num) tptp.mku_num) _let_240))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.num) tptp.mku_num) (tptp.s tptp.ind0 (tptp.i (tptp.s (tptp.fun tptp.ind0 tptp.ind0) tptp.indu_suc) (tptp.s tptp.ind0 (tptp.i (tptp.s (tptp.fun tptp.num tptp.ind0) tptp.destu_num) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc))) (= (= (tptp.s tptp.num (tptp.i _let_3 _let_2)) (tptp.s tptp.num (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (= (= _let_12 _let_12) _let_239) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) _let_1)) _let_1))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (not (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) (tptp.s tptp.num N0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((P0 $$unsorted)) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) P0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))))))))) (forall ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num N0))))))) (forall ((A $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (and (exists ((FN $$unsorted)) (and (= (tptp.s A (tptp.i (tptp.s (tptp.fun tptp.num A) FN) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s A E0)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 FN))) (= (tptp.s A (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) (tptp.s A (tptp.i _let_3 _let_1)))) _let_1))))))))) (forall ((FN $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.num A))) (let ((_let_2 (tptp.s _let_1 XI_))) (let ((_let_3 (tptp.s _let_1 FN))) (let ((_let_4 (tptp.s A E0))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (=> (and (= (tptp.s A (tptp.i _let_3 _let_5)) _let_4) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 FN))) (= (tptp.s A (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) (tptp.s A (tptp.i _let_3 _let_1)))) _let_1))))))) (= (tptp.s A (tptp.i _let_2 _let_5)) _let_4) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 XI_))) (= (tptp.s A (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) (tptp.s A (tptp.i _let_3 _let_1)))) _let_1)))))))) (= _let_3 _let_2)))))))))) (forall ((A $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (exists ((FN $$unsorted)) (and (= (tptp.s A (tptp.i (tptp.s (tptp.fun tptp.num A) FN) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s A E0)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 FN))) (= (tptp.s A (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) (tptp.s A (tptp.i _let_3 _let_1)))) _let_1)))))))))) (forall ((M0 $$unsorted)) (or (= (tptp.s tptp.num M0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (exists ((N0 $$unsorted)) (= (tptp.s tptp.num M0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) (tptp.s tptp.num N0))))))) (forall ((Z $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (exists ((FN $$unsorted)) (and (= (tptp.s Z (tptp.i (tptp.s (tptp.fun tptp.num Z) FN) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s Z E0)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num Z) FN))) (let ((_let_3 (tptp.fun Z Z))) (= (tptp.s Z (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s Z (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) F0) _let_1)) (tptp.s Z (tptp.i _let_2 _let_1)))))))))))) (= (tptp.s tptp.num (tptp.i _let_32 _let_51)) _let_51) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.bit0))) (let ((_let_4 (tptp.s _let_2 tptp.suc))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) _let_1)))))))) (= (tptp.s tptp.num (tptp.i _let_220 _let_51)) _let_51) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.pre) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))) _let_1)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1)) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s _let_3 tptp.suc))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) (tptp.s tptp.num M0))))) (let ((_let_4 (tptp.s _let_2 tptp.suc))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) _let_1))))))))) (= _let_238 (tptp.s tptp.num (tptp.i _let_236 _let_179))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_74 _let_238)) _let_230)) _let_237) (= _let_237 (tptp.s tptp.num (tptp.i _let_236 (tptp.s tptp.num (tptp.i _let_235 _let_230))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_4)) _let_3)) _let_2) (and (= _let_4 _let_2) (= _let_3 _let_2)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) (tptp.s tptp.num M0))))) (= (= (tptp.s tptp.num (tptp.i _let_4 _let_2)) (tptp.s tptp.num (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s tptp.num P0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.p_))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3))) (= _let_2 _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_3)) _let_2)) _let_3) (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s tptp.num N0))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) _let_3)) _let_3) (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_1)) _let_1)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_1)) _let_1)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_4)) _let_4)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_4)) _let_4)))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_74 _let_12)) _let_12)) _let_12) (= _let_17 (tptp.s tptp.num (tptp.i _let_46 _let_51))) (= _let_33 (tptp.s tptp.num (tptp.i _let_46 _let_17))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num M0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) _let_2)) (tptp.s tptp.num N0))) _let_2)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.suc) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))) _let_1))))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num M0))) _let_2)) _let_2)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_2)))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.suc) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i _let_5 _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)) _let_1)))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num M0))))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s _let_3 tptp.p_))) (= (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_4 _let_5)))) (tptp.s tptp.num (tptp.i _let_4 _let_1)))))))))))) (= _let_234 (tptp.s tptp.num (tptp.i _let_232 _let_179))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s _let_4 tptp.p_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) _let_1))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_72 _let_234)) _let_230)) _let_233) (= _let_233 (tptp.s tptp.num (tptp.i _let_232 (tptp.s tptp.num (tptp.i _let_231 _let_230))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) _let_4)) _let_3)) _let_2) (or (= _let_4 _let_2) (= _let_3 _let_2)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_4)))) (= (= (tptp.s tptp.num (tptp.i _let_5 _let_2)) (tptp.s tptp.num (tptp.i _let_5 _let_1))) (or (= _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (= _let_2 _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_1) tptp.t_))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_5 _let_4)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_5 _let_3)) _let_2))) (or (= _let_4 _let_3) (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) _let_1)) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) _let_4)) _let_3)) _let_2) (and (= _let_4 _let_2) (= _let_3 _let_2)))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.exp0) (tptp.s tptp.num M0))) (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.exp0) _let_2)))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.suc) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_2)) (tptp.s tptp.num (tptp.i _let_5 _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0) _let_4)) _let_3)) _let_2) (and (= _let_4 _let_2) (not (= _let_3 _let_2))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (let ((_let_6 (tptp.s tptp.num X))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.exp0) _let_6)) _let_4)) _let_5) (or (= _let_6 _let_5) (= _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))) (forall ((N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun tptp.num _let_2))) (let ((_let_7 (tptp.s tptp.num N0))) (and (= (tptp.p _let_5) (= _let_7 _let_4)) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 tptp.exp0) _let_4)) _let_7)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_5)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) _let_4))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.exp0) (tptp.s tptp.num M0))))) (let ((_let_5 (tptp.s tptp.num N0))) (= (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) _let_5)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num (tptp.i _let_4 _let_5)))) (tptp.s tptp.num (tptp.i _let_4 _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0) _let_2)) (tptp.s tptp.num N0))) _let_2)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.exp0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.exp0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) _let_1)) _let_1))))))) (forall ((P0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.exp0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s _let_4 tptp.t_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.exp0))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num M0))))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_2)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_6 _let_2)))) _let_1)))))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1))) (= _let_2 _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (or (= _let_2 _let_5) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))))))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_) (tptp.s tptp.num M0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.bool tptp.f0)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_2)))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1))))) (or (= _let_2 _let_1) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((N0 $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.g_a_) _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1)))))))) (forall ((N0 $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.g_) _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.max) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_1)) _let_2)))) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.min) _let_2)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1)))) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_2)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.num N0)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) (tptp.s tptp.num N0))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_1)) _let_1)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (= _let_2 _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.num M0))))) (let ((_let_5 (tptp.s tptp.num N0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) tptp.l_))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.num M0))))) (let ((_let_5 (tptp.s tptp.num N0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.l_))) (let ((_let_6 (tptp.s tptp.num N0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.l_) (tptp.s tptp.num M0))))) (let ((_let_5 (tptp.s tptp.num N0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.l_a_) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (= _let_2 _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))) (= _let_2 _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))) (not (= _let_2 _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_1)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_1)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (= _let_2 _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_1)) _let_2))) (not (= _let_2 _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (not (= _let_1 _let_2)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_2)) _let_1)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i _let_4 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_1)) _let_2))) (not (= _let_2 _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) _let_4))) (not (= _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_a_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0)))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) (tptp.s tptp.num M0))) (tptp.s tptp.num D0))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0)))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) (tptp.s tptp.num M0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) (tptp.s tptp.num D0))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_1)) (tptp.s tptp.num N0)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_1)) (tptp.s tptp.num M0)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) (tptp.s tptp.num M0))) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.s tptp.num M0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_5)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.s tptp.num N0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num M0))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_6 _let_2)))) (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.s tptp.num P0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.p_))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num M0))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_6 _let_2)))) (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.s tptp.num P0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.p_))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.l_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.l_a_) _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.l_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.l_a_) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_5 (tptp.s tptp.num M0))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_5)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_5 (tptp.s tptp.num P0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_))) (=> (and (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_4 _let_5)))) (tptp.s tptp.num (tptp.i _let_4 _let_1)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.t_) _let_6)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_7 _let_2)))) (tptp.s tptp.num (tptp.i _let_7 _let_1))))) (or (= _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_1) tptp.t_))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_3)) _let_2))))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))) (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.t_) _let_6)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_7 _let_2)))) (tptp.s tptp.num (tptp.i _let_7 _let_1))))) (and (not (= _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_1) tptp.t_))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_3)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))) (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_5 (tptp.s tptp.num P0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_1)) _let_1))))))))) (=> (and (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p0) _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p0) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (=> (and (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p0) _let_1)) _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p0) _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p0) (tptp.s tptp.num M0))) (tptp.s tptp.num Y))))))) (forall ((P0 $$unsorted)) (=> (forall ((N0 $$unsorted)) (=> (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num N0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num N0)))))) (forall ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num N0))))))) (forall ((P0 $$unsorted)) (= (exists ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num N0))))) (exists ((N0 $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num N0)))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num N0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))))))) (forall ((P0 $$unsorted)) (= (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num X))))) (exists ((M0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_1)) (tptp.s tptp.num M0)))))))))) (exists ((M0 $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num M0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_1)) (tptp.s tptp.num M0)))))))))))) (= (tptp.s tptp.bool (tptp.i _let_219 _let_51)) _let_217) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1))))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_1)))))))) (= (tptp.s tptp.bool (tptp.i _let_218 _let_51)) _let_215) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1))))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_1)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.even) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.odd) _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.odd) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.even) _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.even) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.odd) _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.even) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.odd) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.p_) _let_3)) _let_1))))) (= (tptp.s tptp.bool (tptp.i _let_2 _let_3)) (tptp.s tptp.bool (tptp.i _let_2 _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.t_) _let_3)) _let_1))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0) _let_3)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_3))) (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.p_) _let_3)) _let_1))))) (not (= (tptp.s tptp.bool (tptp.i _let_2 _let_3)) (tptp.s tptp.bool (tptp.i _let_2 _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.t_) _let_3)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0) _let_3)) _let_2))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_3))) (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num N0)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num N0)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) (tptp.s tptp.num N0)))))) (and (=> _let_1 (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num M0))))))) (=> (not _let_1) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num M0)))))))))))) (forall ((N0 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) (tptp.s tptp.num N0)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num M0)))))))) (forall ((N0 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) (tptp.s tptp.num N0)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num M0)))))))))) (forall ((N0 $$unsorted)) (= (exists ((K0 $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_1))) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.exp0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num K0))))) _let_1)))))))) (not (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.m_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.m_) (tptp.s tptp.num M0))))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.pre) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_2) tptp.m_))) (and (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_3)) _let_1)) _let_3) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) _let_3)) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.m_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.pre) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.suc) _let_2)))) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.m_))) (let ((_let_5 (tptp.s _let_3 tptp.suc))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) _let_2)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_1)) _let_2)))) _let_2)) _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1)))) _let_2)) _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.m_) _let_2)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num _let_1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.m_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.p_) _let_2)) (tptp.s tptp.num N0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num _let_1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.m_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.p_) (tptp.s tptp.num M0))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) _let_2)) _let_1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.m_) _let_1)) _let_2)))) _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.m_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) (tptp.s tptp.num M0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_6 _let_2)))) (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.m_))) (let ((_let_6 (tptp.s tptp.num P0))) (let ((_let_7 (tptp.s _let_4 tptp.p_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_2)) _let_6)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_1)) _let_6)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) _let_3)) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) _let_3)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num M0))))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s _let_3 tptp.m_))) (= (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_4 _let_5)))) (tptp.s tptp.num (tptp.i _let_4 _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s _let_4 tptp.m_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.even))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.m_) _let_4)) _let_1))))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_4)) _let_1))) (= (tptp.s tptp.bool (tptp.i _let_3 _let_4)) (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.odd))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.m_) _let_4)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) _let_4))) (not (= (tptp.s tptp.bool (tptp.i _let_3 _let_4)) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 tptp.fact) _let_51)) _let_17) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.fact))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))) (= (tptp.s tptp.num (tptp.i _let_3 _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_4)) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i _let_216 _let_51)) _let_17))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.fact) (tptp.s tptp.num N0))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.fact) (tptp.s tptp.num N0))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (not (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.fact) (tptp.s tptp.num N0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.num) tptp.fact))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_2 _let_3)))) (tptp.s tptp.num (tptp.i _let_2 _let_1)))))))))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num X))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0) _let_4)) _let_3))))) (or (not (= _let_4 _let_2)) (= _let_3 _let_2))))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s tptp.num X))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s _let_9 tptp.l_))) (let ((_let_11 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.exp0) _let_7)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_11 _let_6)))) (tptp.s tptp.num (tptp.i _let_11 _let_5))))) (or (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_a_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_6)) _let_5)))) (and (= _let_7 _let_4) (not (= _let_6 _let_4)) (= _let_5 _let_4)))))))))))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p (tptp.s tptp.bool V)) (or (= (tptp.s tptp.num X) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_a_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0)))))) (exists ((VI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (and (= (tptp.p (tptp.s tptp.bool VI_)) (=> (= (tptp.s tptp.num M0) _let_1) (= (tptp.s tptp.num N0) _let_1))) (exists ((VI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_I_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.s tptp.num X))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.exp0) _let_4)))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (and (= (tptp.p _let_1) (= _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num M0))))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num N0))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) _let_1)) (tptp.s tptp.bool VI_))) (tptp.s tptp.bool V))))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (= (= _let_1 _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0) (tptp.s tptp.num X))))) (= (= (tptp.s tptp.num (tptp.i _let_2 (tptp.s tptp.num M0))) (tptp.s tptp.num (tptp.i _let_2 (tptp.s tptp.num N0)))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (and (= (tptp.p (tptp.s tptp.bool V)) (= (= (tptp.s tptp.num M0) _let_1) (= (tptp.s tptp.num N0) _let_1))) (exists ((VI_ $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool VI_)) (= (tptp.s tptp.num X) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (exists ((VI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_I_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_1) (or (= (tptp.s tptp.num X) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))) (= (tptp.s tptp.num M0) (tptp.s tptp.num N0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) (tptp.s tptp.bool VI_))) (tptp.s tptp.bool V))) _let_1)))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num Y))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0))) (let ((_let_5 (tptp.s tptp.num X))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num Y))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0))) (let ((_let_5 (tptp.s tptp.num X))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num Y))) (let ((_let_4 (tptp.s tptp.num X))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_3)) _let_2))))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))) (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num Y))) (let ((_let_4 (tptp.s tptp.num X))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_3)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))) (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num Y))) (let ((_let_4 (tptp.s tptp.num X))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_1) tptp.exp0))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_5 _let_4)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_5 _let_3)) _let_2))) (or (= _let_4 _let_3) (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (=> (not (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (exists ((Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num R0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (and (= (tptp.s tptp.num M0) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.t_) (tptp.s tptp.num Q0))) _let_1)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_2)) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (exists ((Q0 $$unsorted) (R0 $$unsorted) (V $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool V)) (and (= (tptp.s tptp.num Q0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (= (tptp.s tptp.num R0) (tptp.s tptp.num M0)))) (exists ((VI_ $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool VI_)) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (exists ((VI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_I_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.s tptp.num R0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (and (= (tptp.p _let_1) (and (= (tptp.s tptp.num M0) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.t_) (tptp.s tptp.num Q0))) _let_4)))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_) _let_5)) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) (tptp.s tptp.bool VI_))) (tptp.s tptp.bool V))) _let_1)))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (and (= (tptp.p (tptp.s tptp.bool V)) (and (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.div) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.mod) _let_1)) _let_2)) _let_1))) (exists ((VI_ $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool VI_)) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (exists ((VI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_I_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.mod) _let_5)) _let_4)))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (and (= (tptp.p _let_1) (and (= _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.div) _let_5)) _let_4)))) _let_4)))) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_) _let_8)) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) (tptp.s tptp.bool VI_))) (tptp.s tptp.bool V))) _let_1))))))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.mod) _let_2)) _let_1)))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (and (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.div) _let_2)) _let_1)))) _let_1)))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_) _let_5)) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.div) _let_1)) _let_2)))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.mod) _let_1)) _let_2)))) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.div) _let_1)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.mod) _let_1)) _let_2)))) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (Q1 $$unsorted) (R1 $$unsorted) (Q2 $$unsorted) (R2 $$unsorted)) (let ((_let_1 (tptp.s tptp.num R2))) (let ((_let_2 (tptp.s tptp.num R1))) (let ((_let_3 (tptp.s tptp.num Q2))) (let ((_let_4 (tptp.s tptp.num Q1))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s _let_9 tptp.t_))) (let ((_let_11 (tptp.s _let_9 tptp.p_))) (let ((_let_12 (tptp.s tptp.num M0))) (=> (and (= _let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_5)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (= _let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_5)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num R0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s tptp.num Q0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (=> (and (= _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.t_) _let_6)) _let_2)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_) _let_1)) _let_2)))) (and (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.div) _let_3)) _let_2)) _let_6) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.mod) _let_3)) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num R0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (= _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.t_) (tptp.s tptp.num Q0))) _let_2)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_) _let_1)) _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.mod) _let_3)) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s tptp.num R0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (=> (and (= _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.t_) _let_1)) _let_2)))) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_) _let_6)) _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.div) _let_3)) _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num _let_1))) (=> (not (= _let_3 _let_2)) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.mod) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.t_) _let_3)) (tptp.s tptp.num N0))))) _let_3)) _let_2))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.div) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_2)) _let_1)))) _let_2)) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_) _let_1)) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mod) _let_1)) _let_2)) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.mod))) (let ((_let_6 (tptp.s tptp.num M0))) (=> (= _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num Q0))) _let_1))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.div) _let_1)) _let_2)))) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.div) _let_1)) _let_2)))))) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s tptp.num N0))) (=> (not (= _let_3 _let_2)) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mod) _let_2)) _let_3)) _let_2)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s tptp.num N0))) (=> (not (= _let_3 _let_2)) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.div) _let_2)) _let_3)) _let_2)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mod) (tptp.s tptp.num N0))) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.div) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_) _let_3)) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.div) _let_3)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.mod))) (let ((_let_5 (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num M0))))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) _let_1)) (tptp.s tptp.num P0))))) (=> (not (= _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_6)))) _let_1)) (tptp.s tptp.num (tptp.i _let_5 _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) tptp.mod))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.num M0))) _let_1)))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) _let_1)) _let_4))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.div))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num M0))))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (=> (not (= _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_6 _let_2)))) _let_7)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.mod))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num M0))))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (=> (not (= _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_6 _let_2)))) _let_7)) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (= (exists ((Q0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num M0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num N0))) (tptp.s tptp.num Q0)))))) (exists ((V $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool V)) (= (tptp.s tptp.num M0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (exists ((VI_ $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool VI_)) (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (exists ((VI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_I_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_1) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mod) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) (tptp.s tptp.bool VI_))) (tptp.s tptp.bool V))) _let_1))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num B0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num A5))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (=> (not (= _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.div) _let_1)) _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.t_) _let_3)) _let_2)))) _let_1)))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num _let_2))) (let ((_let_6 (tptp.s tptp.num A5))) (let ((_let_7 (tptp.s tptp.num B0))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (=> (not (= _let_6 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.div) _let_7)) _let_6)))) _let_4)) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_) _let_7)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.t_) _let_6)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.p_) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num A5))) (let ((_let_3 (tptp.s tptp.num B0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (=> (and (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.t_) _let_2)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.div) _let_3)) _let_2)))) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.div))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (=> (and (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.div))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (=> (and (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_6)) _let_1)))) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (=> (not (= _let_1 _let_5)) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.div) _let_2)) _let_1)) _let_5) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s tptp.num N0))) (=> (not (= _let_3 _let_2)) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mod) (tptp.s tptp.num M0))) _let_3)) _let_2) (exists ((Q0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num M0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num Q0))) (tptp.s tptp.num N0)))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num N0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mod) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num N0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mod) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num M0))))) (let ((_let_6 (tptp.s _let_4 tptp.mod))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_2)) _let_1)))))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.t_))) (let ((_let_7 (tptp.s _let_5 tptp.mod))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.t_))) (let ((_let_7 (tptp.s _let_5 tptp.mod))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_2)) _let_1)))))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.exp0))) (let ((_let_7 (tptp.s _let_5 tptp.mod))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.mod))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num M0))) _let_1)))) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num B0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.div))) (let ((_let_6 (tptp.s tptp.num A5))) (let ((_let_7 (tptp.s _let_4 tptp.p_))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_6)) _let_1)))) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num B0))) (let ((_let_3 (tptp.s tptp.num A5))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.p_))) (let ((_let_7 (tptp.s _let_5 tptp.mod))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_2)) _let_1)))))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))) _let_1)))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num B0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.div))) (let ((_let_6 (tptp.s tptp.num A5))) (let ((_let_7 (tptp.s _let_4 tptp.p_))) (let ((_let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) (let ((_let_9 (tptp.s _let_4 tptp.mod))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_9 _let_8)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_9 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_9 _let_2)) _let_1))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_8)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num N0))) (=> (not (= _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.div) _let_4)) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (not (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mod) _let_1)) _let_2)))) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.div) (tptp.s tptp.num N0))))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_))) (=> (and (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num B0))) (let ((_let_2 (tptp.s tptp.num A5))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.div))) (let ((_let_6 (tptp.s tptp.num D0))) (let ((_let_7 (tptp.s tptp.num C0))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s tptp.num tptp.u_0))) (let ((_let_11 (tptp.s _let_3 tptp.numeral))) (let ((_let_12 (tptp.s _let_4 tptp.t_))) (=> (and (not (= _let_1 (tptp.s tptp.num (tptp.i _let_11 _let_10)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_12 _let_1)) _let_7)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_10)))))))) _let_6)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_7)) _let_6)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i _let_216 (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_72 _let_224)) _let_229)))) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_72 (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_74 _let_225)) _let_17)))) _let_228))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i _let_216 (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_72 _let_225)) _let_228)))) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_72 (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_74 _let_229)) _let_17)))) _let_224)))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_222 _let_225)) _let_224)) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_222 _let_229)) _let_228)))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num M0))))) (let ((_let_6 (tptp.s _let_4 tptp.div))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_2)) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) _let_1)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_2)) _let_1)))) (let ((_let_6 (tptp.s _let_4 tptp.div))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_6 (tptp.s tptp.num M0))))) (=> (not (= _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_7 _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i _let_7 _let_5)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_1)) _let_2)))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s _let_4 tptp.mod))) (let ((_let_8 (tptp.s _let_4 tptp.div))) (=> (not (= _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_6)) _let_1)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_5)))) _let_1))))))))))))) (forall ((X $$unsorted) (P0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s tptp.num P0))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.exp0) _let_5)))) (let ((_let_7 (tptp.s _let_4 tptp.mod))) (let ((_let_8 (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num X))))) (=> (not (= _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_8 (tptp.s tptp.num (tptp.i _let_6 _let_2)))))) (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (tptp.s tptp.num (tptp.i _let_8 (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.min) _let_2)) _let_1))))))))))))))))) (= _let_227 (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_4 (tptp.s tptp.num tptp.n))) (=> (or (= _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1))) (and (= _let_1 _let_3) (= _let_4 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.p0) _let_1)))))))))) (= _let_227 (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_4 (tptp.s tptp.num tptp.n))) (and (or (= _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1))) (and (= _let_1 _let_3) (= _let_4 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.p0) _let_1)))))))))) (= _let_226 (forall ((D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num D0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num tptp.b0))) (let ((_let_5 (tptp.s tptp.num tptp.a0))) (=> (or (= _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_4)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_5)) _let_4))) (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))))))))))) (= _let_226 (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num D0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num tptp.b0))) (let ((_let_5 (tptp.s tptp.num tptp.a0))) (and (or (= _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_4)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_5)) _let_4))) (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))))))))))) (= _let_223 (forall ((Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num R0))) (let ((_let_2 (tptp.s tptp.num Q0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s tptp.num tptp.n))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s tptp.num tptp.m))) (let ((_let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (=> (or (and (= _let_5 _let_9) (= _let_2 _let_9) (= _let_1 _let_8)) (and (= _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.t_) _let_2)) _let_5)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_1)) _let_5))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p0) _let_2)) _let_1))))))))))))))) (= _let_223 (exists ((Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num R0))) (let ((_let_2 (tptp.s tptp.num Q0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s tptp.num tptp.n))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s tptp.num tptp.m))) (let ((_let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (and (or (and (= _let_5 _let_9) (= _let_2 _let_9) (= _let_1 _let_8)) (and (= _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.t_) _let_2)) _let_5)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_1)) _let_5))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p0) _let_2)) _let_1))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num N0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.minimal) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.h_) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (= (exists ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num N0))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.minimal) _let_2))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.minimal) _let_3))))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))))))) (forall ((R0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Z0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) R0))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.num X))))) (let ((_let_5 (tptp.s tptp.num Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (= (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 R0) _let_2)) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) R0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1))))))))))) (forall ((R0 $$unsorted)) (=> (and (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Z0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) R0))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.num X))))) (let ((_let_5 (tptp.s tptp.num Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) R0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 R0) _let_2)) _let_1))))))))))) (forall ((R0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) R0) _let_1)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Z0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) R0))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.num X))))) (let ((_let_5 (tptp.s tptp.num Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))))))))))) (= (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 R0) _let_2)) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) R0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1))))))))))) (forall ((R0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) R0) _let_1)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Z0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) R0))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.num X))))) (let ((_let_5 (tptp.s tptp.num Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) R0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 R0) _let_2)) _let_1))))))))))) (forall ((A $$unsorted) (L_L_ $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 L_L_)))) (forall ((P0 $$unsorted)) (=> (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) L_L_) _let_1)) (tptp.s A X)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (forall ((P0 $$unsorted)) (= (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))) (exists ((X $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.l_l_) _let_1)) (tptp.s A X)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (forall ((P0 $$unsorted)) (=> (forall ((X $$unsorted)) (=> (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.l_l_) _let_1)) (tptp.s A X)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (not (exists ((S0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num A) S0))) (let ((_let_3 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.l_l_) (tptp.s A (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))))) (tptp.s A (tptp.i _let_2 _let_1)))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (forall ((H0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_2) H0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.l_l_) _let_1)) (tptp.s A X)))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G0) _let_1)))))))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 F0))) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 G0))) _let_1)))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G0))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1)))))))) (= (tptp.s _let_1 F0) (tptp.s _let_1 G0)))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (forall ((H0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_2) H0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.l_l_) _let_1)) (tptp.s A X)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 G0) _let_1))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 F0))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 G0))) _let_1)))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s tptp.bool (tptp.i _let_3 _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 G0))) (= (tptp.s tptp.bool (tptp.i _let_3 _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1)))))))) (= (tptp.s _let_1 F0) (tptp.s _let_1 G0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (forall ((H0 $$unsorted) (S0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_2) H0))) (let ((_let_4 (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 F0))) _let_1)))) (let ((_let_5 (tptp.fun B tptp.bool))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.l_l_) _let_1)) (tptp.s A X)))) (and (= _let_3 (tptp.s B (tptp.i (tptp.s _let_2 G0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) S0) _let_1)) _let_3))))))))))) (and (= _let_4 (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 G0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) S0) _let_1)) _let_4))))))))))) (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1))))))))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (forall ((H0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_2) H0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.l_l_) _let_1)) (tptp.s A X)))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G0) _let_1)))))))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 F0))) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 G0))) _let_1)))))))) (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (forall ((H0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_2) H0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.l_l_) _let_1)) (tptp.s A X)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 G0) _let_1)))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 F0))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 G0))) _let_1)))))))) (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s tptp.num (tptp.i _let_3 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (forall ((H0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_2) H0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.l_l_) _let_1)) (tptp.s A X)))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G0) _let_1)))))))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 F0))) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 G0))) _let_1)))))))) (and (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1)))))))) (forall ((F0 $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.fun A B))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 XI_))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1)))))))) (= (tptp.s _let_1 F0) (tptp.s _let_1 XI_))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun A _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_l_) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_l_l_) _let_2)) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s _let_1 tptp.l_l_l_))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s _let_1 tptp.l_l_)))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((X $$unsorted) (M0 $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 M0))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) U_1) _let_4)) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.l_l_) (tptp.s B (tptp.i _let_3 _let_4)))) (tptp.s B (tptp.i _let_3 _let_1))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((M0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun A _let_4))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_2)) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) U_1) _let_3)) _let_2)))))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_3 (tptp.fun B (tptp.fun B tptp.bool)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.wf) (tptp.s _let_3 tptp.l_l_)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.wf) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 M0))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((R0 $$unsorted) (S0 $$unsorted) (R1 $$unsorted) (S1 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_2 (tptp.fun A (tptp.fun B (tptp.fun B tptp.bool))))) (let ((_let_3 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun A _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_1) (tptp.s _let_3 R0))) (tptp.s _let_2 S0))) (tptp.s A R1))) (tptp.s B S1))) (tptp.s _let_1 F0)))) (forall ((R2 $$unsorted) (S2 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s B S2))) (let ((_let_3 (tptp.s A R2))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.s A R1))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun B _let_8))) (let ((_let_10 (tptp.fun A tptp.bool))) (and (= (tptp.p _let_1) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun A _let_10) R0) _let_7)) _let_3))) (and (= _let_7 _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun A _let_9) S0) _let_7)) (tptp.s B S1))) _let_2)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_3)) _let_2)))))) _let_1))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((R0 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun _let_1 tptp.bool)))) (let ((_let_3 (tptp.fun A (tptp.fun B (tptp.fun B tptp.bool))))) (let ((_let_4 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 R0))) (tptp.s _let_3 S0))) (tptp.s _let_2 F0)))) (forall ((R1 $$unsorted) (S1 $$unsorted)) (let ((_let_1 (tptp.s B S1))) (let ((_let_2 (tptp.s A R1))) (let ((_let_3 (tptp.fun A (tptp.fun B (tptp.fun B tptp.bool))))) (let ((_let_4 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_5 (tptp.prod A B))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun B _let_7))) (let ((_let_9 (tptp.fun A _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun B _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.geq) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.c_) _let_2)) _let_1)))))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.gabs) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) U_1) (tptp.s _let_4 R0))) (tptp.s _let_3 S0))) _let_2)) _let_1))))))))))))))))))))))))))) (forall ((R0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B (tptp.fun B tptp.bool))))) (let ((_let_2 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_3 (tptp.s _let_2 R0))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun _let_4 (tptp.fun _let_4 tptp.bool)))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.wf) _let_3))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B tptp.bool)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) S0) (tptp.s A A5))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.wf) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) U_0) _let_3)) (tptp.s _let_1 S0))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((R0 $$unsorted) (R1 $$unsorted) (S0 $$unsorted) (S1 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_2 (tptp.fun B (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun A _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_1) (tptp.s _let_3 R0))) (tptp.s A R1))) (tptp.s _let_2 S0))) (tptp.s B S1))) (tptp.s _let_1 F0)))) (forall ((R2 $$unsorted) (S2 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s B S2))) (let ((_let_3 (tptp.s A R2))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun B tptp.bool))) (let ((_let_8 (tptp.s A R1))) (let ((_let_9 (tptp.fun A tptp.bool))) (and (= (tptp.p _let_1) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun A _let_9) R0) _let_8)) _let_3))) (and (= _let_8 _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun B _let_7) S0) (tptp.s B S1))) _let_2)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_3)) _let_2)))))) _let_1)))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((R0 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun _let_1 tptp.bool)))) (let ((_let_3 (tptp.fun B (tptp.fun B tptp.bool)))) (let ((_let_4 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 R0))) (tptp.s _let_3 S0))) (tptp.s _let_2 F0)))) (forall ((R1 $$unsorted) (S1 $$unsorted)) (let ((_let_1 (tptp.s B S1))) (let ((_let_2 (tptp.fun B (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.s A R1))) (let ((_let_4 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_5 (tptp.prod A B))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun B _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.fun A _let_9))) (let ((_let_11 (tptp.fun B _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.geq) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.c_) _let_3)) _let_1)))))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.gabs) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) U_1) (tptp.s _let_4 R0))) _let_3)) (tptp.s _let_2 S0))) _let_1))))))))))))))))))))))))))) (forall ((R0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_4 (tptp.s _let_3 R0))) (let ((_let_5 (tptp.prod A B))) (let ((_let_6 (tptp.fun _let_5 (tptp.fun _let_5 tptp.bool)))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.wf) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.wf) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.gabs) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_0) _let_4)) _let_2))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) U_1) (tptp.s A X1))) (tptp.s B Y1))) (tptp.s _let_1 F0)))) (forall ((X2 $$unsorted) (Y2 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s B Y2))) (let ((_let_3 (tptp.s A X2))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun B tptp.bool))) (let ((_let_8 (tptp.fun A tptp.bool))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) tptp.l_l_) (tptp.s A X1))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun B _let_7) tptp.l_l_l_) (tptp.s B Y1))) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_3)) _let_2)))))) _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun _let_1 tptp.bool)))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun B (tptp.fun B tptp.bool)))) (let ((_let_5 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun _let_1 tptp.bool)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) U_0) (tptp.s _let_2 F0)))) (forall ((X1 $$unsorted) (Y1 $$unsorted)) (let ((_let_1 (tptp.s B Y1))) (let ((_let_2 (tptp.s A X1))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.fun B _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.geq) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) F0) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.c_) _let_2)) _let_1)))))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) U_1) _let_2)) _let_1))))))))))))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.wf) (tptp.s _let_5 tptp.l_l_)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.wf) (tptp.s _let_4 tptp.l_l_l_))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.wf) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.gabs) (tptp.s _let_3 U_0)))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_48 tptp.bool) tptp.wf) _let_216))) (forall ((A $$unsorted) (H0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_2) H0))) (=> (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_1)) (tptp.s tptp.num N0)))) (= (tptp.s A (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s A (tptp.i (tptp.s _let_2 G0) _let_1)))))))) (= (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 F0))) _let_1)) (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 G0))) _let_1)))))))) (exists ((F0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s A (tptp.i _let_3 _let_1)) (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1)))))))))) (forall ((Q12515 $$unsorted) (M0 $$unsorted) (X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s Q12515 XI_))) (let ((_let_2 (tptp.fun Q12515 tptp.num))) (let ((_let_3 (tptp.s _let_2 M0))) (let ((_let_4 (tptp.s Q12515 X))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun Q12515 tptp.bool))) (let ((_let_7 (tptp.fun Q12515 _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.measure0) _let_3)) _let_4)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))) (forall ((A $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A (tptp.fun A tptp.bool)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.wf) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.measure0) (tptp.s _let_1 M0))))))))) (forall ((Q12545 $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun Q12545 tptp.num) tptp.m))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (= (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q12545 tptp.num))) (let ((_let_2 (tptp.fun Q12545 tptp.bool))) (let ((_let_3 (tptp.fun Q12545 _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.measure0) (tptp.s _let_1 tptp.m))) (tptp.s Q12545 Y))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s Q12545 tptp.a0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s Q12545 tptp.b0)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_1 (tptp.s Q12545 tptp.a0))))) (tptp.s tptp.num (tptp.i _let_1 (tptp.s Q12545 tptp.b0)))))))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.l_l_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.wf) _let_4))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) _let_1)))))))))) (forall ((A $$unsorted) (U_1 $$unsorted)) (=> (forall ((Y $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) U_1) (tptp.s A Y))) (tptp.s tptp.bool tptp.f0))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) U_0) (tptp.s A X))) (tptp.s _let_1 U_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 U_0))))))))) (forall ((B $$unsorted) (A $$unsorted) (P0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun B B))) (let ((_let_5 (tptp.fun B _let_4))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1)))) (tptp.s B (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s (tptp.fun A A) G0) _let_1)))))) (tptp.s B (tptp.i (tptp.s _let_2 H0) _let_1))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (P0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (forall ((F0 $$unsorted) (G1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G1))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_2) H0))) (let ((_let_5 (tptp.s _let_2 F0))) (let ((_let_6 (tptp.fun A A))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_6) G0))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_2 _let_8) P0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.l_l_) _let_1)) (tptp.s A X)))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G1) _let_1)))))))) (and (= (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_1))) (= (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_1)) (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_1))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_5)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_3)) _let_1))))))))))))))) (forall ((F0 $$unsorted) (G1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_2) H0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.l_l_) _let_1)) (tptp.s A X)))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G1) _let_1)))))))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 F0))) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s _let_2 G1))) _let_1)))))))) (forall ((F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.l_l_) (tptp.s A Y))))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A A))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) P0) _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) G0) _let_5)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))))) (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A A))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun B B))) (let ((_let_7 (tptp.fun B _let_6))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) P0) _let_3)) _let_1)))) (tptp.s B (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) G0) _let_3)) _let_1)))))) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1))))))))))))))))) (= (tptp.s tptp.num (tptp.i _let_16 _let_51)) _let_51) (= (tptp.s tptp.num (tptp.i _let_32 _let_12)) _let_12) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.suc))) (let ((_let_4 (tptp.s _let_2 tptp.numeral))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (= (tptp.s tptp.num (tptp.i _let_46 _let_12)) _let_15) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.suc))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))) (= (tptp.s tptp.num (tptp.i _let_220 _let_12)) _let_12) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.pre))) (let ((_let_4 (tptp.s _let_2 tptp.numeral))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (forall ((N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.pre))) (let ((_let_4 (tptp.s tptp.num tptp.u_0))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun tptp.num _let_2))) (and (= (tptp.p _let_5) (= _let_1 _let_4)) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_5)) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.pre) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s _let_3 tptp.numeral))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) (tptp.s tptp.num tptp.u_0))) _let_2)) _let_2)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) (tptp.s tptp.num tptp.u_0))) _let_2)) _let_2)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num tptp.u_0))) _let_2)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num tptp.u_0))) _let_2)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s _let_3 tptp.bit0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s _let_3 tptp.bit1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s _let_3 tptp.bit1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s _let_3 tptp.bit1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_72 _let_12)) _let_12)) _let_12) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_5 (tptp.s _let_3 tptp.numeral))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num N0))))) _let_1)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num N0))))) _let_1)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num N0))))) _let_1)) _let_1)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num N0))))) _let_1)) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_5 (tptp.s _let_3 tptp.bit0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 tptp.bit0))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_6 _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_7)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_7)) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 tptp.bit0))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))) _let_7)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_7)) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 tptp.bit0))) (let ((_let_7 (tptp.s _let_4 tptp.p_))) (let ((_let_8 (tptp.s _let_3 tptp.bit1))) (let ((_let_9 (tptp.s tptp.num (tptp.i _let_8 _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_9)) (tptp.s tptp.num (tptp.i _let_8 _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_9)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_71 tptp.exp0) _let_12)) _let_12)) _let_15) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.bit1))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num M0))))) (let ((_let_5 (tptp.fun tptp.num _let_2))) (let ((_let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.exp0) _let_4)))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (let ((_let_8 (tptp.s _let_5 tptp.t_))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_8 _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_8 _let_7)) _let_7)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num M0))))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.exp0) _let_3)))) (let ((_let_6 (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (let ((_let_7 (tptp.s _let_4 tptp.t_))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_7 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_7 _let_6)) _let_6))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.exp0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num N0))))) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.exp0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num M0))))))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (= (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) _let_5)) _let_5))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.bit0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.exp0) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num M0))))))) (let ((_let_6 (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.t_) _let_6)) _let_6)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.exp0) (tptp.s tptp.num tptp.u_0))))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (= (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) _let_5)) _let_5))))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.bit1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.exp0) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num M0))))) _let_1)) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.exp0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num M0))))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0))) (let ((_let_5 (tptp.s _let_3 tptp.numeral))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (= (tptp.s tptp.bool (tptp.i _let_219 _let_12)) _let_217) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even))) (= (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) _let_1)))) (tptp.s tptp.bool (tptp.i _let_2 _let_1)))))) (forall ((N0 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) (tptp.s tptp.num N0))))) (tptp.s tptp.bool tptp.t))) (forall ((N0 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))) (tptp.s tptp.bool tptp.f0))) (= (tptp.s tptp.bool (tptp.i _let_218 _let_12)) _let_215) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd))) (= (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) _let_1)))) (tptp.s tptp.bool (tptp.i _let_2 _let_1)))))) (forall ((N0 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) (tptp.s tptp.num N0))))) (tptp.s tptp.bool tptp.f0))) (forall ((N0 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))) (tptp.s tptp.bool tptp.t))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))) (or (= _let_2 _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1)))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_48 tptp.l_a_) _let_12)) _let_12)) _let_217) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) _let_2)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.bool tptp.f0)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_a_) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) (tptp.s tptp.num N0))))) (tptp.s tptp.bool tptp.t)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_a_) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))) (tptp.s tptp.bool tptp.t)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i _let_216 _let_12)) _let_12)) _let_215) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) (tptp.s tptp.num N0))))) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.bool tptp.f0)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.bool tptp.f0)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))) (tptp.s tptp.bool tptp.t)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_a_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_48 tptp.g_a_) _let_12)) _let_12))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.g_a_) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.g_a_) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.g_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) (tptp.s tptp.num N0))))) (tptp.s tptp.num tptp.u_0)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.g_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))) (tptp.s tptp.num tptp.u_0)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_a_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.g_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.g_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_a_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_48 tptp.g_) _let_12)) _let_12)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.g_) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) (tptp.s tptp.num N0))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.g_) (tptp.s tptp.num tptp.u_0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) _let_2)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.g_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))))) (tptp.s tptp.num tptp.u_0)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.g_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.g_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.g_))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral))) (= (= (tptp.s tptp.num (tptp.i _let_3 _let_2)) (tptp.s tptp.num (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.s tptp.num N0))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) _let_2)) _let_1) (= _let_2 _let_1))))) (forall ((N0 $$unsorted)) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0))) (tptp.s tptp.num tptp.u_0)) (tptp.p (tptp.s tptp.bool tptp.f0)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (= (= _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0) _let_1))) (= _let_2 _let_1))))) (forall ((N0 $$unsorted)) (= (= (tptp.s tptp.num tptp.u_0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1) (tptp.s tptp.num N0)))) (tptp.p (tptp.s tptp.bool tptp.f0)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit0))) (= (= (tptp.s tptp.num (tptp.i _let_3 _let_2)) (tptp.s tptp.num (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num M0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num N0)))) (tptp.p (tptp.s tptp.bool tptp.f0))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num M0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num N0)))) (tptp.p (tptp.s tptp.bool tptp.f0))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.num) tptp.bit1))) (= (= (tptp.s tptp.num (tptp.i _let_3 _let_2)) (tptp.s tptp.num (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_214 _let_12)) _let_12)) _let_12) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.m_))) (let ((_let_5 (tptp.s _let_3 tptp.numeral))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.m_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num N0))))) _let_1)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.m_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num N0))))) _let_1)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) _let_2)) (tptp.s tptp.num tptp.u_0))) _let_2)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) _let_2)) (tptp.s tptp.num tptp.u_0))) _let_2)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.m_))) (let ((_let_5 (tptp.s _let_3 tptp.bit0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.m_))) (let ((_let_5 (tptp.s _let_3 tptp.bit0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.pre) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.m_))) (let ((_let_6 (tptp.s _let_3 tptp.bit1))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_6 _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.bool _let_4) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_) _let_1)) _let_2)))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.m_))) (let ((_let_5 (tptp.s _let_3 tptp.bit1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted) (P0 $$unsorted)) (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.s B Y2))) (let ((_let_2 (tptp.s B Y1))) (let ((_let_3 (tptp.s A X2))) (let ((_let_4 (tptp.s A X1))) (let ((_let_5 (tptp.fun B C))) (let ((_let_6 (tptp.s (tptp.fun A _let_5) P0))) (= (= (tptp.s C (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)) (tptp.s C (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_1))) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))) (exists ((X $$unsorted) (Y $$unsorted)) (forall ((X0 $$unsorted) (Y0 $$unsorted)) (let ((_let_1 (tptp.s B Y0))) (let ((_let_2 (tptp.s A X0))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.s C (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) P0) _let_2)) _let_1)))) (and (= (tptp.s A (tptp.i (tptp.s (tptp.fun C A) X) _let_4)) _let_2) (= (tptp.s B (tptp.i (tptp.s (tptp.fun C B) Y) _let_4)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num Y))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) (let ((_let_6 (tptp.fun tptp.num _let_1))) (let ((_let_7 (tptp.s _let_6 tptp.t_))) (let ((_let_8 (tptp.s tptp.num X))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.numpair) _let_8)) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.exp0) _let_5)) _let_8)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_5)) _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))))))) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.s tptp.num X2))) (let ((_let_2 (tptp.s tptp.num X1))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.numpair))) (=> (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num Y1))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.num Y2)))) (= _let_2 _let_1))))))) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Y2))) (let ((_let_2 (tptp.s tptp.num Y1))) (let ((_let_3 (tptp.s tptp.num X2))) (let ((_let_4 (tptp.s tptp.num X1))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.numpair))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_1))) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num Y))) (let ((_let_2 (tptp.s tptp.num X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.numpair) _let_2)) _let_1)))) (and (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numfst) _let_4)) _let_2) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numsnd) _let_4)) _let_1))))))) (forall ((B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)))) (let ((_let_5 (tptp.s tptp.bool B0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.bool _let_2) tptp.numsum) _let_5)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_4)))) _let_4))))))))) (forall ((B1 $$unsorted) (X1 $$unsorted) (B2 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.s tptp.num X2))) (let ((_let_2 (tptp.s tptp.num X1))) (let ((_let_3 (tptp.s tptp.bool B2))) (let ((_let_4 (tptp.s tptp.bool B1))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s (tptp.fun tptp.bool _let_5) tptp.numsum))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_1))) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num Y))) (let ((_let_2 (tptp.s tptp.bool X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.numsum) _let_2)) _let_1)))) (and (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.numleft) _let_4)) _let_2) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numright) _let_4)) _let_1))))))) (forall ((A $$unsorted) (M0 $$unsorted) (X $$unsorted) (X0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.injn) _let_1)) _let_2)) (tptp.s A X0)))) (= _let_2 _let_1))))))) (forall ((A $$unsorted) (N1 $$unsorted) (N2 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N2))) (let ((_let_2 (tptp.s tptp.num N1))) (let ((_let_3 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.injn))) (= (= (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_3 (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((A $$unsorted) (A5 $$unsorted) (X $$unsorted) (X0 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.s A X0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.inja) _let_1)) (tptp.s tptp.num X))) _let_2))) (= _let_2 _let_1))))))) (forall ((A $$unsorted) (A10 $$unsorted) (A20 $$unsorted)) (let ((_let_1 (tptp.s A A20))) (let ((_let_2 (tptp.s A A10))) (let ((_let_3 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.inja))) (= (= (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_3 (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((A $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.injf) _let_6)) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numfst) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numsnd) _let_1)))))))))))) (forall ((A $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F2))) (let ((_let_4 (tptp.s _let_2 F1))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_1) tptp.injf))) (= (= (tptp.s _let_1 (tptp.i _let_5 _let_4)) (tptp.s _let_1 (tptp.i _let_5 _let_3))) (= _let_4 _let_3)))))))) (forall ((A $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (X $$unsorted) (X0 $$unsorted)) (let ((_let_1 (tptp.s A X0))) (let ((_let_2 (tptp.s tptp.num X))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numright) _let_2)))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 F2))) (let ((_let_7 (tptp.s _let_5 F1))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun tptp.bool _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.injp) _let_7)) _let_6)) _let_2)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.numleft) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))) (forall ((A $$unsorted) (F1 $$unsorted) (F1I_ $$unsorted) (F2 $$unsorted) (F2I_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.s _let_1 F2I_))) (let ((_let_3 (tptp.s _let_1 F2))) (let ((_let_4 (tptp.s _let_1 F1I_))) (let ((_let_5 (tptp.s _let_1 F1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.injp))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2))) (and (= _let_5 _let_4) (= _let_3 _let_2))))))))))) (forall ((A $$unsorted) (C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 R0))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (let ((_let_5 (tptp.s A I0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.injp))) (let ((_let_8 (tptp.s tptp.num C0))) (let ((_let_9 (tptp.fun A _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.zconstr) _let_8)) _let_5)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.injn) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_8)))))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) tptp.inja) _let_5)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.injf) _let_3))))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 Z0))) (tptp.s tptp.bool tptp.t)))) (= (tptp.s _let_1 tptp.zbot) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.injp) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.injn) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.h_) (tptp.s _let_2 U_0))))))))))) (forall ((A $$unsorted) (C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun A _let_3))) (not (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.zconstr) (tptp.s tptp.num C0))) (tptp.s A I0))) (tptp.s _let_2 R0))) (tptp.s _let_1 tptp.zbot)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.zrecspace) (tptp.s _let_1 tptp.zbot)))))) (forall ((A $$unsorted) (C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun A _let_3))) (=> (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.zrecspace) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) R0) (tptp.s tptp.num N0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.zrecspace) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.zconstr) (tptp.s tptp.num C0))) (tptp.s A I0))) (tptp.s _let_2 R0)))))))))))) (forall ((A $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.s _let_1 A5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.zrecspace) _let_2))) (or (= _let_2 (tptp.s _let_1 tptp.zbot)) (exists ((C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun A _let_3))) (and (= (tptp.s _let_1 A5) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.zconstr) (tptp.s tptp.num C0))) (tptp.s A I0))) (tptp.s _let_2 R0)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.zrecspace) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) R0) (tptp.s tptp.num N0))))))))))))))))))) (forall ((A $$unsorted) (ZRECSPACEI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) ZRECSPACEI_) (tptp.s _let_1 tptp.zbot)))) (forall ((C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun A _let_3))) (=> (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) ZRECSPACEI_) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) R0) (tptp.s tptp.num N0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) ZRECSPACEI_) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.zconstr) (tptp.s tptp.num C0))) (tptp.s A I0))) (tptp.s _let_2 R0))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.zrecspace) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 ZRECSPACEI_) _let_2))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.recspace A))) (= (tptp.s _let_2 tptp.bottom) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.u_mku_rec) (tptp.s _let_1 tptp.zbot))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((R0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.recspace A))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 R0))) (let ((_let_5 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_1)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.u_destu_rec) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))) (forall ((C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.recspace A))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 R0))) (let ((_let_4 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s A I0))) (let ((_let_7 (tptp.s tptp.num C0))) (let ((_let_8 (tptp.fun _let_5 _let_4))) (let ((_let_9 (tptp.fun A _let_8))) (let ((_let_10 (tptp.fun _let_2 _let_1))) (let ((_let_11 (tptp.fun A _let_10))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.constr) _let_7)) _let_6)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.u_mku_rec) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.zconstr) _let_7)) _let_6)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3))))))))))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.zrecspace))) (let ((_let_5 (tptp.recspace A))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.u_mku_rec))) (=> (= (tptp.s _let_5 (tptp.i _let_6 _let_3)) (tptp.s _let_5 (tptp.i _let_6 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))) (= _let_3 _let_2)))))))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.recspace A))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.u_destu_rec))) (= (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2)))))))) (forall ((A $$unsorted) (C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.recspace A))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun A _let_3))) (not (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.constr) (tptp.s tptp.num C0))) (tptp.s A I0))) (tptp.s _let_2 R0))) (tptp.s _let_1 tptp.bottom)))))))) (forall ((A $$unsorted) (C1 $$unsorted) (I1 $$unsorted) (R1 $$unsorted) (C2 $$unsorted) (I2 $$unsorted) (R2 $$unsorted)) (let ((_let_1 (tptp.recspace A))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 R2))) (let ((_let_4 (tptp.s _let_2 R1))) (let ((_let_5 (tptp.s A I2))) (let ((_let_6 (tptp.s A I1))) (let ((_let_7 (tptp.s tptp.num C2))) (let ((_let_8 (tptp.s tptp.num C1))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (let ((_let_10 (tptp.fun A _let_9))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.constr))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_8)) _let_6)) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_7)) _let_5)) _let_3))) (and (= _let_8 _let_7) (= _let_6 _let_5) (= _let_4 _let_3))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.recspace A))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 tptp.bottom)))) (forall ((C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.recspace A))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun A _let_3))) (=> (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.recspace A))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) R0) (tptp.s tptp.num N0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.constr) (tptp.s tptp.num C0))) (tptp.s A I0))) (tptp.s _let_2 R0))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.recspace A))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 X))))))))) (forall ((B $$unsorted) (A $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (R0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.recspace A))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 R0))) (let ((_let_5 (tptp.fun _let_2 B))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun tptp.num B))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (= (tptp.s B (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) _let_6)) _let_4)) _let_1)) (tptp.s B (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))) (forall ((FN $$unsorted)) (exists ((F0 $$unsorted)) (forall ((C0 $$unsorted) (I0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.recspace A))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 R0))) (let ((_let_4 (tptp.fun _let_1 B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun tptp.num B))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.s A I0))) (let ((_let_9 (tptp.s tptp.num C0))) (let ((_let_10 (tptp.fun _let_6 B))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun A _let_11))) (let ((_let_13 (tptp.fun _let_2 _let_1))) (let ((_let_14 (tptp.fun A _let_13))) (= (tptp.s B (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.num _let_14) tptp.constr) _let_9)) _let_8)) _let_3)))) (tptp.s B (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) FN) _let_9)) _let_8)) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)) _let_3)))))))))))))))))))))))) (forall ((A $$unsorted) (A5 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.fcons) _let_1)) (tptp.s _let_2 F0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1))))) (forall ((A $$unsorted) (A5 $$unsorted) (F0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.fcons) (tptp.s A A5))) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s A (tptp.i _let_3 _let_1)))))))) (forall ((A $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.fcons) (tptp.s A (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.o) _let_3)) (tptp.s _let_1 tptp.suc)))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) U_0) (tptp.s A X))) (tptp.s tptp.bool tptp.t))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun tptp.num A) tptp.fnil) (tptp.s tptp.num N0))) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.h_) (tptp.s _let_1 U_0)))))))) (forall ((A $$unsorted) (B $$unsorted) (P0 $$unsorted)) (=> (and (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.sum0 A B))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) tptp.inl) (tptp.s A A5)))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.sum0 A B))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun B _let_1) tptp.inr) (tptp.s B A5))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.sum0 A B))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 X)))))))) (forall ((A $$unsorted) (Z $$unsorted) (B $$unsorted) (INLI_ $$unsorted) (INRI_ $$unsorted)) (exists ((FN $$unsorted)) (and (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.sum0 A B))) (= (tptp.s Z (tptp.i (tptp.s (tptp.fun _let_2 Z) FN) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.inl) _let_1)))) (tptp.s Z (tptp.i (tptp.s (tptp.fun A Z) INLI_) _let_1)))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s B A5))) (let ((_let_2 (tptp.sum0 A B))) (= (tptp.s Z (tptp.i (tptp.s (tptp.fun _let_2 Z) FN) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.inr) _let_1)))) (tptp.s Z (tptp.i (tptp.s (tptp.fun B Z) INRI_) _let_1))))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.s A tptp.x))) (let ((_let_2 (tptp.sum0 A B))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) tptp.outl) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.inl) _let_1)))) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.s B tptp.y))) (let ((_let_2 (tptp.sum0 A B))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun _let_2 B) tptp.outr) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.inr) _let_1)))) _let_1)))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.option A))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 tptp.none)))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.option A))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) tptp.some) (tptp.s A A5))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.option A))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 X))))))))) (forall ((Z $$unsorted) (A $$unsorted) (NONEI_ $$unsorted) (SOMEI_ $$unsorted)) (exists ((FN $$unsorted)) (let ((_let_1 (tptp.option A))) (and (= (tptp.s Z (tptp.i (tptp.s (tptp.fun _let_1 Z) FN) (tptp.s _let_1 tptp.none))) (tptp.s Z NONEI_)) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.option A))) (= (tptp.s Z (tptp.i (tptp.s (tptp.fun _let_2 Z) FN) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.some) _let_1)))) (tptp.s Z (tptp.i (tptp.s (tptp.fun A Z) SOMEI_) _let_1)))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.list A))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 tptp.nil)))) (forall ((A01 $$unsorted) (A10 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 A10))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) P0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.cons) (tptp.s A A01))) _let_2)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.list A))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 X))))))))) (forall ((Z $$unsorted) (A $$unsorted) (NILI_ $$unsorted) (CONSI_ $$unsorted)) (exists ((FN $$unsorted)) (let ((_let_1 (tptp.list A))) (and (= (tptp.s Z (tptp.i (tptp.s (tptp.fun _let_1 Z) FN) (tptp.s _let_1 tptp.nil))) (tptp.s Z NILI_)) (forall ((A01 $$unsorted) (A10 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 A10))) (let ((_let_3 (tptp.s (tptp.fun _let_1 Z) FN))) (let ((_let_4 (tptp.s A A01))) (let ((_let_5 (tptp.fun Z Z))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s Z (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.cons) _let_4)) _let_2)))) (tptp.s Z (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) CONSI_) _let_4)) _let_2)) (tptp.s Z (tptp.i _let_3 _let_2))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (A5 $$unsorted) (AI_ $$unsorted)) (let ((_let_1 (tptp.sum0 A B))) (not (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) tptp.inl) (tptp.s A A5))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun B _let_1) tptp.inr) (tptp.s B AI_))))))) (forall ((A $$unsorted) (B $$unsorted) (A5 $$unsorted) (AI_ $$unsorted)) (let ((_let_1 (tptp.s B AI_))) (let ((_let_2 (tptp.s B A5))) (let ((_let_3 (tptp.sum0 A B))) (let ((_let_4 (tptp.s (tptp.fun B _let_3) tptp.inr))) (= (= (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_3 (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (A5 $$unsorted) (AI_ $$unsorted)) (let ((_let_1 (tptp.s A AI_))) (let ((_let_2 (tptp.s A A5))) (let ((_let_3 (tptp.sum0 A B))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.inl))) (= (= (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_3 (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((B $$unsorted) (A $$unsorted) (G0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B A))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.iso0) (tptp.s _let_2 F0))) (tptp.s _let_1 G0)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s B X))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_1)))) _let_1))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) _let_1))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun A A))) (let ((_let_2 (tptp.s _let_1 U_0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) U_0) _let_1)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.iso0) _let_2)) _let_2)))))))) (forall ((AP $$unsorted) (BP $$unsorted) (A $$unsorted) (B $$unsorted) (U_3 $$unsorted)) (=> (forall ((H0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun AP BP))) (let ((_let_3 (tptp.s _let_2 H0))) (let ((_let_4 (tptp.fun A B))) (= (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_3) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s (tptp.fun BP B) tptp.gi_) (tptp.s BP (tptp.i _let_3 (tptp.s AP (tptp.i (tptp.s (tptp.fun A AP) tptp.f) _let_1)))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((H0 $$unsorted)) (let ((_let_1 (tptp.fun AP BP))) (let ((_let_2 (tptp.s _let_1 H0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_2) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_3) _let_2)))))))) (forall ((U_1 $$unsorted)) (=> (forall ((H0 $$unsorted) (AI_ $$unsorted)) (let ((_let_1 (tptp.s AP AI_))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 H0))) (let ((_let_4 (tptp.fun AP BP))) (= (tptp.s BP (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_1) _let_3)) _let_1)) (tptp.s BP (tptp.i (tptp.s (tptp.fun B BP) tptp.g) (tptp.s B (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s (tptp.fun AP A) tptp.fi_) _let_1)))))))))))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun AP BP))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun BP B))) (let ((_let_7 (tptp.fun B BP))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.fun AP A))) (let ((_let_10 (tptp.fun A AP))) (let ((_let_11 (tptp.fun _let_9 tptp.bool))) (=> (forall ((H0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 H0))) (let ((_let_3 (tptp.fun AP BP))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_1) _let_2)))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_10 _let_11) tptp.iso0) (tptp.s _let_10 tptp.f))) (tptp.s _let_9 tptp.fi_)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) tptp.iso0) (tptp.s _let_7 tptp.g))) (tptp.s _let_6 tptp.gi_))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.iso0) (tptp.s _let_4 U_0))) (tptp.s _let_3 U_2)))))))))))))))))))))))) (forall ((Q17931 $$unsorted) (Q17928 $$unsorted)) (let ((_let_1 (tptp.fun Q17928 Q17931))) (let ((_let_2 (tptp.fun Q17931 Q17928))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.iso0) (tptp.s _let_2 tptp.f))) (tptp.s _let_1 tptp.g)))) (and (forall ((P0 $$unsorted)) (= (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q17931 tptp.bool) P0) (tptp.s Q17931 X))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q17931 tptp.bool) P0) (tptp.s Q17931 (tptp.i (tptp.s (tptp.fun Q17928 Q17931) tptp.g) (tptp.s Q17928 X))))))))) (forall ((P0 $$unsorted)) (= (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q17931 tptp.bool) P0) (tptp.s Q17931 X))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q17931 tptp.bool) P0) (tptp.s Q17931 (tptp.i (tptp.s (tptp.fun Q17928 Q17931) tptp.g) (tptp.s Q17928 X))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s Q17928 B0))) (let ((_let_2 (tptp.s Q17931 A5))) (= (= _let_2 (tptp.s Q17931 (tptp.i (tptp.s (tptp.fun Q17928 Q17931) tptp.g) _let_1))) (= (tptp.s Q17928 (tptp.i (tptp.s (tptp.fun Q17931 Q17928) tptp.f) _let_2)) _let_1))))))))))) (forall ((A $$unsorted) (T0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.s A H0))) (let ((_let_2 (tptp.list A))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) tptp.hd) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.cons) _let_1)) (tptp.s _let_2 T0))))) _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.h0))) (let ((_let_2 (tptp.list A))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) tptp.hd) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.cons) _let_1)) (tptp.s _let_2 tptp.t0))))) _let_1))))) (forall ((A $$unsorted) (H0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.tl) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.cons) (tptp.s A H0))) _let_2)))) _let_2))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.tl) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.cons) (tptp.s A tptp.h0))) _let_2)))) _let_2))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.append) (tptp.s _let_1 tptp.nil))) _let_2)) _let_2))))) (forall ((A $$unsorted) (H0 $$unsorted) (T0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.append))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.cons) (tptp.s A H0))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 tptp.nil))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.reverse) _let_2)) _let_2)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.cons) (tptp.s A tptp.x))))) (let ((_let_4 (tptp.s _let_1 tptp.l0))) (let ((_let_5 (tptp.s _let_2 tptp.reverse))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_3 _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.append) (tptp.s _let_1 (tptp.i _let_5 _let_4)))) (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 tptp.nil)))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) (tptp.s _let_1 tptp.nil))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((A $$unsorted) (H0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.length))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.cons) (tptp.s A H0))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.list B))) (let ((_let_2 (tptp.list A))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.map0) (tptp.s _let_3 F0))) (tptp.s _let_2 tptp.nil))) (tptp.s _let_1 tptp.nil))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (H0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.list B))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.map0) _let_4)))) (let ((_let_8 (tptp.s A H0))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun A _let_10) tptp.cons) _let_8)) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.cons) (tptp.s B (tptp.i _let_4 _let_8)))) (tptp.s _let_5 (tptp.i _let_7 _let_2)))))))))))))))) (forall ((A $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 A) tptp.last0))) (let ((_let_4 (tptp.s A tptp.h0))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun A A))) (let ((_let_7 (tptp.fun A _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (and (= (tptp.p _let_5) (= _let_2 (tptp.s _let_1 tptp.nil))) (= (tptp.s A (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) tptp.cons) _let_4)) _let_2)))) (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_5)) _let_4)) (tptp.s A (tptp.i _let_3 _let_2)))))))))))))))) (forall ((Q18547 $$unsorted)) (let ((_let_1 (tptp.list Q18547))) (let ((_let_2 (tptp.s _let_1 tptp.nil))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.butlast) _let_2)) _let_2)))) (forall ((Q18547 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.list Q18547))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 tptp.butlast))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q18547 _let_3) tptp.cons) (tptp.s Q18547 tptp.h0))))) (let ((_let_6 (tptp.s _let_1 tptp.nil))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.fun _let_1 _let_3))) (and (= (tptp.p _let_7) (= _let_2 _let_6)) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i _let_5 _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) _let_7)) _let_6)) (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))))))))))))) (forall ((Q18568 $$unsorted)) (let ((_let_1 (tptp.list Q18568))) (let ((_let_2 (tptp.fun Q18568 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.replicate) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s Q18568 tptp.x))) (tptp.s _let_1 tptp.nil))))) (forall ((Q18568 $$unsorted)) (let ((_let_1 (tptp.s Q18568 tptp.x))) (let ((_let_2 (tptp.s tptp.num tptp.n))) (let ((_let_3 (tptp.list Q18568))) (let ((_let_4 (tptp.fun Q18568 _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.replicate))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_2)))) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q18568 _let_6) tptp.cons) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))))) (forall ((Q18583 $$unsorted)) (let ((_let_1 (tptp.list Q18583))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.null) (tptp.s _let_1 tptp.nil))) (tptp.s tptp.bool tptp.t)))) (forall ((Q18583 $$unsorted)) (let ((_let_1 (tptp.list Q18583))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.null) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q18583 _let_2) tptp.cons) (tptp.s Q18583 tptp.h0))) (tptp.s _let_1 tptp.t0))))) (tptp.s tptp.bool tptp.f0))))) (forall ((Q18603 $$unsorted)) (let ((_let_1 (tptp.list Q18603))) (let ((_let_2 (tptp.fun Q18603 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.all0) (tptp.s _let_2 tptp.p0))) (tptp.s _let_1 tptp.nil))) (tptp.s tptp.bool tptp.t)))))) (forall ((Q18603 $$unsorted)) (let ((_let_1 (tptp.list Q18603))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.fun Q18603 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.p0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.all0) _let_4)))) (let ((_let_7 (tptp.s Q18603 tptp.h0))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q18603 _let_8) tptp.cons) _let_7)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))))))))))))) (forall ((Q18624 $$unsorted)) (let ((_let_1 (tptp.list Q18624))) (let ((_let_2 (tptp.fun Q18624 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.ex0) (tptp.s _let_2 tptp.p0))) (tptp.s _let_1 tptp.nil))) (tptp.s tptp.bool tptp.f0)))))) (forall ((Q18624 $$unsorted)) (let ((_let_1 (tptp.list Q18624))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.fun Q18624 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.p0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.ex0) _let_4)))) (let ((_let_7 (tptp.s Q18624 tptp.h0))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q18624 _let_8) tptp.cons) _let_7)) _let_2))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))))))))))))) (forall ((Q18647 $$unsorted) (Q18646 $$unsorted)) (let ((_let_1 (tptp.s Q18646 tptp.b0))) (let ((_let_2 (tptp.list Q18647))) (let ((_let_3 (tptp.fun Q18646 Q18646))) (let ((_let_4 (tptp.fun Q18647 _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_3))) (= (tptp.s Q18646 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.itlist) (tptp.s _let_4 tptp.f))) (tptp.s _let_2 tptp.nil))) _let_1)) _let_1))))))) (forall ((Q18647 $$unsorted) (Q18646 $$unsorted)) (let ((_let_1 (tptp.s Q18646 tptp.b0))) (let ((_let_2 (tptp.list Q18647))) (let ((_let_3 (tptp.s _let_2 tptp.t0))) (let ((_let_4 (tptp.fun Q18646 Q18646))) (let ((_let_5 (tptp.fun Q18647 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.f))) (let ((_let_7 (tptp.fun _let_2 _let_4))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.itlist) _let_6)))) (let ((_let_9 (tptp.s Q18647 tptp.h0))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (= (tptp.s Q18646 (tptp.i (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q18647 _let_10) tptp.cons) _let_9)) _let_3)))) _let_1)) (tptp.s Q18646 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_9)) (tptp.s Q18646 (tptp.i (tptp.s _let_4 (tptp.i _let_8 _let_3)) _let_1)))))))))))))))) (forall ((Q18672 $$unsorted)) (let ((_let_1 (tptp.list Q18672))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q18672 _let_2) tptp.mem) (tptp.s Q18672 tptp.x))) (tptp.s _let_1 tptp.nil))) (tptp.s tptp.bool tptp.f0))))) (forall ((Q18672 $$unsorted)) (let ((_let_1 (tptp.list Q18672))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.s Q18672 tptp.x))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q18672 _let_4) tptp.mem) _let_3)))) (let ((_let_6 (tptp.s Q18672 tptp.h0))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q18672 _let_7) tptp.cons) _let_6)) _let_2))))) (or (= _let_3 _let_6) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))))) (forall ((Q18705 $$unsorted) (Q18712 $$unsorted)) (let ((_let_1 (tptp.list Q18712))) (let ((_let_2 (tptp.s _let_1 tptp.l2))) (let ((_let_3 (tptp.list Q18705))) (let ((_let_4 (tptp.fun Q18705 (tptp.fun Q18712 tptp.bool)))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.all2) (tptp.s _let_4 tptp.p0))) (tptp.s _let_3 tptp.nil))) _let_2))) (= _let_2 (tptp.s _let_1 tptp.nil)))))))))) (forall ((Q18705 $$unsorted) (Q18712 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.list Q18712))) (let ((_let_2 (tptp.s _let_1 tptp.l2))) (let ((_let_3 (tptp.list Q18705))) (let ((_let_4 (tptp.fun Q18712 tptp.bool))) (let ((_let_5 (tptp.fun Q18705 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.p0))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (and (= (tptp.p (tptp.s tptp.bool V)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s Q18705 tptp.h1))) (tptp.s Q18712 (tptp.i (tptp.s (tptp.fun _let_1 Q18712) tptp.hd) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.all2) _let_6)) (tptp.s _let_3 tptp.t1))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.tl) _let_2))))))) (exists ((VI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.list Q18712))) (let ((_let_5 (tptp.s _let_4 tptp.l2))) (let ((_let_6 (tptp.list Q18705))) (let ((_let_7 (tptp.fun _let_6 _let_6))) (let ((_let_8 (tptp.fun Q18705 (tptp.fun Q18712 tptp.bool)))) (let ((_let_9 (tptp.fun _let_4 tptp.bool))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (and (= (tptp.p _let_1) (= _let_5 (tptp.s _let_4 tptp.nil))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.all2) (tptp.s _let_8 tptp.p0))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q18705 _let_7) tptp.cons) (tptp.s Q18705 tptp.h1))) (tptp.s _let_6 tptp.t1))))) _let_5)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) _let_1)) (tptp.s tptp.bool tptp.f0))) (tptp.s tptp.bool V))))))))))))))))))))))))))) (forall ((Q18767 $$unsorted) (Q18766 $$unsorted)) (let ((_let_1 (tptp.list Q18766))) (let ((_let_2 (tptp.list Q18767))) (let ((_let_3 (tptp.fun Q18767 (tptp.fun Q18766 tptp.bool)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.all2) (tptp.s _let_3 tptp.p0))) (tptp.s _let_2 tptp.nil))) (tptp.s _let_1 tptp.nil))) (tptp.s tptp.bool tptp.t)))))))) (forall ((Q18767 $$unsorted) (Q18766 $$unsorted)) (let ((_let_1 (tptp.list Q18766))) (let ((_let_2 (tptp.list Q18767))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun Q18767 (tptp.fun Q18766 tptp.bool)))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.all2) (tptp.s _let_4 tptp.p0))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q18767 _let_3) tptp.cons) (tptp.s Q18767 tptp.h1))) (tptp.s _let_2 tptp.t1))))) (tptp.s _let_1 tptp.nil))) (tptp.s tptp.bool tptp.f0))))))))) (forall ((Q18767 $$unsorted) (Q18766 $$unsorted)) (let ((_let_1 (tptp.list Q18766))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.list Q18767))) (let ((_let_4 (tptp.fun Q18767 (tptp.fun Q18766 tptp.bool)))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.all2) (tptp.s _let_4 tptp.p0))) (tptp.s _let_3 tptp.nil))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q18766 _let_2) tptp.cons) (tptp.s Q18766 tptp.h2))) (tptp.s _let_1 tptp.t2))))) (tptp.s tptp.bool tptp.f0))))))))) (forall ((Q18767 $$unsorted) (Q18766 $$unsorted)) (let ((_let_1 (tptp.list Q18766))) (let ((_let_2 (tptp.s _let_1 tptp.t2))) (let ((_let_3 (tptp.list Q18767))) (let ((_let_4 (tptp.s _let_3 tptp.t1))) (let ((_let_5 (tptp.fun Q18766 tptp.bool))) (let ((_let_6 (tptp.fun Q18767 _let_5))) (let ((_let_7 (tptp.s _let_6 tptp.p0))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.all2) _let_7)))) (let ((_let_11 (tptp.s Q18766 tptp.h2))) (let ((_let_12 (tptp.s Q18767 tptp.h1))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (let ((_let_14 (tptp.fun _let_3 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun Q18767 _let_14) tptp.cons) _let_12)) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun Q18766 _let_13) tptp.cons) _let_11)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_12)) _let_11))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2)))))))))))))))))))) (forall ((Q18797 $$unsorted) (Q18804 $$unsorted) (Q18794 $$unsorted)) (let ((_let_1 (tptp.list Q18794))) (let ((_let_2 (tptp.list Q18804))) (let ((_let_3 (tptp.list Q18797))) (let ((_let_4 (tptp.fun Q18797 (tptp.fun Q18804 Q18794)))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.map2) (tptp.s _let_4 tptp.f))) (tptp.s _let_3 tptp.nil))) (tptp.s _let_2 tptp.l0))) (tptp.s _let_1 tptp.nil))))))))) (forall ((Q18794 $$unsorted) (Q18797 $$unsorted) (Q18804 $$unsorted)) (let ((_let_1 (tptp.list Q18804))) (let ((_let_2 (tptp.s _let_1 tptp.l0))) (let ((_let_3 (tptp.list Q18797))) (let ((_let_4 (tptp.s _let_3 tptp.t1))) (let ((_let_5 (tptp.fun Q18804 Q18794))) (let ((_let_6 (tptp.fun Q18797 _let_5))) (let ((_let_7 (tptp.s _let_6 tptp.f))) (let ((_let_8 (tptp.list Q18794))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.map2) _let_7)))) (let ((_let_12 (tptp.s Q18797 tptp.h1))) (let ((_let_13 (tptp.fun _let_8 _let_8))) (let ((_let_14 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s _let_3 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun Q18797 _let_14) tptp.cons) _let_12)) _let_4)))) _let_2)) (tptp.s _let_8 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun Q18794 _let_13) tptp.cons) (tptp.s Q18794 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_12)) (tptp.s Q18804 (tptp.i (tptp.s (tptp.fun _let_1 Q18804) tptp.hd) _let_2)))))) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.tl) _let_2)))))))))))))))))))))) (forall ((Q18839 $$unsorted) (Q18838 $$unsorted) (Q18845 $$unsorted)) (let ((_let_1 (tptp.list Q18845))) (let ((_let_2 (tptp.list Q18838))) (let ((_let_3 (tptp.list Q18839))) (let ((_let_4 (tptp.fun Q18839 (tptp.fun Q18838 Q18845)))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.map2) (tptp.s _let_4 tptp.f))) (tptp.s _let_3 tptp.nil))) (tptp.s _let_2 tptp.nil))) (tptp.s _let_1 tptp.nil))))))))) (forall ((Q18845 $$unsorted) (Q18839 $$unsorted) (Q18838 $$unsorted)) (let ((_let_1 (tptp.list Q18838))) (let ((_let_2 (tptp.s _let_1 tptp.t2))) (let ((_let_3 (tptp.list Q18839))) (let ((_let_4 (tptp.s _let_3 tptp.t1))) (let ((_let_5 (tptp.fun Q18838 Q18845))) (let ((_let_6 (tptp.fun Q18839 _let_5))) (let ((_let_7 (tptp.s _let_6 tptp.f))) (let ((_let_8 (tptp.list Q18845))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.map2) _let_7)))) (let ((_let_12 (tptp.s Q18838 tptp.h2))) (let ((_let_13 (tptp.s Q18839 tptp.h1))) (let ((_let_14 (tptp.fun _let_8 _let_8))) (let ((_let_15 (tptp.fun _let_1 _let_1))) (let ((_let_16 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s _let_3 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun Q18839 _let_16) tptp.cons) _let_13)) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun Q18838 _let_15) tptp.cons) _let_12)) _let_2)))) (tptp.s _let_8 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun Q18845 _let_14) tptp.cons) (tptp.s Q18845 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_13)) _let_12)))) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_4)) _let_2)))))))))))))))))))))) (forall ((Q18865 $$unsorted)) (let ((_let_1 (tptp.list Q18865))) (let ((_let_2 (tptp.s _let_1 tptp.l0))) (let ((_let_3 (tptp.fun _let_1 Q18865))) (= (tptp.s Q18865 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.el) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_2)) (tptp.s Q18865 (tptp.i (tptp.s _let_3 tptp.hd) _let_2))))))) (forall ((Q18865 $$unsorted)) (let ((_let_1 (tptp.list Q18865))) (let ((_let_2 (tptp.s _let_1 tptp.l0))) (let ((_let_3 (tptp.s tptp.num tptp.n))) (let ((_let_4 (tptp.fun _let_1 Q18865))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.el))) (= (tptp.s Q18865 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_3)))) _let_2)) (tptp.s Q18865 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.tl) _let_2))))))))))) (forall ((Q18890 $$unsorted)) (let ((_let_1 (tptp.list Q18890))) (let ((_let_2 (tptp.s _let_1 tptp.nil))) (let ((_let_3 (tptp.fun Q18890 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.filter0) (tptp.s _let_3 tptp.p0))) _let_2)) _let_2)))))) (forall ((Q18890 $$unsorted)) (let ((_let_1 (tptp.list Q18890))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.fun Q18890 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.p0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.filter0) _let_4)))) (let ((_let_7 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (let ((_let_8 (tptp.s Q18890 tptp.h0))) (let ((_let_9 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q18890 _let_5) tptp.cons) _let_8)))) (let ((_let_10 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_9 _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i _let_4 _let_8)))) (tptp.s _let_1 (tptp.i _let_9 _let_7)))) _let_7)))))))))))))) (forall ((Q18919 $$unsorted) (Q18913 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.prod Q18919 Q18913))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.s _let_2 tptp.t0))) (let ((_let_4 (tptp.s Q18919 tptp.a0))) (let ((_let_5 (tptp.fun _let_2 Q18913))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q18919 _let_5) tptp.assoc) _let_4)))) (let ((_let_7 (tptp.s _let_1 tptp.h0))) (let ((_let_8 (tptp.s tptp.bool V))) (let ((_let_9 (tptp.fun Q18913 Q18913))) (let ((_let_10 (tptp.fun Q18913 _let_9))) (let ((_let_11 (tptp.fun _let_2 _let_2))) (and (= (tptp.p _let_8) (= (tptp.s Q18919 (tptp.i (tptp.s (tptp.fun _let_1 Q18919) tptp.fst) _let_7)) _let_4)) (= (tptp.s Q18913 (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.cons) _let_7)) _let_3)))) (tptp.s Q18913 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) _let_8)) (tptp.s Q18913 (tptp.i (tptp.s (tptp.fun _let_1 Q18913) tptp.snd) _let_7)))) (tptp.s Q18913 (tptp.i _let_6 _let_3))))))))))))))))))) (forall ((Q18943 $$unsorted) (Q18951 $$unsorted) (Q18941 $$unsorted)) (let ((_let_1 (tptp.s Q18941 tptp.b0))) (let ((_let_2 (tptp.list Q18951))) (let ((_let_3 (tptp.list Q18943))) (let ((_let_4 (tptp.fun Q18941 Q18941))) (let ((_let_5 (tptp.fun Q18943 (tptp.fun Q18951 _let_4)))) (let ((_let_6 (tptp.fun _let_2 _let_4))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s Q18941 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.itlist2) (tptp.s _let_5 tptp.f))) (tptp.s _let_3 tptp.nil))) (tptp.s _let_2 tptp.l2))) _let_1)) _let_1))))))))) (forall ((Q18943 $$unsorted) (Q18951 $$unsorted) (Q18941 $$unsorted)) (let ((_let_1 (tptp.s Q18941 tptp.b0))) (let ((_let_2 (tptp.list Q18951))) (let ((_let_3 (tptp.s _let_2 tptp.l2))) (let ((_let_4 (tptp.list Q18943))) (let ((_let_5 (tptp.s _let_4 tptp.t1))) (let ((_let_6 (tptp.fun Q18941 Q18941))) (let ((_let_7 (tptp.fun Q18951 _let_6))) (let ((_let_8 (tptp.fun Q18943 _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.f))) (let ((_let_10 (tptp.fun _let_2 _let_6))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (let ((_let_12 (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.itlist2) _let_9)))) (let ((_let_13 (tptp.s Q18943 tptp.h1))) (let ((_let_14 (tptp.fun _let_4 _let_4))) (= (tptp.s Q18941 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i _let_12 (tptp.s _let_4 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun Q18943 _let_14) tptp.cons) _let_13)) _let_5)))) _let_3)) _let_1)) (tptp.s Q18941 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_13)) (tptp.s Q18951 (tptp.i (tptp.s (tptp.fun _let_2 Q18951) tptp.hd) _let_3)))) (tptp.s Q18941 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i _let_12 _let_5)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.tl) _let_3)))) _let_1)))))))))))))))))))) (forall ((Q18985 $$unsorted) (Q18984 $$unsorted) (Q18983 $$unsorted)) (let ((_let_1 (tptp.s Q18983 tptp.b0))) (let ((_let_2 (tptp.list Q18984))) (let ((_let_3 (tptp.list Q18985))) (let ((_let_4 (tptp.fun Q18983 Q18983))) (let ((_let_5 (tptp.fun Q18985 (tptp.fun Q18984 _let_4)))) (let ((_let_6 (tptp.fun _let_2 _let_4))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s Q18983 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.itlist2) (tptp.s _let_5 tptp.f))) (tptp.s _let_3 tptp.nil))) (tptp.s _let_2 tptp.nil))) _let_1)) _let_1))))))))) (forall ((Q18985 $$unsorted) (Q18984 $$unsorted) (Q18983 $$unsorted)) (let ((_let_1 (tptp.s Q18983 tptp.b0))) (let ((_let_2 (tptp.list Q18984))) (let ((_let_3 (tptp.s _let_2 tptp.t2))) (let ((_let_4 (tptp.list Q18985))) (let ((_let_5 (tptp.s _let_4 tptp.t1))) (let ((_let_6 (tptp.fun Q18983 Q18983))) (let ((_let_7 (tptp.fun Q18984 _let_6))) (let ((_let_8 (tptp.fun Q18985 _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.f))) (let ((_let_10 (tptp.fun _let_2 _let_6))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (let ((_let_12 (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.itlist2) _let_9)))) (let ((_let_13 (tptp.s Q18984 tptp.h2))) (let ((_let_14 (tptp.s Q18985 tptp.h1))) (let ((_let_15 (tptp.fun _let_2 _let_2))) (let ((_let_16 (tptp.fun _let_4 _let_4))) (= (tptp.s Q18983 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i _let_12 (tptp.s _let_4 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun Q18985 _let_16) tptp.cons) _let_14)) _let_5)))) (tptp.s _let_2 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun Q18984 _let_15) tptp.cons) _let_13)) _let_3)))) _let_1)) (tptp.s Q18983 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_14)) _let_13)) (tptp.s Q18983 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i _let_12 _let_5)) _let_3)) _let_1)))))))))))))))))))))) (forall ((Q19015 $$unsorted) (Q19023 $$unsorted)) (let ((_let_1 (tptp.list (tptp.prod Q19015 Q19023)))) (let ((_let_2 (tptp.list Q19023))) (let ((_let_3 (tptp.list Q19015))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.zip0) (tptp.s _let_3 tptp.nil))) (tptp.s _let_2 tptp.l2))) (tptp.s _let_1 tptp.nil))))))) (forall ((Q19015 $$unsorted) (Q19023 $$unsorted)) (let ((_let_1 (tptp.list Q19023))) (let ((_let_2 (tptp.s _let_1 tptp.l2))) (let ((_let_3 (tptp.list Q19015))) (let ((_let_4 (tptp.s _let_3 tptp.t1))) (let ((_let_5 (tptp.prod Q19015 Q19023))) (let ((_let_6 (tptp.list _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s (tptp.fun _let_3 _let_7) tptp.zip0))) (let ((_let_9 (tptp.s Q19015 tptp.h1))) (let ((_let_10 (tptp.fun Q19023 _let_5))) (let ((_let_11 (tptp.fun _let_6 _let_6))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun Q19015 _let_12) tptp.cons) _let_9)) _let_4)))) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_5 _let_11) tptp.cons) (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q19015 _let_10) tptp.c_) _let_9)) (tptp.s Q19023 (tptp.i (tptp.s (tptp.fun _let_1 Q19023) tptp.hd) _let_2)))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.tl) _let_2)))))))))))))))))))) (forall ((Q19034 $$unsorted) (Q19035 $$unsorted)) (let ((_let_1 (tptp.list (tptp.prod Q19034 Q19035)))) (let ((_let_2 (tptp.list Q19035))) (let ((_let_3 (tptp.list Q19034))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.zip0) (tptp.s _let_3 tptp.nil))) (tptp.s _let_2 tptp.nil))) (tptp.s _let_1 tptp.nil))))))) (forall ((Q19059 $$unsorted) (Q19060 $$unsorted)) (let ((_let_1 (tptp.list Q19060))) (let ((_let_2 (tptp.s _let_1 tptp.t2))) (let ((_let_3 (tptp.list Q19059))) (let ((_let_4 (tptp.s _let_3 tptp.t1))) (let ((_let_5 (tptp.prod Q19059 Q19060))) (let ((_let_6 (tptp.list _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s (tptp.fun _let_3 _let_7) tptp.zip0))) (let ((_let_9 (tptp.s Q19060 tptp.h2))) (let ((_let_10 (tptp.s Q19059 tptp.h1))) (let ((_let_11 (tptp.fun Q19060 _let_5))) (let ((_let_12 (tptp.fun _let_6 _let_6))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (let ((_let_14 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun Q19059 _let_14) tptp.cons) _let_10)) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun Q19060 _let_13) tptp.cons) _let_9)) _let_2)))) (tptp.s _let_6 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) tptp.cons) (tptp.s _let_5 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q19059 _let_11) tptp.c_) _let_10)) _let_9)))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_2)))))))))))))))))))) (forall ((A $$unsorted) (H0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (not (= (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.cons) (tptp.s A H0))) (tptp.s _let_1 T0))) (tptp.s _let_1 tptp.nil)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.h0))) (let ((_let_2 (tptp.list A))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) tptp.last0) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.cons) _let_1)) (tptp.s _let_2 tptp.nil))))) _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s (tptp.fun A _let_2) tptp.cons))) (let ((_let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A tptp.k))) (tptp.s _let_1 tptp.t0))))) (let ((_let_5 (tptp.s (tptp.fun _let_1 A) tptp.last0))) (= (tptp.s A (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A tptp.h0))) _let_4)))) (tptp.s A (tptp.i _let_5 _let_4))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.append) _let_2)) (tptp.s _let_1 tptp.nil))) _let_2))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 N0))) (let ((_let_3 (tptp.s _let_1 M0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.append))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 L))))) (= (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 tptp.reverse))) (let ((_let_5 (tptp.s _let_1 M0))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_3) tptp.append))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_2)) _let_5)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.reverse))) (= (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 (tptp.i _let_3 _let_2)))) _let_2))))) (forall ((A $$unsorted) (H1 $$unsorted) (H2 $$unsorted) (T1 $$unsorted) (T2 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 T2))) (let ((_let_3 (tptp.s _let_1 T1))) (let ((_let_4 (tptp.s A H2))) (let ((_let_5 (tptp.s A H1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.cons))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2))) (and (= _let_5 _let_4) (= _let_3 _let_2))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (or (= (tptp.s _let_1 L) (tptp.s _let_1 tptp.nil)) (exists ((H0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 L) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.cons) (tptp.s A H0))) (tptp.s _let_1 T0)))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.length))) (let ((_let_4 (tptp.s _let_1 L))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.append) _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L2))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.list B))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.map0) (tptp.s _let_3 F0))))) (let ((_let_7 (tptp.s _let_1 L1))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.append) _let_7)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.append) (tptp.s _let_4 (tptp.i _let_6 _let_7)))) (tptp.s _let_4 (tptp.i _let_6 _let_2))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (L $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.list B))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.length) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.map0) (tptp.s _let_3 F0))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (= _let_2 (tptp.s _let_1 tptp.nil)))))) (forall ((Q19367 $$unsorted) (L $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.list Q19367))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) (tptp.s _let_1 L))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) (tptp.s tptp.num N0)))) (exists ((H0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.list Q19367))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (and (= (tptp.s _let_1 L) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q19367 _let_3) tptp.cons) (tptp.s Q19367 H0))) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2)) (tptp.s tptp.num N0)))))))))) (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.list B))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun B C))) (let ((_let_8 (tptp.s _let_7 G0))) (let ((_let_9 (tptp.list C))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.fun A C))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun _let_1 _let_9))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.map0) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_7 _let_12) tptp.o) _let_8)) _let_4)))) _let_2)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.map0) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.map0) _let_4)) _let_2))))))))))))))))))) (forall ((Q19442 $$unsorted) (Q19431 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q19431 X))) (let ((_let_2 (tptp.fun Q19431 Q19442))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun Q19431 tptp.bool))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_4)) _let_3)) _let_1))) (= (tptp.s Q19442 (tptp.i _let_4 _let_1)) (tptp.s Q19442 (tptp.i _let_3 _let_1))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19431))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19431 Q19442))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.list Q19442))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_3 _let_6) tptp.map0))) (let ((_let_8 (tptp.s _let_3 F0))) (let ((_let_9 (tptp.fun Q19431 tptp.bool))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.all0) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_8)) _let_4)))) _let_2))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2)))))))))))))))))) (forall ((Q19472 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19472))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19472 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_3 _let_4) tptp.all0))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q19472 X))) (let ((_let_2 (tptp.fun Q19472 tptp.bool))) (let ((_let_3 (tptp.list Q19472))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q19472 _let_4) tptp.mem) _let_1)) (tptp.s _let_3 L)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 P0))) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 Q0))) _let_2)))))))))) (forall ((Q19500 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q19500 X))) (let ((_let_2 (tptp.fun Q19500 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))) (forall ((P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19500))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19500 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.ex0) _let_4)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.all0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_0) _let_4)))) _let_2))))))))))))) (forall ((Q19522 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q19522 X))) (let ((_let_2 (tptp.fun Q19522 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))) (forall ((P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19522))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19522 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.all0) _let_4)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.ex0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_0) _let_4)))) _let_2))))))))))))) (forall ((Q19544 $$unsorted) (Q19543 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19543))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19543 Q19544))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q19544 tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun Q19543 tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.list Q19544))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun _let_10 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) tptp.all0) _let_6)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.map0) _let_4)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.all0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.o) _let_6)) _let_4)))) _let_2)))))))))))))))) (forall ((Q19562 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q19562 tptp.bool) U_0) (tptp.s Q19562 X))) (tptp.s tptp.bool tptp.t))) (forall ((L $$unsorted)) (let ((_let_1 (tptp.list Q19562))) (let ((_let_2 (tptp.fun Q19562 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.all0) (tptp.s _let_2 U_0))) (tptp.s _let_1 L)))))))))) (forall ((Q19598 $$unsorted) (Q19587 $$unsorted) (U_1 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q19587 Y))) (let ((_let_2 (tptp.s (tptp.fun Q19587 Q19598) tptp.f))) (let ((_let_3 (tptp.s Q19587 X))) (let ((_let_4 (tptp.fun Q19587 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q19587 _let_4) U_1) _let_3)) _let_1))) (= (tptp.s Q19598 (tptp.i _let_2 _let_3)) (tptp.s Q19598 (tptp.i _let_2 _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q19587 X))) (let ((_let_2 (tptp.fun Q19587 tptp.bool))) (let ((_let_3 (tptp.fun Q19587 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_0) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_1) _let_1))))))) (forall ((L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list Q19587))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.fun Q19587 Q19598))) (let ((_let_4 (tptp.list Q19598))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.map0) (tptp.s _let_3 tptp.f))))) (let ((_let_7 (tptp.s _let_1 L))) (let ((_let_8 (tptp.fun Q19587 (tptp.fun Q19587 tptp.bool)))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.all2) (tptp.s _let_8 U_0))) _let_7)) _let_2))) (= (tptp.s _let_4 (tptp.i _let_6 _let_7)) (tptp.s _let_4 (tptp.i _let_6 _let_2))))))))))))))))))) (forall ((Q19629 $$unsorted) (Q19630 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q19630 A5))) (let ((_let_2 (tptp.fun Q19630 Q19629))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q19630 tptp.bool))) (let ((_let_5 (tptp.fun Q19629 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_2 _let_4))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) U_0) _let_6)) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s Q19629 (tptp.i _let_3 _let_1)))) _let_1))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19630))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19630 Q19629))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q19630 tptp.bool))) (let ((_let_6 (tptp.fun Q19629 _let_5))) (let ((_let_7 (tptp.s _let_6 P0))) (let ((_let_8 (tptp.fun _let_3 _let_5))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.list Q19629))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun _let_10 _let_9))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_6 _let_12) tptp.all2) _let_7)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.map0) _let_4)) _let_2)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.all0) (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) U_0) _let_7)) _let_4)))) _let_2)))))))))))))))))) (forall ((Q19647 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q19647 X))) (let ((_let_2 (tptp.fun Q19647 Q19647))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q19647 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1))) (= (tptp.s Q19647 (tptp.i _let_3 _let_1)) _let_1))))))) (forall ((L $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.list Q19647))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19647 Q19647))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun Q19647 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.all0) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.map0) _let_4)) _let_2)) _let_2)))))))))))) (forall ((Q19690 $$unsorted) (Q19689 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (Q0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q19689 Y))) (let ((_let_2 (tptp.s Q19690 X))) (let ((_let_3 (tptp.fun Q19689 tptp.bool))) (let ((_let_4 (tptp.fun Q19690 _let_3))) (let ((_let_5 (tptp.s _let_4 Q0))) (let ((_let_6 (tptp.fun Q19690 tptp.bool))) (let ((_let_7 (tptp.s _let_6 P0))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) U_1) _let_7)) _let_5)) _let_2)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (Q0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q19690 X))) (let ((_let_2 (tptp.fun Q19689 tptp.bool))) (let ((_let_3 (tptp.fun Q19690 _let_2))) (let ((_let_4 (tptp.s _let_3 Q0))) (let ((_let_5 (tptp.fun Q19690 tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_5 _let_7))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_0) _let_6)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_1) _let_6)) _let_4)) _let_1)))))))))))) (forall ((L $$unsorted) (M0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.list Q19689))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.list Q19690))) (let ((_let_4 (tptp.s _let_3 L))) (let ((_let_5 (tptp.fun Q19690 (tptp.fun Q19689 tptp.bool)))) (let ((_let_6 (tptp.s _let_5 Q0))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.s (tptp.fun _let_5 _let_8) tptp.all2))) (let ((_let_10 (tptp.fun Q19690 tptp.bool))) (let ((_let_11 (tptp.s _let_10 P0))) (let ((_let_12 (tptp.fun _let_3 tptp.bool))) (let ((_let_13 (tptp.fun _let_5 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_10 _let_13) U_0) _let_11)) _let_6)))) _let_4)) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.all0) _let_11)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_4)) _let_2))))))))))))))))))))))) (forall ((Q19728 $$unsorted) (Q19718 $$unsorted) (F0 $$unsorted) (A5 $$unsorted) (L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.s Q19718 A5))) (let ((_let_2 (tptp.list Q19728))) (let ((_let_3 (tptp.s _let_2 L2))) (let ((_let_4 (tptp.fun Q19718 Q19718))) (let ((_let_5 (tptp.fun Q19728 _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_4))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.itlist) (tptp.s _let_5 F0))))) (let ((_let_8 (tptp.s _let_2 L1))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (= (tptp.s Q19718 (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_2 _let_9) tptp.append) _let_8)) _let_3)))) _let_1)) (tptp.s Q19718 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_8)) (tptp.s Q19718 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1))))))))))))))) (forall ((Q19765 $$unsorted) (Q19764 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.s Q19764 tptp.b0))) (let ((_let_2 (tptp.s Q19765 tptp.a0))) (let ((_let_3 (tptp.fun Q19764 Q19764))) (let ((_let_4 (tptp.fun Q19765 _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.f))) (let ((_let_6 (tptp.list Q19765))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.fun _let_6 _let_3))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.itlist) _let_5)))) (let ((_let_10 (tptp.fun _let_6 _let_6))) (= (tptp.s Q19764 (tptp.i (tptp.s _let_3 (tptp.i _let_9 (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.append) _let_7)) (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q19765 _let_10) tptp.cons) _let_2)) (tptp.s _let_6 tptp.nil))))))) _let_1)) (tptp.s Q19764 (tptp.i (tptp.s _let_3 (tptp.i _let_9 _let_7)) (tptp.s Q19764 (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))) (forall ((Q19791 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (Q0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q19791 X))) (let ((_let_2 (tptp.fun Q19791 tptp.bool))) (let ((_let_3 (tptp.s _let_2 Q0))) (let ((_let_4 (tptp.s _let_2 P0))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_4)) _let_3)) _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((P0 $$unsorted) (Q0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19791))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19791 tptp.bool))) (let ((_let_4 (tptp.s _let_3 Q0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.all0))) (let ((_let_7 (tptp.s _let_3 P0))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_0) _let_7)) _let_4)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))))) (forall ((Q19821 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q19821 X))) (let ((_let_2 (tptp.fun Q19821 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 U_0) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1)))))))) (forall ((L $$unsorted)) (let ((_let_1 (tptp.list Q19821))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19821 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_3 _let_4) tptp.all0))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 tptp.p0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 tptp.q0))) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 U_0))) _let_2)))))))))))) (forall ((Q19851 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19851))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19851 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_3 _let_4) tptp.ex0))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q19851 X))) (let ((_let_2 (tptp.fun Q19851 tptp.bool))) (let ((_let_3 (tptp.list Q19851))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q19851 _let_4) tptp.mem) _let_1)) (tptp.s _let_3 L)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 P0))) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 Q0))) _let_2)))))))))) (forall ((Q19878 $$unsorted) (P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19878))) (let ((_let_2 (tptp.fun Q19878 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q19878 X))) (let ((_let_2 (tptp.list Q19878))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q19878 _let_3) tptp.mem) _let_1)) (tptp.s _let_2 L)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q19878 tptp.bool) P0) _let_1)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.all0) (tptp.s _let_2 P0))) (tptp.s _let_1 L))))))))) (forall ((Q19896 $$unsorted) (N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.list Q19896))) (let ((_let_3 (tptp.fun Q19896 _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.length) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.replicate) _let_1)) (tptp.s Q19896 X))))) _let_1))))) (forall ((Q19920 $$unsorted) (Q19919 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19919))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q19919 Q19920))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q19920 tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun Q19919 tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.list Q19920))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun _let_10 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) tptp.ex0) _let_6)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.map0) _let_4)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.ex0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.o) _let_6)) _let_4)))) _let_2)))))))))))))))) (forall ((Q19958 $$unsorted) (Q19957 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q19957 tptp.bool))) (let ((_let_2 (tptp.fun Q19958 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_0) (tptp.s _let_2 P0))) (tptp.s Q19957 S0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun Q19957 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q19958 _let_1) P0) (tptp.s Q19958 X))) (tptp.s Q19957 S0)))))))))) (forall ((P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19957))) (let ((_let_2 (tptp.fun Q19957 tptp.bool))) (let ((_let_3 (tptp.fun Q19958 _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.list Q19957))) (let ((_let_2 (tptp.fun Q19957 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.ex0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q19958 _let_2) P0) (tptp.s Q19958 X))))) (tptp.s _let_1 L)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.ex0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) U_0) (tptp.s _let_3 P0))))) (tptp.s _let_1 L)))))))))))) (forall ((Q19988 $$unsorted) (Q19987 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q19987 tptp.bool))) (let ((_let_2 (tptp.fun Q19988 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_0) (tptp.s _let_2 P0))) (tptp.s Q19987 S0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q19987 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q19988 _let_1) P0) (tptp.s Q19988 X))) (tptp.s Q19987 S0)))))))))) (forall ((P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q19987))) (let ((_let_2 (tptp.fun Q19987 tptp.bool))) (let ((_let_3 (tptp.fun Q19988 _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.list Q19987))) (let ((_let_2 (tptp.fun Q19987 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.all0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q19988 _let_2) P0) (tptp.s Q19988 X))))) (tptp.s _let_1 L)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.all0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) U_0) (tptp.s _let_3 P0))))) (tptp.s _let_1 L)))))))))))) (forall ((Q20016 $$unsorted) (X $$unsorted) (L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list Q20016))) (let ((_let_2 (tptp.s _let_1 L2))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q20016 _let_3) tptp.mem) (tptp.s Q20016 X))))) (let ((_let_5 (tptp.s _let_1 L1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.append) _let_5)) _let_2))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))))) (forall ((Q20049 $$unsorted) (Q20052 $$unsorted) (F0 $$unsorted) (Y $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20052))) (let ((_let_2 (tptp.fun Q20052 Q20049))) (let ((_let_3 (tptp.list Q20049))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q20049 _let_5) tptp.mem) (tptp.s Q20049 Y))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.map0) (tptp.s _let_2 F0))) (tptp.s _let_1 L)))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q20052 X))) (let ((_let_2 (tptp.list Q20052))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q20052 _let_3) tptp.mem) _let_1)) (tptp.s _let_2 L)))) (= (tptp.s Q20049 Y) (tptp.s Q20049 (tptp.i (tptp.s (tptp.fun Q20052 Q20049) F0) _let_1))))))))))))))) (forall ((Q20083 $$unsorted) (P0 $$unsorted) (L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list Q20083))) (let ((_let_2 (tptp.s _let_1 L2))) (let ((_let_3 (tptp.fun Q20083 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.filter0) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.s _let_1 L1))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_4) tptp.append))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_5 _let_6)))) (tptp.s _let_1 (tptp.i _let_5 _let_2))))))))))))) (forall ((Q20110 $$unsorted) (Q20117 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20117))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q20117 Q20110))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q20110 tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun Q20117 tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.list Q20110))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.map0) _let_4)))) (let ((_let_13 (tptp.fun _let_10 _let_10))) (= (tptp.s _let_10 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_5 _let_13) tptp.filter0) _let_6)) (tptp.s _let_10 (tptp.i _let_12 _let_2)))) (tptp.s _let_10 (tptp.i _let_12 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.filter0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.o) _let_6)) _let_4)))) _let_2))))))))))))))))))) (forall ((Q20144 $$unsorted) (P0 $$unsorted) (L $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list Q20144))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s Q20144 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q20144 _let_4) tptp.mem) _let_3)))) (let ((_let_6 (tptp.fun Q20144 tptp.bool))) (let ((_let_7 (tptp.s _let_6 P0))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.filter0) _let_7)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))))))))))))) (forall ((Q20165 $$unsorted) (P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20165))) (let ((_let_2 (tptp.fun Q20165 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.list Q20165))) (let ((_let_2 (tptp.s Q20165 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q20165 tptp.bool) P0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q20165 _let_3) tptp.mem) _let_2)) (tptp.s _let_1 L))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.ex0) (tptp.s _let_2 P0))) (tptp.s _let_1 L))))))))) (forall ((Q20187 $$unsorted) (Q20185 $$unsorted) (L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list Q20185))) (let ((_let_2 (tptp.s _let_1 L1))) (let ((_let_3 (tptp.list Q20187))) (let ((_let_4 (tptp.s _let_3 L2))) (let ((_let_5 (tptp.prod Q20185 Q20187))) (let ((_let_6 (tptp.list _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_5 Q20185))) (let ((_let_9 (tptp.fun _let_6 _let_1))) (=> (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.length) _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_8 _let_9) tptp.map0) (tptp.s _let_8 tptp.fst))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.zip0) _let_2)) _let_4)))) _let_2)))))))))))) (forall ((Q20216 $$unsorted) (Q20218 $$unsorted) (L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list Q20218))) (let ((_let_2 (tptp.s _let_1 L2))) (let ((_let_3 (tptp.list Q20216))) (let ((_let_4 (tptp.s _let_3 L1))) (let ((_let_5 (tptp.prod Q20216 Q20218))) (let ((_let_6 (tptp.list _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_5 Q20218))) (let ((_let_9 (tptp.fun _let_6 _let_1))) (=> (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.length) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_8 _let_9) tptp.map0) (tptp.s _let_8 tptp.snd))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.zip0) _let_4)) _let_2)))) _let_2)))))))))))) (forall ((Q20262 $$unsorted) (Q20246 $$unsorted) (L $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.prod Q20262 Q20246))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.s _let_2 L))) (let ((_let_4 (tptp.fun _let_1 Q20262))) (let ((_let_5 (tptp.list Q20262))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s Q20262 X))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.fun _let_2 Q20246))) (let ((_let_10 (tptp.fun Q20246 _let_1))) (let ((_let_11 (tptp.fun _let_2 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.mem) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q20262 _let_10) tptp.c_) _let_7)) (tptp.s Q20246 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q20262 _let_9) tptp.assoc) _let_7)) _let_3)))))) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q20262 _let_8) tptp.mem) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.map0) (tptp.s _let_4 tptp.fst))) _let_3))))))))))))))))) (forall ((Q20283 $$unsorted) (P0 $$unsorted) (L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list Q20283))) (let ((_let_2 (tptp.s _let_1 L2))) (let ((_let_3 (tptp.fun Q20283 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.all0) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.s _let_1 L1))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.append) _let_6)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))))) (forall ((Q20306 $$unsorted) (L $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.list Q20306))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun _let_1 Q20306))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q20306 _let_5) tptp.mem) (tptp.s Q20306 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.el) _let_3)) _let_2)))) _let_2))))))))))) (forall ((Q20354 $$unsorted) (L $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.list Q20354))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q20354 _let_2) tptp.mem) (tptp.s Q20354 X))) (tptp.s _let_1 L)))) (exists ((I0 $$unsorted)) (let ((_let_1 (tptp.list Q20354))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun _let_1 Q20354))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2))))) (= (tptp.s Q20354 X) (tptp.s Q20354 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.el) _let_3)) _let_2)))))))))))))) (forall ((Q20380 $$unsorted) (P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20380))) (let ((_let_2 (tptp.fun Q20380 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.list Q20380))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun _let_1 Q20380))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q20380 tptp.bool) P0) (tptp.s Q20380 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.el) _let_3)) _let_2)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.all0) (tptp.s _let_2 P0))) (tptp.s _let_1 L))))))))) (forall ((Q20423 $$unsorted) (Q20422 $$unsorted) (Q20424 $$unsorted) (Q20425 $$unsorted) (U_1 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q20425 Y))) (let ((_let_2 (tptp.s Q20424 X))) (let ((_let_3 (tptp.fun Q20422 tptp.bool))) (let ((_let_4 (tptp.fun Q20425 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q20424 _let_4) U_1) _let_2)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q20423 _let_3) tptp.p0) (tptp.s Q20423 (tptp.i (tptp.s (tptp.fun Q20424 Q20423) tptp.f) _let_2)))) (tptp.s Q20422 (tptp.i (tptp.s (tptp.fun Q20425 Q20422) tptp.g) _let_1)))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q20424 X))) (let ((_let_2 (tptp.fun Q20425 tptp.bool))) (let ((_let_3 (tptp.fun Q20424 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_0) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_1) _let_1))))))) (forall ((L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list Q20425))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.list Q20424))) (let ((_let_4 (tptp.s _let_3 L))) (let ((_let_5 (tptp.fun Q20424 (tptp.fun Q20425 tptp.bool)))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun Q20425 Q20422))) (let ((_let_9 (tptp.list Q20422))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun Q20424 Q20423))) (let ((_let_12 (tptp.list Q20423))) (let ((_let_13 (tptp.fun _let_3 _let_12))) (let ((_let_14 (tptp.fun Q20423 (tptp.fun Q20422 tptp.bool)))) (let ((_let_15 (tptp.fun _let_9 tptp.bool))) (let ((_let_16 (tptp.fun _let_12 _let_15))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_14 _let_16) tptp.all2) (tptp.s _let_14 tptp.p0))) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.map0) (tptp.s _let_11 tptp.f))) _let_4)))) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.map0) (tptp.s _let_8 tptp.g))) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.all2) (tptp.s _let_5 U_0))) _let_4)) _let_2)))))))))))))))))))))))) (forall ((Q20471 $$unsorted) (Q20470 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (Q0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q20470 Y))) (let ((_let_2 (tptp.s Q20471 X))) (let ((_let_3 (tptp.fun Q20470 tptp.bool))) (let ((_let_4 (tptp.fun Q20471 _let_3))) (let ((_let_5 (tptp.s _let_4 Q0))) (let ((_let_6 (tptp.s _let_4 P0))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_1) _let_6)) _let_5)) _let_2)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (Q0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q20471 X))) (let ((_let_2 (tptp.fun Q20470 tptp.bool))) (let ((_let_3 (tptp.fun Q20471 _let_2))) (let ((_let_4 (tptp.s _let_3 Q0))) (let ((_let_5 (tptp.s _let_3 P0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_1) _let_5)) _let_4)) _let_1))))))))))) (forall ((P0 $$unsorted) (Q0 $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list Q20470))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.list Q20471))) (let ((_let_4 (tptp.s _let_3 L))) (let ((_let_5 (tptp.fun Q20471 (tptp.fun Q20470 tptp.bool)))) (let ((_let_6 (tptp.s _let_5 Q0))) (let ((_let_7 (tptp.s _let_5 P0))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.s (tptp.fun _let_5 _let_10) tptp.all2))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_7)) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_6)) _let_4)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) _let_7)) _let_6)))) _let_4)) _let_2)))))))))))))))))))) (forall ((Q20493 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q20493 X))) (let ((_let_2 (tptp.fun Q20493 tptp.bool))) (let ((_let_3 (tptp.fun Q20493 _let_2))) (let ((_let_4 (tptp.s _let_3 P0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) U_0) _let_4)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) _let_1)))))))) (forall ((P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20493))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q20493 tptp.bool))) (let ((_let_4 (tptp.fun Q20493 _let_3))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.all2) _let_5)) _let_2)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.all0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) U_0) _let_5)))) _let_2))))))))))))) (forall ((Q20522 $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list Q20522))) (let ((_let_2 (tptp.s _let_1 tptp.nil))) (let ((_let_3 (tptp.s _let_1 M0))) (let ((_let_4 (tptp.s _let_1 L))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.append) _let_4)) _let_3)) _let_2) (and (= _let_4 _let_2) (= _let_3 _let_2))))))))) (forall ((Q20555 $$unsorted) (Q20542 $$unsorted) (Q20544 $$unsorted) (F0 $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list Q20544))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2)))) (let ((_let_4 (tptp.list Q20542))) (let ((_let_5 (tptp.s _let_4 L))) (let ((_let_6 (tptp.fun Q20542 (tptp.fun Q20544 Q20555)))) (let ((_let_7 (tptp.list Q20555))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (=> (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.length) _let_5)) _let_3) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.length) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.map2) (tptp.s _let_6 F0))) _let_5)) _let_2)))) _let_3)))))))))))) (forall ((Q20576 $$unsorted) (Q20580 $$unsorted) (F0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20580))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.list Q20576))) (let ((_let_4 (tptp.fun Q20580 Q20576))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (= (= (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.map0) (tptp.s _let_4 F0))) _let_2)) (tptp.s _let_3 tptp.nil)) (= _let_2 (tptp.s _let_1 tptp.nil))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted)) (= (forall ((L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s _let_1 L))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.list B))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.map0) (tptp.s _let_4 F0))))) (=> (= (tptp.s _let_5 (tptp.i _let_7 _let_3)) (tptp.s _let_5 (tptp.i _let_7 _let_2))) (= _let_3 _let_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (=> (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted)) (= (forall ((M0 $$unsorted)) (exists ((L $$unsorted)) (let ((_let_1 (tptp.list B))) (let ((_let_2 (tptp.list A))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.map0) (tptp.s _let_3 F0))) (tptp.s _let_2 L))) (tptp.s _let_1 M0)))))))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))) (tptp.s B Y)))))) (forall ((Q20694 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q20694 X))) (= (tptp.s Q20694 (tptp.i (tptp.s (tptp.fun Q20694 Q20694) U_0) _let_1)) _let_1))) (forall ((L $$unsorted)) (let ((_let_1 (tptp.list Q20694))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q20694 Q20694))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.map0) (tptp.s _let_3 U_0))) _let_2)) _let_2)))))))) (forall ((Q20703 $$unsorted)) (let ((_let_1 (tptp.list Q20703))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun Q20703 Q20703))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.map0) (tptp.s _let_3 tptp.i1))) (tptp.s _let_2 tptp.i1)))))) (forall ((Q20730 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20730))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s _let_1 tptp.nil))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (not (= _let_2 _let_3)) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.append) (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.butlast) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q20730 _let_4) tptp.cons) (tptp.s Q20730 (tptp.i (tptp.s (tptp.fun _let_1 Q20730) tptp.last0) _let_2)))) _let_3)))) _let_2))))))) (forall ((Q20755 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.list Q20755))) (let ((_let_2 (tptp.s _let_1 Q0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 Q20755) tptp.last0))) (let ((_let_4 (tptp.s _let_1 P0))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun Q20755 Q20755))) (let ((_let_7 (tptp.fun Q20755 _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (and (= (tptp.p _let_5) (= _let_2 (tptp.s _let_1 tptp.nil))) (= (tptp.s Q20755 (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.append) _let_4)) _let_2)))) (tptp.s Q20755 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_5)) (tptp.s Q20755 (tptp.i _let_3 _let_4)))) (tptp.s Q20755 (tptp.i _let_3 _let_2)))))))))))))))) (forall ((Q20771 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.list Q20771))) (let ((_let_3 (tptp.s _let_2 L))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.num) tptp.length))) (=> (not (= _let_3 (tptp.s _let_2 tptp.nil))) (= (tptp.s tptp.num (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.tl) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) (tptp.s tptp.num (tptp.i _let_4 _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((Q20804 $$unsorted) (K0 $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.list Q20804))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s _let_1 L))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_3)))) (let ((_let_5 (tptp.s tptp.num K0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun _let_1 Q20804))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.el))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 _let_5)))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.fun Q20804 Q20804))) (let ((_let_12 (tptp.fun Q20804 _let_11))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (= (tptp.s Q20804 (tptp.i _let_9 (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_1 _let_13) tptp.append) _let_3)) _let_2)))) (tptp.s Q20804 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.bool _let_12) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.l_) _let_5)) _let_4)))) (tptp.s Q20804 (tptp.i _let_9 _let_3)))) (tptp.s Q20804 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.m_) _let_5)) _let_4)))) _let_2))))))))))))))))))) (forall ((Q20835 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.list Q20835))) (let ((_let_2 (tptp.s _let_1 tptp.l0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun _let_1 Q20835))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.el))) (= (tptp.s Q20835 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.tl) _let_2)))) (tptp.s Q20835 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)))))))))) (forall ((Q20861 $$unsorted) (N0 $$unsorted) (H0 $$unsorted) (T0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.list Q20861))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s tptp.num tptp.u_0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s _let_4 tptp.numeral))) (let ((_let_6 (tptp.s tptp.num N0))) (let ((_let_7 (tptp.fun _let_1 Q20861))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.el))) (let ((_let_9 (tptp.s Q20861 H0))) (let ((_let_10 (tptp.s tptp.bool V))) (let ((_let_11 (tptp.fun Q20861 Q20861))) (let ((_let_12 (tptp.fun Q20861 _let_11))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (and (= (tptp.p _let_10) (= _let_6 (tptp.s tptp.num (tptp.i _let_5 _let_3)))) (= (tptp.s Q20861 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun Q20861 _let_13) tptp.cons) _let_9)) _let_2)))) (tptp.s Q20861 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.bool _let_12) tptp.cond) _let_10)) _let_9)) (tptp.s Q20861 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.m_) _let_6)) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) _let_3)))))))) _let_2))))))))))))))))))))) (forall ((Q20886 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20886))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun _let_1 Q20886))) (=> (not (= _let_2 (tptp.s _let_1 tptp.nil))) (= (tptp.s Q20886 (tptp.i (tptp.s _let_4 tptp.last0) _let_2)) (tptp.s Q20886 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.el) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s (tptp.fun _let_1 A) tptp.hd))) (let ((_let_4 (tptp.s _let_1 M0))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun A A))) (let ((_let_7 (tptp.fun A _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (and (= (tptp.p _let_5) (= _let_2 (tptp.s _let_1 tptp.nil))) (= (tptp.s A (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.append) _let_2)) _let_4)))) (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_5)) (tptp.s A (tptp.i _let_3 _let_4)))) (tptp.s A (tptp.i _let_3 _let_2)))))))))))))))) (forall ((Q20949 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20949))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (not (= _let_2 (tptp.s _let_1 tptp.nil))) (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q20949 _let_3) tptp.cons) (tptp.s Q20949 (tptp.i (tptp.s (tptp.fun _let_1 Q20949) tptp.hd) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.tl) _let_2)))))))))) (forall ((Q20978 $$unsorted) (Q20979 $$unsorted) (F0 $$unsorted) (N0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q20979))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun _let_1 Q20979))) (let ((_let_5 (tptp.fun Q20979 Q20978))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.list Q20978))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_7 Q20978))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.l_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2))))) (= (tptp.s Q20978 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.el) _let_3)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.map0) _let_6)) _let_2)))) (tptp.s Q20978 (tptp.i _let_6 (tptp.s Q20979 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.el) _let_3)) _let_2))))))))))))))))) (forall ((Q21004 $$unsorted) (Q21006 $$unsorted) (F0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q21006))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q21006 Q21004))) (let ((_let_4 (tptp.list Q21004))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.map0) (tptp.s _let_3 F0))))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.reverse) (tptp.s _let_4 (tptp.i _let_6 _let_2)))) (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.reverse) _let_2)))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((Q0 $$unsorted) (P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.s _let_2 Q0))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_4)) _let_3)) _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((P0 $$unsorted) (Q0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.s _let_3 Q0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_3 _let_7) tptp.all0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.filter0) _let_5)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_5)) _let_4)))) _let_2))))))))))))))) (forall ((Q21057 $$unsorted) (H0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.list Q21057))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q21057 _let_3) tptp.cons) (tptp.s Q21057 H0))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.append) (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 tptp.nil))))) _let_2)) (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))) (forall ((Q18672 $$unsorted) (H0 $$unsorted) (X $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.list Q18672))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s Q18672 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q18672 _let_4) tptp.mem) _let_3)))) (let ((_let_6 (tptp.s Q18672 H0))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (and (= (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 tptp.nil))) (tptp.s tptp.bool tptp.f0)) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q18672 _let_7) tptp.cons) _let_6)) _let_2))))) (or (= _let_3 _let_6) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.mem) (tptp.s A X))) (tptp.s _let_1 L)))) (exists ((L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_1 L1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (and (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.mem) _let_2)) _let_4)))) (= (tptp.s _let_1 L) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.append) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.cons) _let_2)) (tptp.s _let_1 L2))))))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.mem) (tptp.s A X))) (tptp.s _let_1 L)))) (exists ((L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 L) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.append) (tptp.s _let_1 L1))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.cons) (tptp.s A X))) (tptp.s _let_1 L2))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 tptp.l0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_3 _let_4) tptp.all0))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 tptp.p0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 tptp.q0))) _let_2))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.list B))) (let ((_let_2 (tptp.s _let_1 tptp.li_0))) (let ((_let_3 (tptp.list A))) (let ((_let_4 (tptp.s _let_3 tptp.l0))) (let ((_let_5 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s (tptp.fun _let_5 _let_7) tptp.all2))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun A _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p0) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.q0) _let_2)) _let_1))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_5 tptp.p0))) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_5 tptp.q0))) _let_4)) _let_2)))))))))))))) (forall ((P0 $$unsorted)) (=> (forall ((A01 $$unsorted) (A10 $$unsorted) (A20 $$unsorted) (A30 $$unsorted) (A40 $$unsorted) (A5 $$unsorted) (A6 $$unsorted) (A7 $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.char))) (let ((_let_2 (tptp.fun tptp.bool _let_1))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.char tptp.bool) P0) (tptp.s tptp.char (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.ascii) (tptp.s tptp.bool A01))) (tptp.s tptp.bool A10))) (tptp.s tptp.bool A20))) (tptp.s tptp.bool A30))) (tptp.s tptp.bool A40))) (tptp.s tptp.bool A5))) (tptp.s tptp.bool A6))) (tptp.s tptp.bool A7)))))))))))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.char tptp.bool) P0) (tptp.s tptp.char X))))))) (forall ((Z $$unsorted) (F0 $$unsorted)) (exists ((FN $$unsorted)) (forall ((A01 $$unsorted) (A10 $$unsorted) (A20 $$unsorted) (A30 $$unsorted) (A40 $$unsorted) (A5 $$unsorted) (A6 $$unsorted) (A7 $$unsorted)) (let ((_let_1 (tptp.s tptp.bool A7))) (let ((_let_2 (tptp.s tptp.bool A6))) (let ((_let_3 (tptp.s tptp.bool A5))) (let ((_let_4 (tptp.s tptp.bool A40))) (let ((_let_5 (tptp.s tptp.bool A30))) (let ((_let_6 (tptp.s tptp.bool A20))) (let ((_let_7 (tptp.s tptp.bool A10))) (let ((_let_8 (tptp.s tptp.bool A01))) (let ((_let_9 (tptp.fun tptp.bool Z))) (let ((_let_10 (tptp.fun tptp.bool _let_9))) (let ((_let_11 (tptp.fun tptp.bool _let_10))) (let ((_let_12 (tptp.fun tptp.bool _let_11))) (let ((_let_13 (tptp.fun tptp.bool _let_12))) (let ((_let_14 (tptp.fun tptp.bool _let_13))) (let ((_let_15 (tptp.fun tptp.bool _let_14))) (let ((_let_16 (tptp.fun tptp.bool tptp.char))) (let ((_let_17 (tptp.fun tptp.bool _let_16))) (let ((_let_18 (tptp.fun tptp.bool _let_17))) (let ((_let_19 (tptp.fun tptp.bool _let_18))) (let ((_let_20 (tptp.fun tptp.bool _let_19))) (let ((_let_21 (tptp.fun tptp.bool _let_20))) (let ((_let_22 (tptp.fun tptp.bool _let_21))) (= (tptp.s Z (tptp.i (tptp.s (tptp.fun tptp.char Z) FN) (tptp.s tptp.char (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun tptp.bool _let_22) tptp.ascii) _let_8)) _let_7)) _let_6)) _let_5)) _let_4)) _let_3)) _let_2)) _let_1)))) (tptp.s Z (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun tptp.bool _let_15) F0) _let_8)) _let_7)) _let_6)) _let_5)) _let_4)) _let_3)) _let_2)) _let_1)))))))))))))))))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.prod tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dist) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1)))) _let_1))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.prod tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dist) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.c_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))) (forall ((M0 $$unsorted) (P0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.prod tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.num) tptp.dist))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.p_) (tptp.s tptp.num M0))))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_8 _let_2)))) (tptp.s tptp.num (tptp.i _let_8 _let_1)))))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))))))) (forall ((M0 $$unsorted) (P0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.prod tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.num) tptp.dist))) (let ((_let_7 (tptp.s tptp.num P0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.p_))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7)))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) _let_7)))))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.prod tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dist) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1)))) _let_2)))) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.prod tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dist) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.c_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1)))))) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) (tptp.s tptp.num M0))))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.prod tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.c_))) (let ((_let_8 (tptp.s (tptp.fun _let_5 tptp.num) tptp.dist))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i _let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_1)))))) (tptp.s tptp.num (tptp.i _let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.prod tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.c_))) (let ((_let_9 (tptp.s (tptp.fun _let_6 tptp.num) tptp.dist))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_9 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_2)))))) _let_1)) (tptp.s tptp.num (tptp.i _let_9 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_19 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_60 tptp.num) tptp.dist) (tptp.s _let_60 (tptp.i (tptp.s _let_213 (tptp.i (tptp.s (tptp.fun tptp.num _let_213) tptp.c_) (tptp.s tptp.num tptp.x))) (tptp.s tptp.num tptp.y)))))))) (forall ((D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num D0))) (let ((_let_2 (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.p0) _let_1))))) (let ((_let_3 (tptp.s tptp.num tptp.x))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.p_))) (let ((_let_6 (tptp.s tptp.num tptp.y))) (and (=> (= _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_1))) _let_2) (=> (= _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))) _let_2)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (let ((_let_8 (tptp.prod tptp.num tptp.num))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dist) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.c_) _let_2)) _let_5)))))) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.prod tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dist) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.prod tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.num) tptp.dist))) (let ((_let_7 (tptp.s tptp.num P0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.p_))) (let ((_let_10 (tptp.s tptp.num M0))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_10)) _let_7)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_10)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_7)) _let_1)))))))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.prod tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.num) tptp.dist))) (let ((_let_7 (tptp.s tptp.num P0))) (let ((_let_8 (tptp.s tptp.num M0))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.p_))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_8)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_7)) _let_1)))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_8)) _let_7)))))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted) (R0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num S0))) (let ((_let_2 (tptp.s tptp.num R0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.p_))) (let ((_let_5 (tptp.s tptp.num Q0))) (let ((_let_6 (tptp.s tptp.num N0))) (let ((_let_7 (tptp.prod tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.c_))) (let ((_let_10 (tptp.s (tptp.fun _let_7 tptp.num) tptp.dist))) (let ((_let_11 (tptp.s tptp.num P0))) (let ((_let_12 (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num M0))))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.s (tptp.fun tptp.num _let_13) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.num (tptp.i _let_10 (tptp.s _let_7 (tptp.i _let_12 _let_6)))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.num (tptp.i _let_10 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_11)) _let_5)))))) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.num (tptp.i _let_10 (tptp.s _let_7 (tptp.i _let_12 _let_11)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_10 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_5)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.t_))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num A5))) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num B0))) _let_1)))) (tptp.s tptp.num C0)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_a_) (tptp.s tptp.num A5))) (tptp.s tptp.num B0))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (= (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.t_) (tptp.s tptp.num A5))) (tptp.s tptp.num N0))))) (tptp.s tptp.num B0))))))) (= (tptp.s tptp.num A5) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((P0 $$unsorted)) (= (exists ((B0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) P0) (tptp.s tptp.num N0))))) (tptp.s tptp.num B0))))))) (exists ((A5 $$unsorted) (B0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.t_))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 P0) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num A5))) _let_1)))) (tptp.s tptp.num B0))))))))))))))) (forall ((P0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (=> (and (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) P0) _let_2)) _let_2)) _let_2) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.p_))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 P0) _let_2)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num A5))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))) (tptp.s tptp.num B0)))))))))))))) (exists ((B0 $$unsorted)) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 P0) _let_2)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1)))))))))))))))))) (forall ((P0 $$unsorted) (Q0 $$unsorted)) (= (exists ((B0 $$unsorted)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 P0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 Q0) _let_1)))) (tptp.s tptp.num B0))))))))))) (exists ((B0 $$unsorted) (N0 $$unsorted)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num N0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 P0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 Q0) _let_1)))) (tptp.s tptp.num B0))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.isu_nadd) (tptp.s _let_1 X)))) (exists ((B0 $$unsorted)) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 X))) (let ((_let_7 (tptp.prod tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dist) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) (tptp.s tptp.num (tptp.i _let_6 _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1))))))))))))))))))))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (=> (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.isu_nadd) (tptp.s _let_1 U_0))))))) (= (tptp.s tptp.nadd (tptp.i _let_210 (tptp.s _let_13 (tptp.i _let_211 _let_212)))) _let_212) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_13 tptp.bool) tptp.isu_nadd) _let_209))) (= (tptp.s _let_13 (tptp.i _let_211 (tptp.s tptp.nadd (tptp.i _let_210 _let_209)))) _let_209)) (forall ((X $$unsorted)) (exists ((B0 $$unsorted)) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.destu_nadd) (tptp.s tptp.nadd X))))) (let ((_let_7 (tptp.prod tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dist) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) (tptp.s tptp.num (tptp.i _let_6 _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1))))))))))))))))))) (forall ((X $$unsorted)) (exists ((A5 $$unsorted) (B0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd) (tptp.s tptp.nadd X))) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num A5))) _let_1)))) (tptp.s tptp.num B0))))))))))))) (forall ((X $$unsorted)) (exists ((B0 $$unsorted)) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num B0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s tptp.num N0))) (let ((_let_7 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.destu_nadd) (tptp.s tptp.nadd X))))) (let ((_let_8 (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (let ((_let_9 (tptp.prod tptp.num tptp.num))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dist) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.c_) (tptp.s tptp.num (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_8 _let_6)))))) (tptp.s tptp.num (tptp.i _let_8 (tptp.s tptp.num (tptp.i _let_7 _let_6)))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) _let_2)))) _let_1))))))))))))))))))) (forall ((X $$unsorted)) (exists ((B0 $$unsorted)) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd) (tptp.s tptp.nadd X))))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_2) tptp.p_))) (let ((_let_6 (tptp.prod tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dist) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.c_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (tptp.s tptp.num B0))))))))))))))) (forall ((X $$unsorted)) (exists ((B0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd) (tptp.s tptp.nadd X))))) (let ((_let_4 (tptp.prod tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dist) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.c_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))))) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))) (tptp.s tptp.num B0))))))))))))) (forall ((X $$unsorted)) (exists ((B0 $$unsorted)) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd) (tptp.s tptp.nadd X))))) (let ((_let_6 (tptp.prod tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dist) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.c_) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) _let_4)) _let_1)))))) (tptp.s tptp.num (tptp.i _let_5 _let_4)))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num B0))) _let_1)))))))))))))))) (forall ((X $$unsorted)) (exists ((B0 $$unsorted)) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.prod tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.num) tptp.dist))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_7) tptp.destu_nadd) (tptp.s tptp.nadd X))))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_8 _let_2)))) (tptp.s tptp.num (tptp.i _let_8 _let_1)))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.t_) (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((A5 $$unsorted) (B0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.t_))) (let ((_let_5 (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.nadd Y))) _let_1)))) (let ((_let_7 (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.nadd X))))) (let ((_let_8 (tptp.prod tptp.num tptp.num))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dist) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) (tptp.s tptp.num (tptp.i _let_7 _let_6)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_7 _let_1)))) _let_6)))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num A5))) _let_1)))) (tptp.s tptp.num B0))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd Y)))) (exists ((B0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd))) (let ((_let_4 (tptp.prod tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dist) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.nadd X))) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.nadd Y))) _let_1)))))))) (tptp.s tptp.num B0))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_eq) _let_1)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_eq))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_eq))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.nadd X))))) (let ((_let_5 (tptp.s tptp.nadd Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((K0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.t_) _let_2)) _let_1)))))))) (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) _let_1)) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun _let_2 tptp.nadd) tptp.mku_nadd) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) _let_1)))))))))) (forall ((K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.destu_nadd) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.nadd tptp.bool))) (=> (= _let_3 _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i _let_2 _let_3)))) (tptp.s tptp.nadd (tptp.i _let_2 _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num))) (let ((_let_4 (tptp.fun tptp.nadd tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i _let_3 _let_2)))) (tptp.s tptp.nadd (tptp.i _let_3 _let_1))))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_le) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd Y)))) (exists ((B0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.nadd X))) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.nadd Y))) _let_1)))) (tptp.s tptp.num B0))))))))))))))) (forall ((X $$unsorted) (XI_ $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd YI_))) (let ((_let_2 (tptp.s tptp.nadd XI_))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.naddu_le))) (let ((_let_6 (tptp.s tptp.nadd Y))) (let ((_let_7 (tptp.s tptp.nadd X))) (let ((_let_8 (tptp.s _let_4 tptp.naddu_eq))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_7)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_6)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_7)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (XI_ $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd YI_))) (let ((_let_2 (tptp.s tptp.nadd XI_))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.naddu_le))) (let ((_let_6 (tptp.s tptp.nadd Y))) (let ((_let_7 (tptp.s tptp.nadd X))) (let ((_let_8 (tptp.s _let_4 tptp.naddu_eq))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_7)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_6)) _let_1)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_7)) _let_6)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_le) _let_1)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_le))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.nadd X))))) (let ((_let_5 (tptp.s tptp.nadd Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.naddu_le))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.naddu_eq) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_le) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd Y))))) (forall ((B0 $$unsorted)) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (and (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.nadd Y))) _let_1)))) (tptp.s tptp.num B0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.nadd X))) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_le))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted)) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_le) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num N0))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num))) (let ((_let_5 (tptp.fun tptp.nadd tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_le) (tptp.s tptp.nadd (tptp.i _let_4 _let_2)))) (tptp.s tptp.nadd (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.destu_nadd))) (let ((_let_6 (tptp.s tptp.nadd X))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) U_0) _let_6)) _let_2)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (= (tptp.s tptp.nadd (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_add) _let_2)) _let_1)) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun _let_3 tptp.nadd) tptp.mku_nadd) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) U_0) _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (X0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num X0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.destu_nadd))) (let ((_let_5 (tptp.s tptp.nadd X))) (let ((_let_6 (tptp.fun tptp.nadd tptp.nadd))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_add) _let_5)) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (XI_ $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd YI_))) (let ((_let_2 (tptp.s tptp.nadd XI_))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_add))) (let ((_let_5 (tptp.s tptp.nadd Y))) (let ((_let_6 (tptp.s tptp.nadd X))) (let ((_let_7 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.nadd _let_7) tptp.naddu_eq))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_add))) (let ((_let_5 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_add))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd X))))) (let ((_let_6 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i _let_5 (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd (tptp.i _let_5 _let_2)))) _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_add) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_eq))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_add) (tptp.s tptp.nadd X))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd (tptp.i _let_6 _let_2)))) (tptp.s tptp.nadd (tptp.i _let_6 _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_le) _let_1)) (tptp.s tptp.nadd (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_add) _let_1)) (tptp.s tptp.nadd Y)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_le) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd Y)))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_eq) (tptp.s tptp.nadd Y))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_add) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd D0)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_6 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_add) (tptp.s tptp.nadd (tptp.i _let_4 _let_2)))) (tptp.s tptp.nadd (tptp.i _let_4 _let_1)))))) (tptp.s tptp.nadd (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.destu_nadd))) (let ((_let_6 (tptp.s tptp.nadd X))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) U_0) _let_6)) _let_2)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (= (tptp.s tptp.nadd (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_mul) _let_2)) _let_1)) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun _let_3 tptp.nadd) tptp.mku_nadd) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) U_0) _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (X0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num X0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.destu_nadd))) (let ((_let_5 (tptp.s tptp.nadd X))) (let ((_let_6 (tptp.fun tptp.nadd tptp.nadd))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_mul) _let_5)) _let_2)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_mul))) (let ((_let_5 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_mul))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd X))))) (let ((_let_6 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i _let_5 (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd (tptp.i _let_5 _let_2)))) _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_mul) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)))) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_3 (tptp.fun tptp.nadd _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.naddu_mul) (tptp.s tptp.nadd X))))) (let ((_let_5 (tptp.s tptp.nadd Y))) (let ((_let_6 (tptp.s _let_3 tptp.naddu_add))) (let ((_let_7 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_7) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i _let_4 (tptp.s tptp.nadd (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.nadd (tptp.i _let_4 _let_5)))) (tptp.s tptp.nadd (tptp.i _let_4 _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd YI_))) (let ((_let_2 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_mul) (tptp.s tptp.nadd X))))) (let ((_let_4 (tptp.s tptp.nadd Y))) (let ((_let_5 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_eq))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.nadd (tptp.i _let_3 _let_4)))) (tptp.s tptp.nadd (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (XI_ $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd YI_))) (let ((_let_2 (tptp.s tptp.nadd XI_))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_mul))) (let ((_let_5 (tptp.s tptp.nadd Y))) (let ((_let_6 (tptp.s tptp.nadd X))) (let ((_let_7 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.nadd _let_7) tptp.naddu_eq))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_6 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_mul) (tptp.s tptp.nadd (tptp.i _let_4 _let_2)))) (tptp.s tptp.nadd (tptp.i _let_4 _let_1)))))) (tptp.s tptp.nadd (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_le) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.nadd X)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.naddu_eq) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.naddu_le) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_mul) (tptp.s tptp.nadd X))))) (let ((_let_4 (tptp.s tptp.nadd Y))) (let ((_let_5 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.nadd (tptp.i _let_3 _let_4)))) (tptp.s tptp.nadd (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_mul))) (let ((_let_5 (tptp.s tptp.nadd X))) (let ((_let_6 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_le))) (let ((_let_5 (tptp.s tptp.nadd Z0))) (let ((_let_6 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_7 (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_add))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_le))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_add) (tptp.s tptp.nadd X))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.nadd (tptp.i _let_6 _let_2)))) (tptp.s tptp.nadd (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Z0))) (let ((_let_2 (tptp.s tptp.nadd Y))) (let ((_let_3 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.naddu_mul))) (let ((_let_6 (tptp.s tptp.nadd X))) (let ((_let_7 (tptp.s _let_4 tptp.naddu_add))) (let ((_let_8 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_8) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))) (forall ((X $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num))) (let ((_let_2 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_3 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_le) (tptp.s tptp.nadd (tptp.i _let_1 (tptp.s tptp.num K0))))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_mul) (tptp.s tptp.nadd (tptp.i _let_1 (tptp.s tptp.num N0))))) (tptp.s tptp.nadd X))))))))))))) (forall ((X $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_le) (tptp.s tptp.nadd (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_mul) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num N0))))) (tptp.s tptp.nadd X))))) (tptp.s tptp.nadd K0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_2 (tptp.fun tptp.nadd _let_1))) (let ((_let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.naddu_mul) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num N0))))))) (let ((_let_4 (tptp.fun tptp.nadd tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) tptp.naddu_le) (tptp.s tptp.nadd (tptp.i _let_3 (tptp.s tptp.nadd X))))) (tptp.s tptp.nadd (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.naddu_add) (tptp.s tptp.nadd (tptp.i _let_3 (tptp.s tptp.nadd Y))))) (tptp.s tptp.nadd Z0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_le) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd Y))))))) (forall ((P0 $$unsorted)) (=> (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.nadd tptp.bool) P0) (tptp.s tptp.nadd X))))) (exists ((M0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_le) _let_1)) (tptp.s tptp.nadd M0)))))))))) (exists ((M0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_le) _let_1)) (tptp.s tptp.nadd M0)))))))) (forall ((MI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_le) _let_1)) (tptp.s tptp.nadd MI_)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_le) (tptp.s tptp.nadd M0))) (tptp.s tptp.nadd MI_))))))))))) (forall ((X $$unsorted)) (exists ((B0 $$unsorted) (N0 $$unsorted)) (forall ((N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num N0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd) (tptp.s tptp.nadd X))) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) (tptp.s tptp.num B0))) _let_1))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((N0 $$unsorted)) (forall ((N1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N1))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num N0))) _let_2))) (not (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.destu_nadd) (tptp.s tptp.nadd X))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((A5 $$unsorted) (N0 $$unsorted)) (forall ((N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num N0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) (tptp.s tptp.num A5))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.destu_nadd) (tptp.s tptp.nadd X))) _let_1))))))))))))))))) (forall ((X $$unsorted) (X0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num X0))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.naddu_rinv) _let_2)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.div) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.t_) _let_1)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.destu_nadd) _let_2)) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((A5 $$unsorted) (B0 $$unsorted)) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_rinv) (tptp.s tptp.nadd X))) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.t_) (tptp.s tptp.num A5))) _let_1)))) (tptp.s tptp.num B0))))))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.destu_nadd) _let_2)) _let_1)))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_7 (tptp.prod tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (=> (not (= _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dist) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.naddu_rinv) _let_2)) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_1)) _let_1)))))))) _let_5)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((N0 $$unsorted)) (forall ((N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.destu_nadd) _let_2)) _let_1)))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_7 (tptp.prod tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num N0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dist) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.naddu_rinv) _let_2)) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_1)) _let_1)))))))) _let_5))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((N0 $$unsorted)) (forall ((M0 $$unsorted) (N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.s tptp.nadd X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.nadd _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.destu_nadd) _let_2)))) (let ((_let_6 (tptp.s tptp.num (tptp.i _let_5 _let_1)))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_3) tptp.t_))) (let ((_let_9 (tptp.s _let_3 (tptp.i _let_8 (tptp.s tptp.num (tptp.i _let_5 _let_7)))))) (let ((_let_10 (tptp.s _let_3 (tptp.i _let_8 _let_7)))) (let ((_let_11 (tptp.prod tptp.num tptp.num))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.s (tptp.fun tptp.num _let_13) tptp.l_a_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.num N0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_11 tptp.num) tptp.dist) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.c_) (tptp.s tptp.num (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_6)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.naddu_rinv) _let_2)) _let_1)))))))))) (tptp.s tptp.num (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_1)) _let_1)))))))))))) (tptp.s tptp.num (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_9 _let_6))))))))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((N0 $$unsorted)) (forall ((M0 $$unsorted) (N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.p_))) (let ((_let_6 (tptp.s tptp.nadd X))) (let ((_let_7 (tptp.fun tptp.nadd _let_3))) (let ((_let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_7 tptp.destu_nadd) _let_6)))) (let ((_let_9 (tptp.s tptp.num (tptp.i _let_8 _let_1)))) (let ((_let_10 (tptp.s tptp.num (tptp.i _let_8 _let_2)))) (let ((_let_11 (tptp.s _let_4 tptp.t_))) (let ((_let_12 (tptp.s _let_3 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_11 _let_10)) _let_9)))))) (let ((_let_13 (tptp.s _let_3 (tptp.i _let_11 _let_1)))) (let ((_let_14 (tptp.s _let_3 (tptp.i _let_11 _let_2)))) (let ((_let_15 (tptp.prod tptp.num tptp.num))) (let ((_let_16 (tptp.fun tptp.num _let_15))) (let ((_let_17 (tptp.s (tptp.fun tptp.num _let_16) tptp.c_))) (let ((_let_18 (tptp.s (tptp.fun _let_15 tptp.num) tptp.dist))) (let ((_let_19 (tptp.s _let_3 (tptp.i (tptp.s _let_7 tptp.naddu_rinv) _let_6)))) (let ((_let_20 (tptp.fun tptp.num tptp.bool))) (let ((_let_21 (tptp.s (tptp.fun tptp.num _let_20) tptp.l_a_))) (let ((_let_22 (tptp.s _let_20 (tptp.i _let_21 (tptp.s tptp.num N0))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_22 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_22 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i _let_21 (tptp.s tptp.num (tptp.i _let_12 (tptp.s tptp.num (tptp.i _let_18 (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i _let_17 (tptp.s tptp.num (tptp.i _let_14 (tptp.s tptp.num (tptp.i _let_19 _let_1)))))) (tptp.s tptp.num (tptp.i _let_13 (tptp.s tptp.num (tptp.i _let_19 _let_2)))))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_11 (tptp.s tptp.num (tptp.i _let_14 _let_1)))) (tptp.s tptp.num (tptp.i _let_18 (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i _let_17 (tptp.s tptp.num (tptp.i _let_14 _let_9)))) (tptp.s tptp.num (tptp.i _let_13 _let_10)))))))))) (tptp.s tptp.num (tptp.i _let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((B0 $$unsorted) (N0 $$unsorted)) (forall ((M0 $$unsorted) (N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s tptp.nadd X))) (let ((_let_8 (tptp.fun tptp.nadd _let_3))) (let ((_let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_8 tptp.naddu_rinv) _let_7)))) (let ((_let_10 (tptp.prod tptp.num tptp.num))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (let ((_let_12 (tptp.s _let_3 (tptp.i (tptp.s _let_8 tptp.destu_nadd) _let_7)))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.s (tptp.fun tptp.num _let_13) tptp.l_a_))) (let ((_let_15 (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.num N0))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_15 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_15 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_12 _let_2)))) (tptp.s tptp.num (tptp.i _let_12 _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_10 tptp.num) tptp.dist) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.c_) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_9 _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.num (tptp.i _let_9 _let_2)))))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_6 _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1)))))))))))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((B0 $$unsorted) (N0 $$unsorted)) (forall ((M0 $$unsorted) (N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_6 _let_1)))))) (let ((_let_8 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_rinv) (tptp.s tptp.nadd X))))) (let ((_let_9 (tptp.prod tptp.num tptp.num))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.s (tptp.fun tptp.num _let_11) tptp.l_a_))) (let ((_let_13 (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.num N0))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_13 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_13 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.num (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dist) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.c_) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_8 _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.num (tptp.i _let_8 _let_2)))))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1)))))))))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((B0 $$unsorted) (N0 $$unsorted)) (forall ((M0 $$unsorted) (N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_rinv) (tptp.s tptp.nadd X))))) (let ((_let_7 (tptp.prod tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_))) (let ((_let_11 (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num N0))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dist) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) (tptp.s tptp.num (tptp.i _let_6 _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1)))))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((N0 $$unsorted)) (exists ((A5 $$unsorted) (B0 $$unsorted)) (forall ((M0 $$unsorted) (N1 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N1))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.t_))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_rinv) (tptp.s tptp.nadd X))))) (let ((_let_7 (tptp.prod tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_5)) (tptp.s tptp.num N0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dist) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_5)) (tptp.s tptp.num (tptp.i _let_6 _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) (tptp.s tptp.num (tptp.i _let_6 _let_5)))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num A5))) _let_1)))) (tptp.s tptp.num B0))))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_1) tptp.naddu_eq) (tptp.s tptp.nadd X))) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (exists ((B0 $$unsorted)) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.t_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_3) tptp.naddu_rinv) (tptp.s tptp.nadd X))))) (let ((_let_7 (tptp.prod tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dist) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.c_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) (tptp.s tptp.num (tptp.i _let_6 _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_4 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_6 (tptp.fun tptp.nadd _let_5))) (= (tptp.s tptp.nadd (tptp.i (tptp.s _let_5 tptp.naddu_inv) _let_1)) (tptp.s tptp.nadd (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) tptp.naddu_eq) _let_1)) _let_3)))) _let_3)) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun _let_2 tptp.nadd) tptp.mku_nadd) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_rinv) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.nadd _let_2))) (let ((_let_4 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.destu_nadd) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.nadd tptp.nadd) tptp.naddu_inv) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_4) tptp.naddu_eq) _let_1)) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s _let_2 U_0))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.naddu_rinv) _let_1)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num))) (let ((_let_5 (tptp.s tptp.nadd X))) (let ((_let_6 (tptp.fun tptp.nadd tptp.nadd))) (let ((_let_7 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.nadd _let_7) tptp.naddu_eq))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) (tptp.s tptp.nadd (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.nadd (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_6) tptp.naddu_mul) (tptp.s tptp.nadd (tptp.i (tptp.s _let_6 tptp.naddu_inv) _let_5)))) _let_5)))) (tptp.s tptp.nadd (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_196 (tptp.i _let_198 (tptp.s tptp.nadd (tptp.i _let_202 _let_208)))) _let_208))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.nadd tptp.nadd) tptp.naddu_inv))) (let ((_let_3 (tptp.s tptp.nadd X))) (let ((_let_4 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.nadd _let_4) tptp.naddu_eq))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.nadd (tptp.i _let_2 _let_3)))) (tptp.s tptp.nadd (tptp.i _let_2 _let_1)))))))))))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (forall ((U $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd U))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 U_0) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.num tptp.nadd) tptp.naddu_ofu_num) (tptp.s tptp.num tptp.m))))) _let_1)))))) (= (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num) (tptp.s tptp.num tptp.m))) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun _let_1 tptp.hreal) tptp.mku_hreal) (tptp.s _let_1 U_0))))))) (= (tptp.s tptp.hreal (tptp.i _let_199 (tptp.s _let_196 (tptp.i _let_198 (tptp.s tptp.nadd (tptp.i _let_207 _let_179)))))) (tptp.s tptp.hreal (tptp.i _let_192 _let_179))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_2 (tptp.fun tptp.hreal tptp.hreal))) (=> (forall ((U $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.nadd tptp.bool) U_0) (tptp.s tptp.nadd U)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.hreal _let_2) tptp.destu_hreal))) (let ((_let_4 (tptp.s tptp.nadd X))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_add) _let_4)) _let_1)))) (tptp.s tptp.nadd U)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.hreal tptp.x))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.hreal tptp.y))) _let_1)))))))))))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_add) (tptp.s tptp.hreal tptp.x))) (tptp.s tptp.hreal tptp.y))) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun _let_1 tptp.hreal) tptp.mku_hreal) (tptp.s _let_1 U_0)))))))) (= (tptp.s tptp.hreal (tptp.i _let_199 (tptp.s _let_196 (tptp.i _let_198 (tptp.s tptp.nadd (tptp.i (tptp.s _let_201 (tptp.i (tptp.s _let_206 tptp.naddu_add) _let_195)) _let_203)))))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_184 (tptp.i _let_186 _let_200)) _let_204))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_2 (tptp.fun tptp.hreal tptp.hreal))) (=> (forall ((U $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.nadd tptp.bool) U_0) (tptp.s tptp.nadd U)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.hreal _let_2) tptp.destu_hreal))) (let ((_let_4 (tptp.s tptp.nadd X))) (let ((_let_5 (tptp.fun tptp.nadd tptp.nadd))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_5) tptp.naddu_mul) _let_4)) _let_1)))) (tptp.s tptp.nadd U)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.hreal tptp.x))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.hreal tptp.y))) _let_1)))))))))))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_mul) (tptp.s tptp.hreal tptp.x))) (tptp.s tptp.hreal tptp.y))) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun _let_1 tptp.hreal) tptp.mku_hreal) (tptp.s _let_1 U_0)))))))) (= (tptp.s tptp.hreal (tptp.i _let_199 (tptp.s _let_196 (tptp.i _let_198 (tptp.s tptp.nadd (tptp.i (tptp.s _let_201 (tptp.i (tptp.s _let_206 tptp.naddu_mul) _let_195)) _let_203)))))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_184 (tptp.i (tptp.s _let_185 tptp.hrealu_mul) _let_200)) _let_204))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun tptp.hreal tptp.bool))) (=> (forall ((U $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.bool tptp.bool) U_0) (tptp.s tptp.bool U)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd Y))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.hreal _let_2) tptp.destu_hreal))) (let ((_let_4 (tptp.s tptp.nadd X))) (and (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_le) _let_4)) _let_1)) (tptp.s tptp.bool U)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.hreal tptp.x))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.hreal tptp.y))) _let_1))))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_le) (tptp.s tptp.hreal tptp.x))) (tptp.s tptp.hreal tptp.y))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.h_) (tptp.s _let_1 U_0)))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_196 (tptp.i (tptp.s _let_197 tptp.naddu_le) _let_195)) _let_203)) (tptp.s tptp.bool (tptp.i (tptp.s _let_205 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_205) tptp.hrealu_le) _let_200)) _let_204))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nadd tptp.bool))) (=> (forall ((U $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.nadd tptp.bool) U_0) (tptp.s tptp.nadd U)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.nadd X))) (let ((_let_2 (tptp.fun tptp.nadd tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.nadd _let_2) tptp.naddu_eq) (tptp.s tptp.nadd (tptp.i (tptp.s (tptp.fun tptp.nadd tptp.nadd) tptp.naddu_inv) _let_1)))) (tptp.s tptp.nadd U)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.destu_hreal) (tptp.s tptp.hreal tptp.x))) _let_1))))))))) (= (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.hreal tptp.hreal) tptp.hrealu_inv) (tptp.s tptp.hreal tptp.x))) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun _let_1 tptp.hreal) tptp.mku_hreal) (tptp.s _let_1 U_0))))))) (= (tptp.s tptp.hreal (tptp.i _let_199 (tptp.s _let_196 (tptp.i _let_198 (tptp.s tptp.nadd (tptp.i _let_202 _let_195)))))) (tptp.s tptp.hreal (tptp.i _let_194 _let_200))) (forall ((P0 $$unsorted)) (=> (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.hreal tptp.bool) P0) (tptp.s tptp.hreal X))))) (exists ((M0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.fun tptp.hreal tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_le) _let_1)) (tptp.s tptp.hreal M0)))))))))) (exists ((M0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.fun tptp.hreal tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_le) _let_1)) (tptp.s tptp.hreal M0)))))))) (forall ((MI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.hreal tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.fun tptp.hreal tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_le) _let_1)) (tptp.s tptp.hreal MI_)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_1) tptp.hrealu_le) (tptp.s tptp.hreal M0))) (tptp.s tptp.hreal MI_))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num))) (= (= (tptp.s tptp.hreal (tptp.i _let_3 _let_2)) (tptp.s tptp.hreal (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num))) (let ((_let_5 (tptp.fun tptp.hreal tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_5) tptp.hrealu_le) (tptp.s tptp.hreal (tptp.i _let_4 _let_2)))) (tptp.s tptp.hreal (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num))) (let ((_let_5 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_5) tptp.hrealu_add) (tptp.s tptp.hreal (tptp.i _let_4 _let_2)))) (tptp.s tptp.hreal (tptp.i _let_4 _let_1)))) (tptp.s tptp.hreal (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num))) (let ((_let_5 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_5) tptp.hrealu_mul) (tptp.s tptp.hreal (tptp.i _let_4 _let_2)))) (tptp.s tptp.hreal (tptp.i _let_4 _let_1)))) (tptp.s tptp.hreal (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.fun tptp.hreal tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_le) _let_1)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Z0))) (let ((_let_2 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_le))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.hreal X))))) (let ((_let_5 (tptp.s tptp.hreal Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Y))) (let ((_let_2 (tptp.s tptp.hreal X))) (let ((_let_3 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_le))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_le))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_3 (tptp.fun tptp.hreal tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_le) _let_1)) (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_add) _let_1)) (tptp.s tptp.hreal Y)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.hreal tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_1) tptp.hrealu_le) (tptp.s tptp.hreal X))) (tptp.s tptp.hreal Y)))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal Y) (tptp.s tptp.hreal (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_1) tptp.hrealu_add) (tptp.s tptp.hreal X))) (tptp.s tptp.hreal D0))))))))) (forall ((X $$unsorted)) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.hreal tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_1) tptp.hrealu_le) (tptp.s tptp.hreal X))) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num) (tptp.s tptp.num N0))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Z0))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.hreal X))))) (= (tptp.s tptp.hreal (tptp.i _let_5 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.hreal (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_add) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)) _let_1)))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Z0))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add) (tptp.s tptp.hreal X))))) (=> (= (tptp.s tptp.hreal (tptp.i _let_4 _let_2)) (tptp.s tptp.hreal (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_mul))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Z0))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_mul))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.hreal X))))) (= (tptp.s tptp.hreal (tptp.i _let_5 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.hreal (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_mul) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)) _let_1))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Z0))) (let ((_let_2 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_3 (tptp.fun tptp.hreal _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.hrealu_mul) (tptp.s tptp.hreal X))))) (let ((_let_5 (tptp.s tptp.hreal Y))) (let ((_let_6 (tptp.s _let_3 tptp.hrealu_add))) (= (tptp.s tptp.hreal (tptp.i _let_4 (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.hreal (tptp.i _let_4 _let_5)))) (tptp.s tptp.hreal (tptp.i _let_4 _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num))) (let ((_let_5 (tptp.s tptp.hreal X))) (let ((_let_6 (tptp.fun tptp.hreal tptp.hreal))) (=> (not (= _let_5 (tptp.s tptp.hreal (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_6) tptp.hrealu_mul) (tptp.s tptp.hreal (tptp.i (tptp.s _let_6 tptp.hrealu_inv) _let_5)))) _let_5)) (tptp.s tptp.hreal (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))) (= (tptp.s tptp.hreal (tptp.i _let_194 _let_193)) _let_193) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.hreal tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_1) tptp.hrealu_le) (tptp.s tptp.hreal M0))) (tptp.s tptp.hreal N0)))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal N0) (tptp.s tptp.hreal (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_1) tptp.hrealu_add) (tptp.s tptp.hreal M0))) (tptp.s tptp.hreal D0))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal P0))) (let ((_let_2 (tptp.s tptp.hreal N0))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add) (tptp.s tptp.hreal M0))))) (= (= (tptp.s tptp.hreal (tptp.i _let_4 _let_2)) (tptp.s tptp.hreal (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal N0))) (let ((_let_2 (tptp.s tptp.hreal M0))) (let ((_let_3 (tptp.s tptp.hreal P0))) (let ((_let_4 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_5 (tptp.s (tptp.fun tptp.hreal _let_4) tptp.hrealu_add))) (= (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.hreal (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3))) (= _let_2 _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal P0))) (let ((_let_2 (tptp.s tptp.hreal N0))) (let ((_let_3 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_le))) (let ((_let_5 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_5) tptp.hrealu_add) (tptp.s tptp.hreal M0))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.hreal (tptp.i _let_6 _let_2)))) (tptp.s tptp.hreal (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal N0))) (let ((_let_2 (tptp.s tptp.hreal M0))) (let ((_let_3 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_le))) (let ((_let_5 (tptp.s tptp.hreal P0))) (let ((_let_6 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_7 (tptp.s (tptp.fun tptp.hreal _let_6) tptp.hrealu_add))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.hreal (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal N0))) (let ((_let_2 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_add) _let_1)) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal P0))) (let ((_let_2 (tptp.s tptp.hreal N0))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.fun tptp.hreal _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.hrealu_mul))) (let ((_let_6 (tptp.s tptp.hreal M0))) (let ((_let_7 (tptp.s _let_4 tptp.hrealu_add))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_mul) _let_1)) (tptp.s tptp.hreal M0))) _let_1)))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.fun tptp.hreal tptp.hreal))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_2) tptp.hrealu_mul) (tptp.s tptp.hreal M0))) _let_1)) _let_1)))) (= _let_191 (tptp.s tptp.hreal (tptp.i _let_189 _let_183))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_184 (tptp.i _let_186 _let_191)) _let_182)) _let_190) (= _let_190 (tptp.s tptp.hreal (tptp.i _let_189 (tptp.s tptp.hreal (tptp.i _let_187 _let_182))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal D0))) (let ((_let_2 (tptp.s tptp.hreal B0))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add))) (let ((_let_5 (tptp.s tptp.hreal C0))) (let ((_let_6 (tptp.s tptp.hreal A5))) (let ((_let_7 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.hreal _let_7) tptp.hrealu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal C0))) (let ((_let_2 (tptp.s tptp.hreal B0))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_mul))) (let ((_let_5 (tptp.s tptp.hreal A5))) (let ((_let_6 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.hreal _let_6) tptp.hrealu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.fun tptp.hreal _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.trealu_ofu_num) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_4) tptp.c_) (tptp.s tptp.hreal (tptp.i _let_1 _let_2)))) (tptp.s tptp.hreal (tptp.i _let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.fun tptp.hreal _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.hreal _let_4) tptp.c_))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.trealu_neg) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Y2))) (let ((_let_2 (tptp.s tptp.hreal Y1))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add))) (let ((_let_5 (tptp.s tptp.hreal X2))) (let ((_let_6 (tptp.s tptp.hreal X1))) (let ((_let_7 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_8 (tptp.fun tptp.hreal _let_7))) (let ((_let_9 (tptp.s (tptp.fun tptp.hreal _let_8) tptp.c_))) (let ((_let_10 (tptp.fun _let_7 _let_7))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.trealu_add) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_2)))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_1)))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((X1 $$unsorted) (Y2 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X2))) (let ((_let_2 (tptp.s tptp.hreal Y1))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.fun tptp.hreal _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.hrealu_mul))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s tptp.hreal Y2))) (let ((_let_8 (tptp.s tptp.hreal X1))) (let ((_let_9 (tptp.s _let_3 (tptp.i _let_5 _let_8)))) (let ((_let_10 (tptp.s _let_4 tptp.hrealu_add))) (let ((_let_11 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_12 (tptp.fun tptp.hreal _let_11))) (let ((_let_13 (tptp.s (tptp.fun tptp.hreal _let_12) tptp.c_))) (let ((_let_14 (tptp.fun _let_11 _let_11))) (= (tptp.s _let_11 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_11 _let_14) tptp.trealu_mul) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_8)) _let_2)))) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_1)) _let_7)))) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.hreal (tptp.i _let_9 _let_1)))) (tptp.s tptp.hreal (tptp.i _let_6 _let_7)))))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.hreal (tptp.i _let_9 _let_7)))) (tptp.s tptp.hreal (tptp.i _let_6 _let_1)))))))))))))))))))))) (forall ((X1 $$unsorted) (Y2 $$unsorted) (X2 $$unsorted) (Y1 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Y1))) (let ((_let_2 (tptp.s tptp.hreal X2))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add))) (let ((_let_5 (tptp.s tptp.hreal Y2))) (let ((_let_6 (tptp.s tptp.hreal X1))) (let ((_let_7 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_8 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_9 (tptp.fun tptp.hreal _let_8))) (let ((_let_10 (tptp.s (tptp.fun tptp.hreal _let_9) tptp.c_))) (let ((_let_11 (tptp.fun _let_8 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.trealu_le) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_6)) _let_1)))) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_2)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_7) tptp.hrealu_le) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal D0))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s tptp.hreal X))) (let ((_let_5 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_6 (tptp.fun tptp.hreal _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_6) U_0) _let_4)) _let_2)) _let_1))) (= _let_4 (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add) _let_2)) _let_1))))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (let ((_let_2 (tptp.s tptp.hreal Y))) (let ((_let_3 (tptp.fun tptp.hreal tptp.bool))) (let ((_let_4 (tptp.fun tptp.hreal _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.hreal _let_4) U_0))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.hreal) tptp.h_))) (let ((_let_7 (tptp.s (tptp.fun tptp.hreal tptp.hreal) tptp.hrealu_inv))) (let ((_let_8 (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.num tptp.hreal) tptp.hrealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_9 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_10 (tptp.fun tptp.hreal _let_9))) (let ((_let_11 (tptp.s (tptp.fun tptp.hreal _let_10) tptp.c_))) (let ((_let_12 (tptp.s _let_10 (tptp.i _let_11 _let_8)))) (let ((_let_13 (tptp.fun _let_9 _let_9))) (let ((_let_14 (tptp.fun _let_9 _let_13))) (let ((_let_15 (tptp.s (tptp.fun tptp.bool _let_14) tptp.cond))) (let ((_let_16 (tptp.s tptp.bool V))) (and (= (tptp.p _let_16) (= _let_1 _let_2)) (= (tptp.s _let_9 (tptp.i (tptp.s _let_13 tptp.trealu_inv) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_1)) _let_2)))) (tptp.s _let_9 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i _let_15 _let_16)) (tptp.s _let_9 (tptp.i _let_12 _let_8)))) (tptp.s _let_9 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i _let_15 (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.hrealu_le) _let_2)) _let_1)))) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.hreal (tptp.i _let_7 (tptp.s tptp.hreal (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2)))))))) _let_8)))) (tptp.s _let_9 (tptp.i _let_12 (tptp.s tptp.hreal (tptp.i _let_7 (tptp.s tptp.hreal (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))))))))))))))))))) (forall ((X1 $$unsorted) (Y2 $$unsorted) (X2 $$unsorted) (Y1 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Y1))) (let ((_let_2 (tptp.s tptp.hreal X2))) (let ((_let_3 (tptp.fun tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.hreal _let_3) tptp.hrealu_add))) (let ((_let_5 (tptp.s tptp.hreal Y2))) (let ((_let_6 (tptp.s tptp.hreal X1))) (let ((_let_7 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_8 (tptp.fun tptp.hreal _let_7))) (let ((_let_9 (tptp.s (tptp.fun tptp.hreal _let_8) tptp.c_))) (let ((_let_10 (tptp.fun _let_7 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.trealu_eq) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_1)))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_5))))) (= (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)) (tptp.s tptp.hreal (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_eq) _let_2)) _let_2))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_eq))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_eq))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 X))))) (let ((_let_6 (tptp.s _let_1 Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (= _let_3 _let_2) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_eq) _let_3)) _let_2))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.trealu_ofu_num))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.trealu_eq) (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (tptp.s _let_3 (tptp.i _let_4 _let_1))))) (= _let_2 _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.trealu_ofu_num))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.trealu_le) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (tptp.s _let_4 (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.trealu_ofu_num))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.trealu_eq) (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.trealu_add) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (tptp.s _let_4 (tptp.i _let_5 _let_1)))))) (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.trealu_ofu_num))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.trealu_eq) (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.trealu_mul) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (tptp.s _let_4 (tptp.i _let_5 _let_1)))))) (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_add))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_mul))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_add))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_add))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 X))))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.trealu_eq) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_add) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.trealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2)))) _let_2)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_add) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.trealu_neg) _let_2)))) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.trealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_mul))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_mul))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 X))))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.trealu_eq) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_mul) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.trealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)))) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.trealu_mul) (tptp.s _let_1 X))))) (let ((_let_6 (tptp.s _let_1 Y))) (let ((_let_7 (tptp.s _let_4 tptp.trealu_add))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.trealu_eq) (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_5 _let_6)))) (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_le) _let_2)) _let_2))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.trealu_le))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_2)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.trealu_eq) _let_3)) _let_2))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_le))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 X))))) (let ((_let_6 (tptp.s _let_1 Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_le))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_add) (tptp.s _let_1 X))))) (let ((_let_5 (tptp.s _let_1 Y))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.trealu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.trealu_le) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.trealu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_mul) _let_3)) _let_2))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_168 (tptp.i _let_170 (tptp.s _let_166 (tptp.i _let_173 _let_181)))) _let_181))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.trealu_ofu_num))) (let ((_let_6 (tptp.s _let_4 X))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_4 _let_8) tptp.trealu_eq))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.trealu_mul) (tptp.s _let_4 (tptp.i (tptp.s _let_7 tptp.trealu_inv) _let_6)))) _let_6)))) (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) tptp.trealu_ofu_num))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (=> (= _let_4 _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.trealu_eq) (tptp.s _let_2 (tptp.i _let_3 _let_4)))) (tptp.s _let_2 (tptp.i _let_3 _let_1)))))))))))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X2))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.trealu_neg))) (let ((_let_4 (tptp.s _let_1 X1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.trealu_eq))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_3 _let_4)))) (tptp.s _let_1 (tptp.i _let_3 _let_2))))))))))))) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X2))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_add))) (let ((_let_6 (tptp.s _let_1 X1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.trealu_eq))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y2))) (let ((_let_3 (tptp.s _let_1 X2))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_add))) (let ((_let_6 (tptp.s _let_1 Y1))) (let ((_let_7 (tptp.s _let_1 X1))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.trealu_eq))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_7)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) _let_6)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))))))) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X2))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_mul))) (let ((_let_6 (tptp.s _let_1 X1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.trealu_eq))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y2))) (let ((_let_3 (tptp.s _let_1 X2))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.trealu_mul))) (let ((_let_6 (tptp.s _let_1 Y1))) (let ((_let_7 (tptp.s _let_1 X1))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.trealu_eq))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_7)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) _let_6)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.trealu_eq) _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.trealu_le) _let_3)) _let_2)))))))))) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y2))) (let ((_let_3 (tptp.s _let_1 X2))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.trealu_le))) (let ((_let_7 (tptp.s _let_1 Y1))) (let ((_let_8 (tptp.s _let_1 X1))) (let ((_let_9 (tptp.s _let_5 tptp.trealu_eq))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_9 _let_8)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_9 _let_7)) _let_2)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_8)) _let_7)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.trealu_inv))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.trealu_eq))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_3 _let_4)))) (tptp.s _let_1 (tptp.i _let_3 _let_2))))))))))))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.hreal tptp.hreal) tptp.bool))) (=> (forall ((U $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 U_0) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.trealu_ofu_num) (tptp.s tptp.num tptp.m))))) _let_2))))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num tptp.m))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.mku_real) (tptp.s _let_1 U_0))))))) (= (tptp.s tptp.real (tptp.i _let_171 (tptp.s _let_168 (tptp.i _let_170 (tptp.s _let_166 (tptp.i _let_180 _let_179)))))) (tptp.s tptp.real (tptp.i _let_52 _let_179))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.hreal tptp.hreal) tptp.bool))) (=> (forall ((U $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 U)))) (exists ((X1 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.trealu_neg) _let_2)))) (tptp.s _let_1 U)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.destu_real) (tptp.s tptp.real tptp.x1))) _let_2))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real tptp.x1))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.mku_real) (tptp.s _let_1 U_0))))))) (= (tptp.s tptp.real (tptp.i _let_171 (tptp.s _let_168 (tptp.i _let_170 (tptp.s _let_166 (tptp.i (tptp.s _let_172 tptp.trealu_neg) _let_176)))))) (tptp.s tptp.real (tptp.i _let_161 _let_177))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.hreal tptp.hreal) tptp.bool))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (forall ((U $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 U)))) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.destu_real))) (let ((_let_5 (tptp.s _let_1 X1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.trealu_add) _let_5)) _let_2)))) (tptp.s _let_1 U)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real tptp.x1))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real tptp.y1))) _let_2)))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) (tptp.s tptp.real tptp.x1))) (tptp.s tptp.real tptp.y1))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.mku_real) (tptp.s _let_1 U_0)))))))) (= (tptp.s tptp.real (tptp.i _let_171 (tptp.s _let_168 (tptp.i _let_170 (tptp.s _let_166 (tptp.i (tptp.s _let_172 (tptp.i (tptp.s _let_178 tptp.trealu_add) _let_176)) _let_174)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_34 _let_177)) _let_175))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.hreal tptp.hreal) tptp.bool))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (forall ((U $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 U)))) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.destu_real))) (let ((_let_5 (tptp.s _let_1 X1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.trealu_mul) _let_5)) _let_2)))) (tptp.s _let_1 U)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real tptp.x1))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real tptp.y1))) _let_2)))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) (tptp.s tptp.real tptp.x1))) (tptp.s tptp.real tptp.y1))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.mku_real) (tptp.s _let_1 U_0)))))))) (= (tptp.s tptp.real (tptp.i _let_171 (tptp.s _let_168 (tptp.i _let_170 (tptp.s _let_166 (tptp.i (tptp.s _let_172 (tptp.i (tptp.s _let_178 tptp.trealu_mul) _let_176)) _let_174)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 _let_177)) _let_175))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (forall ((U $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.bool tptp.bool) U_0) (tptp.s tptp.bool U)))) (exists ((X1 $$unsorted) (Y1 $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 Y1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.destu_real))) (let ((_let_5 (tptp.s _let_1 X1))) (and (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_le) _let_5)) _let_2)) (tptp.s tptp.bool U)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real tptp.x1))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real tptp.y1))) _let_2)))))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real tptp.x1))) (tptp.s tptp.real tptp.y1))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.h_) (tptp.s _let_1 U_0)))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_168 (tptp.i (tptp.s _let_169 tptp.trealu_le) _let_176)) _let_174)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_132 _let_177)) _let_175))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.hreal tptp.hreal) tptp.bool))) (=> (forall ((U $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 U)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.prod tptp.hreal tptp.hreal))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.trealu_eq) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.trealu_inv) _let_2)))) (tptp.s _let_1 U)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.destu_real) (tptp.s tptp.real tptp.x))) _let_2))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) (tptp.s tptp.real tptp.x))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.mku_real) (tptp.s _let_1 U_0))))))) (= (tptp.s tptp.real (tptp.i _let_171 (tptp.s _let_168 (tptp.i _let_170 (tptp.s _let_166 (tptp.i _let_173 _let_167)))))) (tptp.s tptp.real (tptp.i _let_133 (tptp.s tptp.real (tptp.i _let_171 (tptp.s _let_168 (tptp.i _let_170 _let_167))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real X))))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real X))))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)) _let_1))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_mul) (tptp.s tptp.real X))))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s _let_3 tptp.realu_add))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real X))))) (let ((_let_5 (tptp.s tptp.real Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) (tptp.s tptp.real X))))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) _let_2)) _let_1)))))))))))) (= (tptp.s tptp.real (tptp.i _let_133 _let_55)) _let_55) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (=> (not (= _let_5 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_inv) _let_5)))) _let_5)) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (= (= (tptp.s tptp.real (tptp.i _let_3 _let_2)) (tptp.s tptp.real (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_1)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1)))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_ge) _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_gt) _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_abs) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.bool _let_4) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_2)))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) _let_2)) (tptp.s tptp.real (tptp.i _let_4 _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) (tptp.s tptp.real X))) (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_24 (tptp.i (tptp.s (tptp.fun tptp.real _let_24) tptp.realu_pow) _let_119)) _let_51)) _let_53) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real tptp.x))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_2)))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) _let_2)) (tptp.s tptp.real (tptp.i _let_4 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.realu_div) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.realu_mul) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_inv) _let_1)))))))))) (forall ((N0 $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real M0))) (let ((_let_2 (tptp.s tptp.real N0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_max) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) _let_1)) _let_2)))) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real N0))) (let ((_let_2 (tptp.s tptp.real M0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_min) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) _let_2)) _let_1)))) _let_2)) _let_1))))))))) (exists ((R0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real X)))) (exists ((Y $$unsorted)) (= (tptp.s tptp.real X) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.hreal tptp.real) R0) (tptp.s tptp.hreal Y)))))))) (forall ((Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Z0))) (let ((_let_2 (tptp.s (tptp.fun tptp.hreal tptp.real) R0))) (let ((_let_3 (tptp.s tptp.hreal Y))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.hreal tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_5) tptp.hrealu_le) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (exists ((H0 $$unsorted) (R0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal X))) (= (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.real tptp.hreal) H0) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.hreal tptp.real) R0) _let_1)))) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.hreal tptp.real) R0) (tptp.s tptp.hreal (tptp.i (tptp.s (tptp.fun tptp.real tptp.hreal) H0) _let_1)))) _let_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.hreal tptp.real) R0) (tptp.s tptp.hreal X)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.hreal Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.hreal tptp.real) R0))) (let ((_let_3 (tptp.s tptp.hreal X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.hreal tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.hreal _let_5) tptp.hrealu_le) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((P0 $$unsorted)) (=> (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))) (exists ((M0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real M0)))))))))) (exists ((M0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real M0)))))))) (forall ((MI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real MI_)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real M0))) (tptp.s tptp.real MI_))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((P0 $$unsorted)) (=> (and (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) P0) (tptp.s tptp.real X))))) (exists ((M0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real M0)))))))))) (exists ((M0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real M0)))))))) (forall ((MI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real MI_)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real M0))) (tptp.s tptp.real MI_))))))))))) (= _let_165 (tptp.s tptp.real (tptp.i _let_163 _let_155))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_34 _let_165)) _let_154)) _let_164) (= _let_164 (tptp.s tptp.real (tptp.i _let_163 (tptp.s tptp.real (tptp.i _let_162 _let_154))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) (tptp.s tptp.real X))))) (= (= (tptp.s tptp.real (tptp.i _let_4 _let_2)) (tptp.s tptp.real (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.real Z0))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_add))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3))) (= _let_2 _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) (tptp.s tptp.real X))) _let_1)) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) _let_1)) (tptp.s tptp.real X))) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.real (tptp.i _let_2 _let_1)))) _let_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) (tptp.s tptp.real X))))) (let ((_let_4 (tptp.s _let_2 tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (let ((_let_5 (tptp.s _let_3 tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_neg))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))) (= (tptp.s tptp.real (tptp.i _let_161 _let_55)) _let_55) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) _let_2)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.realu_ofu_num))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) (tptp.s tptp.real (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0) _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s _let_6 tptp.realu_neg))) (let ((_let_8 (tptp.fun tptp.real _let_6))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_7 _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) _let_1)))) _let_5)) (tptp.s tptp.real (tptp.i _let_7 _let_5)))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num N0))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_abs))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_lt) (tptp.s tptp.real X))))) (let ((_let_5 (tptp.s tptp.real Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_le) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_lt))) (let ((_let_6 (tptp.s tptp.real Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real X))))) (let ((_let_5 (tptp.s tptp.real Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_1))) (= _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_1)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_2 _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1))) (not (= _let_2 _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) _let_1)) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_lt) _let_4)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_le) _let_4)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_lt) _let_4)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_le) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) _let_3)) _let_2)) _let_1) (or (= _let_3 _let_1) (= _let_2 _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) _let_1)) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) _let_1)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i _let_4 _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real X))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_5)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i _let_1 (tptp.s tptp.num N0))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_ge) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.g_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_gt) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.g_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_max) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.max) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_min) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.min) _let_2)) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_3 _let_1)))) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) _let_1)) _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.m_) _let_2)) _let_1))))))))))))) (= _let_160 (tptp.s tptp.real (tptp.i _let_158 _let_155))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 _let_160)) _let_154)) _let_159) (= _let_159 (tptp.s tptp.real (tptp.i _let_158 (tptp.s tptp.real (tptp.i _let_156 _let_154))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_mul))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.s _let_4 tptp.realu_add))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) (tptp.s tptp.real X))))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1)) _let_2) (= _let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_1)) _let_2)) _let_2) (= _let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s tptp.real Y))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add) _let_1)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.realu_neg))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_neg))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) (tptp.s tptp.real X))))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (let ((_let_5 (tptp.s _let_3 tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real X))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_6 _let_2)))) (tptp.s tptp.real (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real Z0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_add))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (= (not (= _let_1 _let_2)) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_1)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (or (= _let_1 _let_2) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) _let_2)))) (or (= _let_1 _let_2) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_132 _let_55)) _let_53))) (tptp.p (tptp.s tptp.bool (tptp.i _let_130 _let_53))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real X))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_6 _let_2)))) (tptp.s tptp.real (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.s tptp.real Z0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_add))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s tptp.real W))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s tptp.real W))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) _let_2)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_add))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_neg) _let_2)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) _let_1)))))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_le) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_lt) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_1)) _let_2)))) _let_2)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_1)) _let_2)))) _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_sub) _let_1)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_add) _let_1)) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_2)) _let_1) (= _let_2 _let_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_2)) _let_1)))) _let_2)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg))) (let ((_let_3 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i _let_2 _let_3)) _let_1) (= _let_3 (tptp.s tptp.real (tptp.i _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) _let_2)) _let_1))) (not (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) _let_4)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) _let_1)) _let_4)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) _let_4)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) _let_1)) _let_4)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_sub))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_3)) _let_1)))) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_5)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_5)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_sub) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_add) _let_3)) _let_2)))) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_sub) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_add) _let_3)) _let_2)))) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_5)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real D0))) (let ((_let_2 (tptp.s tptp.real B0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_sub))) (let ((_let_6 (tptp.s tptp.real C0))) (let ((_let_7 (tptp.s tptp.real A5))) (let ((_let_8 (tptp.s _let_4 tptp.realu_add))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_6)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_7)) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_sub) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s tptp.real W))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.realu_le) _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s tptp.real W))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.realu_le) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub))) (let ((_let_5 (tptp.s _let_3 tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real C0))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.realu_sub))) (let ((_let_5 (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.real A5))))) (let ((_let_6 (tptp.s tptp.real B0))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_add) (tptp.s tptp.real (tptp.i _let_5 _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_6)) _let_1)))) (tptp.s tptp.real (tptp.i _let_5 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (= (= _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_sub) _let_1)) _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_add) _let_3)) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_5)) _let_1)) _let_2) (= _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_sub) (tptp.s tptp.real X))))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i _let_3 _let_1)))) _let_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_3)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_neg) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (= _let_2 _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) _let_1)) _let_2))) (not (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.realu_mul))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.s _let_3 tptp.realu_sub))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_add) _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_5)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg))) (= (= (tptp.s tptp.real (tptp.i _let_3 _let_2)) (tptp.s tptp.real (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_mul) (tptp.s tptp.real X))))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s _let_3 tptp.realu_sub))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_mul))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.s _let_4 tptp.realu_sub))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_2)) _let_1) (= _let_2 _let_1))))) (= (tptp.s tptp.real (tptp.i _let_153 _let_55)) _let_55) (= (tptp.s tptp.real (tptp.i _let_153 _let_53)) _let_53) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_abs))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_add))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.realu_abs))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le))) (let ((_let_7 (tptp.s tptp.real X))) (let ((_let_8 (tptp.fun tptp.real _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_8 tptp.realu_add) (tptp.s tptp.real (tptp.i _let_4 _let_7)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_8 tptp.realu_sub) _let_2)) _let_7)))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.realu_abs))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_lt))) (let ((_let_7 (tptp.s tptp.real X))) (let ((_let_8 (tptp.fun tptp.real _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_8 tptp.realu_add) (tptp.s tptp.real (tptp.i _let_4 _let_7)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_8 tptp.realu_sub) _let_2)) _let_7)))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_1))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real X)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub))) (let ((_let_5 (tptp.s _let_3 tptp.realu_abs))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (= (not (= _let_1 _let_2)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs))) (let ((_let_2 (tptp.s tptp.real (tptp.i _let_1 (tptp.s tptp.real X))))) (= (tptp.s tptp.real (tptp.i _let_1 _let_2)) _let_2)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)) _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real D0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.realu_sub))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_2)) _let_1)))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_add) _let_2)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))))) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real D0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_sub) _let_2)) _let_5)))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.realu_abs))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub) _let_1)) _let_2)))))) (tptp.s tptp.real (tptp.i _let_4 _let_2))))) (not (= _let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (or (= _let_1 _let_2) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_sub))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) _let_1)) _let_4)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_neg) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.s _let_1 tptp.realu_abs))) (let ((_let_3 (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.real Y))))) (let ((_let_4 (tptp.s tptp.real H0))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real _let_1))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_2 _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.realu_sub) _let_3)) (tptp.s tptp.real (tptp.i _let_2 _let_5))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.real (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.realu_add) _let_5)) _let_4)))))) _let_3))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub))) (let ((_let_5 (tptp.s _let_3 tptp.realu_abs))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (tptp.s tptp.real (tptp.i _let_5 _let_1)))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub))) (let ((_let_5 (tptp.s _let_3 tptp.realu_abs))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (tptp.s tptp.real (tptp.i _let_5 _let_1)))))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X0 $$unsorted) (X $$unsorted) (Y0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real X0))) (let ((_let_6 (tptp.s tptp.real Y0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.realu_sub))) (let ((_let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_6)) _let_5)))) (let ((_let_11 (tptp.s _let_7 tptp.realu_abs))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (let ((_let_13 (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_13 (tptp.s tptp.real (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_2)) _let_5)))))))) _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_13 (tptp.s tptp.real (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_1)) _let_6)))))))) _let_10)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))))) (forall ((X $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real K0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_abs) _let_2)))) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_neg) _let_1)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real K0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) _let_1)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_abs) _let_2)))) _let_1)))))))))) (forall ((X $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real K0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_neg) _let_1)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_abs) _let_2)))) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_neg))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.realu_min) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.realu_max) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_neg))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.realu_max) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.realu_min) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_max) _let_2)) _let_1)))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) _let_4))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_min) _let_2)) _let_1)))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_max))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_min))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real Z0))))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_max) _let_4)) _let_1))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real Z0))))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_min) _let_4)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real Z0))))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_max) _let_4)) _let_1))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real Z0))))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_min) _let_4)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_max) _let_5)) _let_2)))) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_min) _let_5)) _let_2)))) _let_1))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_max) _let_5)) _let_2)))) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_min) _let_5)) _let_2)))) _let_1))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_max))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real X))))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_min))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real X))))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) _let_1))))))))) (= _let_150 (tptp.s tptp.real (tptp.i _let_151 _let_119))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_148 _let_150)) _let_145)) _let_152) (= _let_152 (tptp.s tptp.real (tptp.i _let_151 (tptp.s tptp.real (tptp.i _let_149 _let_145))))) (= (tptp.s tptp.real (tptp.i _let_149 _let_119)) _let_119) (= (tptp.s tptp.real (tptp.i _let_149 _let_150)) _let_150) (= _let_144 (tptp.s tptp.real (tptp.i _let_146 _let_119))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_142 _let_144)) _let_145)) _let_147) (= _let_147 (tptp.s tptp.real (tptp.i _let_146 (tptp.s tptp.real (tptp.i _let_143 _let_145))))) (= (tptp.s tptp.real (tptp.i _let_143 _let_119)) _let_119) (= (tptp.s tptp.real (tptp.i _let_143 _let_144)) _let_144) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_abs))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_pow) _let_1)) (tptp.s tptp.num N0)))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_pow) _let_1)) (tptp.s tptp.num N0)))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_2)))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) _let_2)))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) _let_2)))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) _let_3)))) (= (= (tptp.s tptp.real (tptp.i _let_5 _let_2)) (tptp.s tptp.real (tptp.i _let_5 _let_1))) (or (= _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_2 _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))) (or (= _let_3 _let_2) (= _let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (=> (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_inv) _let_2)) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (=> (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_inv) _let_2)) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.real (tptp.i _let_2 _let_1)))) _let_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (= (= (tptp.s tptp.real (tptp.i _let_3 _let_2)) (tptp.s tptp.real (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_2)) _let_1) (= _let_2 _let_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_inv))) (let ((_let_4 (tptp.s _let_2 tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (=> (not (= _let_5 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_inv) _let_5)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))) (= (tptp.s tptp.real (tptp.i _let_133 _let_53)) _let_53) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_3)) _let_2) (= _let_3 _let_2)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_div) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (=> (not (= _let_5 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_div) _let_5)) _let_5)) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (=> (not (= _let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_div) _let_1)) _let_2)))) _let_2)) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (=> (not (= _let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_mul) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_div) _let_1)) _let_2)))) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_abs))) (let ((_let_4 (tptp.s _let_2 tptp.realu_inv))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_abs))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_div))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_inv))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_div))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_inv) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_5 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_2)))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_div))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_div) _let_3)) _let_2)) _let_1) (or (= _let_3 _let_1) (= _let_2 _let_1)))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_pow) (tptp.s tptp.real X))))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.p_) _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s _let_1 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s tptp.real X))) (=> (not (= _let_3 _let_2)) (not (= (tptp.s tptp.real (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_pow) _let_3)) (tptp.s tptp.num N0))) _let_2))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_2)))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (=> (and (not (= _let_2 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_) _let_1)) _let_5)))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.m_) _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_div) (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) _let_5)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_7 _let_2)))) (tptp.s tptp.real (tptp.i _let_7 _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real Z0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_le))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_6)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_8 _let_2)))) (tptp.s tptp.real (tptp.i _let_8 _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_le))) (let ((_let_6 (tptp.s tptp.real Z0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_le))) (let ((_let_6 (tptp.s tptp.real Z0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_le))) (let ((_let_6 (tptp.s tptp.real Z0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_6)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_8 _let_2)))) (tptp.s tptp.real (tptp.i _let_8 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real Z0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real Z0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) _let_5)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_7 _let_2)))) (tptp.s tptp.real (tptp.i _let_7 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_6))) (= (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_6)) _let_1)))) (tptp.s tptp.bool (tptp.i _let_5 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)))) (let ((_let_6 (tptp.s tptp.real Y))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_6))) (= (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_1)) _let_6)))) (tptp.s tptp.bool (tptp.i _let_5 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) _let_4)) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) _let_1)) _let_4)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 _let_1)))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_5)) _let_2))))) (or (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_lt))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_5 _let_1)))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_mul) _let_6)) _let_2))))) (or (= _let_6 _let_1) (= _let_2 _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.s _let_7 tptp.realu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_div) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_mul) _let_3)) _let_2)))) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.s _let_7 tptp.realu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_div) _let_5)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_mul) _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_div) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_mul) _let_3)) _let_2)))) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_div) _let_5)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_mul) _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real Z0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (= (= _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_div) _let_1)) _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_mul) _let_3)) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_div) _let_5)) _let_1)) _let_2) (= _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_mul) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.real Z0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_div))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_le))) (let ((_let_6 (tptp.s tptp.real Z0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_div))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_add) _let_1)) _let_1)))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) _let_1)))) (let ((_let_5 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_5)) _let_2)) _let_4) (and (= _let_5 _let_4) (not (= _let_2 _let_1)))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s tptp.real W))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s tptp.real W))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.realu_lt))) (let ((_let_10 (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) _let_2)) _let_2))))) (not (= _let_2 _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_pow) _let_3)) (tptp.s tptp.num N0))) _let_3))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_1)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_1)))) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_2)))) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s tptp.real (tptp.i _let_2 _let_3)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s tptp.real (tptp.i _let_2 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_3 _let_1)))) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_3 _let_2)))) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_1)) (tptp.s tptp.real (tptp.i _let_2 _let_3)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_3)))) _let_2)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_6 (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 _let_2)))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_1)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_6)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_1)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_3)))) _let_2)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_6 (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 _let_2)))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_sub))) (let ((_let_6 (tptp.s _let_3 tptp.realu_inv))) (let ((_let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (=> (and (not (= _let_2 _let_7)) (not (= _let_1 _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_6 _let_2)))) (tptp.s tptp.real (tptp.i _let_6 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_div) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_mul) _let_2)) _let_1)))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i _let_133 _let_140)))) _let_140)) _let_53) (forall ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real D0)))) (exists ((E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_1)) (tptp.s tptp.real D0)))))))))))) (forall ((D1 $$unsorted) (D2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.real D1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.real D2))))) (exists ((E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 _let_1)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real D1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real D2)))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_pow) _let_1)) (tptp.s tptp.num N0))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.realu_ofu_num))) (let ((_let_6 (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_7 (tptp.s tptp.real X))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_7)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) _let_7)) (tptp.s tptp.num N0))))) _let_6)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_2)))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.s _let_7 tptp.realu_lt))) (let ((_let_9 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (=> (and (not (= _let_1 _let_9)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) _let_9)))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_5)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s tptp.num tptp.u_0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 tptp.numeral))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_4)))))))))) (=> (and (not (= _let_1 (tptp.s tptp.num (tptp.i _let_6 _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_2)) _let_1))))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.realu_ofu_num))) (let ((_let_6 (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_7 (tptp.s tptp.num N0))) (let ((_let_8 (tptp.s tptp.real X))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.s _let_10 tptp.realu_lt))) (let ((_let_12 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (=> (and (not (= _let_7 _let_12)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.realu_le) (tptp.s tptp.real (tptp.i _let_5 _let_12)))) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_8)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) _let_8)) _let_7)))) _let_6))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_2)))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))))))))))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real X))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_6 _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.real Z0))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul))) (=> (and (not (= _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3)))) (= _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.real Z0))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) _let_3)))) (=> (and (not (= _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s tptp.real (tptp.i _let_5 _let_2)) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (= _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_div) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_div) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.m_))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_5)))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.real _let_8))) (=> (not (= _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 tptp.realu_div) (tptp.s tptp.real (tptp.i _let_7 _let_1)))) (tptp.s tptp.real (tptp.i _let_7 _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.realu_inv) (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.m_))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_5)))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.real _let_8))) (=> (not (= _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 tptp.realu_div) (tptp.s tptp.real (tptp.i _let_7 _let_1)))) (tptp.s tptp.real (tptp.i _let_7 _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_) _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.realu_inv) (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.realu_ofu_num))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))) (tptp.s tptp.num N0))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.realu_ofu_num))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))))) (tptp.s tptp.num N0))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_3)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le))) (let ((_let_9 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_9 _let_6)))) (tptp.s tptp.real (tptp.i _let_9 _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (let ((_let_9 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_9 _let_6)))) (tptp.s tptp.real (tptp.i _let_9 _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs))) (= (= (tptp.s tptp.real (tptp.i _let_7 _let_6)) (tptp.s tptp.real (tptp.i _let_7 _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) (tptp.s tptp.real X))) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (let ((_let_6 (tptp.s tptp.real Y))) (let ((_let_7 (tptp.s tptp.real X))) (let ((_let_8 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_9 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (let ((_let_10 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_9 _let_7)) _let_8)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_9 _let_6)) _let_8)))) _let_5) (and (= _let_7 _let_5) (= _let_6 _let_5)))))))))))))) (forall ((N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.s _let_5 tptp.realu_ofu_num))) (let ((_let_7 (tptp.s tptp.real (tptp.i _let_6 _let_4)))) (let ((_let_8 (tptp.s tptp.bool V))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.s tptp.num N0))) (and (= (tptp.p _let_8) (= _let_11 _let_4)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_7)) _let_11)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) _let_8)) (tptp.s tptp.real (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) _let_7))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) _let_2)))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s tptp.num tptp.u_0))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.s _let_10 tptp.numeral))) (let ((_let_12 (tptp.s _let_3 tptp.realu_ofu_num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i _let_12 (tptp.s tptp.num (tptp.i _let_11 _let_9)))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s tptp.real (tptp.i _let_12 (tptp.s tptp.num (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) _let_9))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_) _let_1)) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_1))))))))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow))) (let ((_let_8 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (=> (and (not (= _let_5 _let_8)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) _let_8)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_lt))) (let ((_let_6 (tptp.s tptp.num N0))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_pow))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_7 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) _let_6)))))) (=> (and (not (= _let_3 _let_6)) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3)))) (= _let_2 _let_1))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow))) (=> (and (not (= _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) _let_4)))) (= (tptp.s tptp.real (tptp.i _let_2 _let_3)) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.s tptp.num N0))) (=> (and (not (= _let_7 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) _let_6)) _let_7)) _let_5)) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_6)) _let_5)))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 tptp.realu_ofu_num))) (let ((_let_8 (tptp.s tptp.real X))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_8)) _let_5)) _let_10) (or (and (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_8)) _let_10) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_lt) _let_8)) (tptp.s tptp.real (tptp.i _let_7 _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) _let_5))))) (= _let_5 _let_4)))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_3))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3))) (= _let_2 _let_1))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3)))) (= _let_2 _let_1)))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_pow))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real X))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real Y))) _let_1))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs))) (and (= (tptp.p (tptp.s tptp.bool V)) (or (= (tptp.s tptp.num N0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (= (tptp.s tptp.real (tptp.i _let_1 (tptp.s tptp.real X))) (tptp.s tptp.real (tptp.i _let_1 (tptp.s tptp.real Y)))))) (exists ((VI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (= (tptp.s tptp.real X) (tptp.s tptp.real Y))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) (tptp.s tptp.num N0))))) (tptp.s tptp.bool V))) _let_1)))))))))))))))) (forall ((X $$unsorted)) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real X))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num N0))))))))) (forall ((X $$unsorted)) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real X))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num N0))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real X)))) (forall ((Y $$unsorted)) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real Y))) (tptp.s tptp.real (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num N0))))) (tptp.s tptp.real X))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (let ((_let_6 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.s tptp.real X))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_lt))) (let ((_let_11 (tptp.fun tptp.real _let_7))) (let ((_let_12 (tptp.s (tptp.fun tptp.bool _let_11) tptp.cond))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 tptp.realu_sgn) _let_8)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_5)) _let_8)))) _let_6)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_8)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 tptp.realu_neg) _let_6)))) _let_5)))))))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_29 tptp.realu_sgn) _let_55)) _let_55) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_sgn))) (let ((_let_4 (tptp.s _let_2 tptp.realu_neg))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_sgn) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_abs) _let_1)))) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_abs))) (let ((_let_4 (tptp.s _let_2 tptp.realu_sgn))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_sgn) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_div) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_abs) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_sgn))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_sgn))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_inv) _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_sgn))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_div))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_sgn) _let_2)) _let_1) (= _let_2 _let_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_sgn) _let_5)) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_gt) _let_5)) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 tptp.realu_sgn) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 tptp.realu_neg) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) _let_5)) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_sgn) (tptp.s tptp.real X))))) (or (= _let_7 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1))))) (= _let_7 _let_5) (= _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_neg) _let_5)))))))))))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.p0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p0) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.p0) (tptp.s tptp.real X))) (tptp.s tptp.real Y))))))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.p0) _let_1)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.p0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p0) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.p0) (tptp.s tptp.real X))) (tptp.s tptp.real Y))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num Y))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.realu_ofu_num))) (let ((_let_4 (tptp.s tptp.num X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.decimal) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_div) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))) (= (tptp.s tptp.real (tptp.i _let_138 (tptp.s tptp.real (tptp.i _let_139 _let_137)))) (tptp.s tptp.real (tptp.i _let_139 (tptp.s tptp.real (tptp.i _let_138 _let_137))))) (=> (and (not (= _let_120 _let_55)) (not (= _let_123 _let_55))) _let_136) (=> _let_131 _let_136) (=> _let_131 (= (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_135 _let_128)) _let_127)) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_135 _let_125)) _let_122)))) _let_134)))) (=> _let_131 (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_132 _let_128)) _let_127)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_132 _let_125)) _let_122)))) (=> _let_131 (= (= _let_128 _let_127) (= _let_125 _let_122))) (forall ((X $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) tptp.integer) (tptp.s tptp.real X)))) (exists ((N0 $$unsorted)) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real X))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num N0))))))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_117 _let_119))) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num N0))))) (let ((_let_2 (tptp.s tptp.real tptp.x))) (or (= _let_2 _let_1) (= _let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1)))))))) (= (tptp.s tptp.int (tptp.i _let_115 (tptp.s tptp.real (tptp.i _let_116 _let_118)))) _let_118) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_117 _let_114))) (= (tptp.s tptp.real (tptp.i _let_116 (tptp.s tptp.int (tptp.i _let_115 _let_114)))) _let_114)) (forall ((R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real R0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) tptp.integer) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) _let_1)))) _let_1)))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.int A5))) (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int) _let_1)))) _let_1))) (forall ((I0 $$unsorted)) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num N0))))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int) (tptp.s tptp.int I0))))) (or (= _let_2 _let_1) (= _let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (= (= _let_3 _let_1) (= (tptp.s tptp.real (tptp.i _let_2 _let_3)) (tptp.s tptp.real (tptp.i _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_le) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_lt) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_ge) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_ge) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_gt) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_gt) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int I0))) (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) _let_3)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) _let_3)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_sub) _let_3)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_sub) _let_3)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_mul) _let_3)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_mul) _let_3)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i _let_2 _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_sgn) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_sgn) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_sgn) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_sgn) (tptp.s tptp.real (tptp.i _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_max) _let_3)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_max) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_max) _let_3)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_max) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_min) _let_3)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_min) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_min) _let_3)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_min) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow) _let_2)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.real tptp.int) tptp.intu_ofu_real) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int) _let_2)))) _let_1)))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.num tptp.int))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_pow) _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) (tptp.s tptp.real (tptp.i _let_3 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (or (exists ((N0 $$unsorted)) (= (tptp.s tptp.int X) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num N0))))) (exists ((N0 $$unsorted)) (= (tptp.s tptp.int X) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num N0))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_lt) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_add) _let_3)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_gt) _let_4)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_ge) _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))))) (= (tptp.s tptp.int (tptp.i _let_113 _let_83)) _let_83) (= (tptp.s tptp.int (tptp.i _let_113 _let_81)) _let_81) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs))) (let ((_let_2 (tptp.s tptp.int (tptp.i _let_1 (tptp.s tptp.int X))))) (= (tptp.s tptp.int (tptp.i _let_1 _let_2)) _let_2)))) (forall ((X $$unsorted) (Y $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int D0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.s tptp.int Y))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.intu_sub))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_lt))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_2)) _let_1)))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_add) _let_2)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_4 tptp.intu_abs) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))))) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_sub))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 tptp.intu_abs) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))))) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X0 $$unsorted) (X $$unsorted) (Y0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s tptp.int X0))) (let ((_let_6 (tptp.s tptp.int Y0))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.intu_sub))) (let ((_let_10 (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_6)) _let_5)))) (let ((_let_11 (tptp.s _let_7 tptp.intu_abs))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (let ((_let_13 (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.intu_mul) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_13 (tptp.s tptp.int (tptp.i _let_11 (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_2)) _let_5)))))))) _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_13 (tptp.s tptp.int (tptp.i _let_11 (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_1)) _let_6)))))))) _let_10)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int D0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s tptp.int Y))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_abs) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_2)) _let_5)))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (or (= _let_1 _let_2) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.s _let_1 tptp.intu_abs))) (let ((_let_3 (tptp.s tptp.int (tptp.i _let_2 (tptp.s tptp.int Y))))) (let ((_let_4 (tptp.s tptp.int H0))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int _let_1))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i _let_2 _let_4)))) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.intu_sub) _let_3)) (tptp.s tptp.int (tptp.i _let_2 _let_5))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i _let_2 (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.intu_add) _let_5)) _let_4)))))) _let_3))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_abs))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_3 _let_4)))) (tptp.s tptp.int (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_abs))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))) (tptp.s tptp.int (tptp.i _let_3 _let_1))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num N0))))) (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_1)) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (not (= _let_1 _let_2)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.int _let_1) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) (tptp.s tptp.int X)))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_3 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_1)) _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_abs))) (let ((_let_4 (tptp.s _let_2 tptp.intu_sgn))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt))) (let ((_let_4 (tptp.s tptp.int Y))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 tptp.intu_abs) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_sub) _let_1)) _let_4)))))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt))) (let ((_let_4 (tptp.s tptp.int Y))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 tptp.intu_abs) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_sub) _let_1)) _let_4)))))) (tptp.s tptp.int (tptp.i (tptp.s _let_5 tptp.intu_neg) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s _let_3 tptp.intu_abs))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_lt) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_sub) _let_1)) _let_2)))))) (tptp.s tptp.int (tptp.i _let_4 _let_2))))) (not (= _let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_sub))) (let ((_let_5 (tptp.s _let_3 tptp.intu_abs))) (= (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_sub))) (let ((_let_5 (tptp.s _let_3 tptp.intu_abs))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_2)))) (tptp.s tptp.int (tptp.i _let_5 _let_1)))))))) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_abs))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le) (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_3 _let_4)))) (tptp.s tptp.int (tptp.i _let_3 _let_1)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int X))) (= (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_2)) _let_1) (= _let_2 _let_1))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int D0))) (let ((_let_2 (tptp.s tptp.int B0))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.intu_sub))) (let ((_let_6 (tptp.s tptp.int C0))) (let ((_let_7 (tptp.s tptp.int A5))) (let ((_let_8 (tptp.s _let_4 tptp.intu_add))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_7)) _let_2)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_8 _let_6)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_7)) _let_6)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))) (= _let_112 (tptp.s tptp.int (tptp.i _let_110 _let_86))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_84 (tptp.i _let_108 _let_112)) _let_85)) _let_111) (= _let_111 (tptp.s tptp.int (tptp.i _let_110 (tptp.s tptp.int (tptp.i _let_109 _let_85))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int X))))) (= (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_mul) (tptp.s tptp.int X))))) (let ((_let_5 (tptp.s tptp.int Y))) (let ((_let_6 (tptp.s _let_3 tptp.intu_add))) (= (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.int (tptp.i _let_4 _let_5)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.intu_mul))) (let ((_let_6 (tptp.s tptp.int X))) (let ((_let_7 (tptp.s _let_4 tptp.intu_add))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_2)) _let_1)))) _let_2)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int _let_2))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_3)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int K0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_le))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_neg) _let_1)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_abs) _let_2)))) _let_1)))))))))) (forall ((X $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int K0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_lt))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_neg) _let_1)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_abs) _let_2)))) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.intu_mul))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.s _let_3 tptp.intu_sub))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_add) _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_5)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_mul) _let_3)) _let_2)) _let_1) (or (= _let_3 _let_1) (= _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) (tptp.s tptp.int X))))) (= (= (tptp.s tptp.int (tptp.i _let_4 _let_2)) (tptp.s tptp.int (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) _let_1)) _let_2) (= _let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.s tptp.int Z0))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_add))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3))) (= _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_1)) _let_2)) _let_2) (= _let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (= _let_2 _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_mul) _let_3)))) (= (= (tptp.s tptp.int (tptp.i _let_5 _let_2)) (tptp.s tptp.int (tptp.i _let_5 _let_1))) (or (= _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_2 _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_mul))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))) (or (= _let_3 _let_2) (= _let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg))) (= (= (tptp.s tptp.int (tptp.i _let_3 _let_2)) (tptp.s tptp.int (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.int Y))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow))) (let ((_let_6 (tptp.s tptp.int X))) (let ((_let_7 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs))) (= (= (tptp.s tptp.int (tptp.i _let_7 _let_6)) (tptp.s tptp.int (tptp.i _let_7 _let_3))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (= (= _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_sub) _let_1)) _let_2))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_add) _let_3)) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s tptp.int X))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_5)) _let_1)) _let_2) (= _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_lt) _let_4)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_le) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) _let_1)))))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add))) (let ((_let_5 (tptp.s tptp.int Y))) (let ((_let_6 (tptp.s tptp.int W))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.intu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.intu_le) _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.intu_lt))) (let ((_let_6 (tptp.s tptp.int Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_106 (tptp.i (tptp.s _let_107 tptp.intu_le) _let_83)) _let_81))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) _let_1)))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add))) (let ((_let_5 (tptp.s tptp.int Y))) (let ((_let_6 (tptp.s tptp.int W))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le))) (let ((_let_4 (tptp.s tptp.int Y))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) _let_1)) _let_4)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) _let_4)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (= _let_2 _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_add) _let_1)) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) (tptp.s tptp.int X))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_6 _let_2)))) (tptp.s tptp.int (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add) (tptp.s tptp.int X))))) (let ((_let_4 (tptp.s tptp.int Y))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.int (tptp.i _let_3 _let_4)))) (tptp.s tptp.int (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul) _let_2)))) (let ((_let_5 (tptp.s tptp.int Y))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i _let_4 _let_5)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_neg) _let_2)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_1))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_1))) (= _let_2 _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int Z0))))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_max) _let_4)) _let_1))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int Z0))))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_min) _let_4)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)))) (let ((_let_6 (tptp.s tptp.int Y))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_6))) (= (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_mul) _let_1)) _let_6)))) (tptp.s tptp.bool (tptp.i _let_5 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)))) (let ((_let_6 (tptp.s tptp.int X))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_6))) (= (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_mul) _let_6)) _let_1)))) (tptp.s tptp.bool (tptp.i _let_5 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (let ((_let_5 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_1)))) (tptp.s tptp.int (tptp.i _let_5 _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_1)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) _let_1)))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s _let_4 tptp.intu_ofu_num))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_2)))))) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))))) (tptp.s tptp.num N0))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (let ((_let_5 (tptp.s tptp.int Z0))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_add))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) _let_1)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_neg) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul) _let_1)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.int Y))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow))) (let ((_let_6 (tptp.s tptp.int X))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_le))) (let ((_let_9 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i _let_9 _let_6)))) (tptp.s tptp.int (tptp.i _let_9 _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_sub) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_add) _let_3)) _let_2)))) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_5)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int X))))) (let ((_let_5 (tptp.s tptp.int Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s tptp.int X))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add) _let_3)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_lt) _let_4)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_le) _let_4)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) _let_1)))))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add))) (let ((_let_5 (tptp.s tptp.int Y))) (let ((_let_6 (tptp.s tptp.int W))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (let ((_let_9 (tptp.s _let_8 tptp.intu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.intu_le) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_lt) (tptp.s tptp.int X))))) (let ((_let_5 (tptp.s tptp.int Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_le) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_106 (tptp.i (tptp.s _let_107 tptp.intu_lt) _let_83)) _let_81))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_lt) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_le) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_lt) _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add))) (let ((_let_5 (tptp.s tptp.int Y))) (let ((_let_6 (tptp.s tptp.int W))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt))) (let ((_let_4 (tptp.s tptp.int Y))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) _let_1)) _let_4)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.s tptp.int Y))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_add))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 tptp.intu_neg) _let_2)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_add))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_neg) _let_1)))))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) _let_4)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_5)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (not (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt) _let_2)) _let_1))) (not (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) (tptp.s tptp.int X))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_6 _let_2)))) (tptp.s tptp.int (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_1))) (not (= _let_2 _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s tptp.int Z0))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_mul) _let_5)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_7 _let_2)))) (tptp.s tptp.int (tptp.i _let_7 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt) (tptp.s tptp.int Z0))))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_max) _let_4)) _let_1))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt) (tptp.s tptp.int Z0))))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_min) _let_4)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_lt) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.s tptp.int Y))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_mul) _let_1)) _let_4)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_mul) _let_4)) _let_1)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_1)))) (tptp.s tptp.int (tptp.i _let_5 _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt) _let_2)))) (or (= _let_1 _let_2) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s _let_4 tptp.intu_ofu_num))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))) (tptp.s tptp.num N0))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s tptp.int Z0))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_add))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt) _let_1)) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s tptp.int Z0))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_mul))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.int Y))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow))) (let ((_let_6 (tptp.s tptp.int X))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_lt))) (let ((_let_9 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i _let_9 _let_6)))) (tptp.s tptp.int (tptp.i _let_9 _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_sub) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_add) _let_3)) _let_2)))) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int Z0))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_5)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (or (= _let_1 _let_2) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int X))))) (let ((_let_5 (tptp.s tptp.int Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (= _let_103 (tptp.s tptp.int (tptp.i _let_104 _let_82))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_84 (tptp.i _let_101 _let_103)) _let_98)) _let_105) (= _let_105 (tptp.s tptp.int (tptp.i _let_104 (tptp.s tptp.int (tptp.i _let_102 _let_98))))) (= (tptp.s tptp.int (tptp.i _let_102 _let_82)) _let_82) (= (tptp.s tptp.int (tptp.i _let_102 _let_103)) _let_103) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_max))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int X))))) (= (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_max) _let_5)) _let_2)))) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_max) _let_5)) _let_2)))) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_max) _let_2)) _let_1)))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_le))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) _let_4))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_neg))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int _let_2))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.intu_max) _let_4)) _let_1)) (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.intu_min) (tptp.s tptp.int (tptp.i _let_3 _let_4)))) (tptp.s tptp.int (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_max))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (= _let_97 (tptp.s tptp.int (tptp.i _let_99 _let_82))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_84 (tptp.i _let_95 _let_97)) _let_98)) _let_100) (= _let_100 (tptp.s tptp.int (tptp.i _let_99 (tptp.s tptp.int (tptp.i _let_96 _let_98))))) (= (tptp.s tptp.int (tptp.i _let_96 _let_82)) _let_82) (= (tptp.s tptp.int (tptp.i _let_96 _let_97)) _let_97) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_min))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int X))))) (= (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_min) _let_5)) _let_2)))) _let_1))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_min) _let_5)) _let_2)))) _let_1))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_neg))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.fun tptp.int _let_2))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.intu_min) _let_4)) _let_1)) (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 tptp.intu_max) (tptp.s tptp.int (tptp.i _let_3 _let_4)))) (tptp.s tptp.int (tptp.i _let_3 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_min) _let_2)) _let_1)))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_min))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (= _let_93 (tptp.s tptp.int (tptp.i _let_91 _let_86))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_84 (tptp.i _let_88 _let_93)) _let_85)) _let_92) (= _let_92 (tptp.s tptp.int (tptp.i _let_91 (tptp.s tptp.int (tptp.i _let_89 _let_85))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int X))))) (= (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)) _let_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul))) (let ((_let_5 (tptp.s _let_3 tptp.intu_neg))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul) _let_1)) (tptp.s tptp.int X))) _let_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.intu_lt))) (let ((_let_6 (tptp.s tptp.int X))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_5 _let_1)))) (let ((_let_8 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.int _let_8) tptp.intu_mul) _let_6)) _let_2))))) (or (= _let_6 _let_1) (= _let_2 _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 _let_1)))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_mul) _let_5)) _let_2))))) (or (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul) (tptp.s tptp.int X))))) (let ((_let_4 (tptp.s _let_2 tptp.intu_neg))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul) (tptp.s tptp.int X))) _let_1)) _let_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg))) (= (tptp.s tptp.int (tptp.i _let_2 (tptp.s tptp.int (tptp.i _let_2 _let_1)))) _let_1)))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_84 tptp.intu_neg) _let_83)) _let_83) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_neg))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_3 _let_4)))) (tptp.s tptp.int (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg))) (let ((_let_3 (tptp.s tptp.int X))) (= (= (tptp.s tptp.int (tptp.i _let_2 _let_3)) _let_1) (= _let_3 (tptp.s tptp.int (tptp.i _let_2 _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int X))) (= (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_2)) _let_1) (= _let_2 _let_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s _let_3 tptp.intu_neg))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul))) (= (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_4 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s _let_3 tptp.intu_neg))) (= (tptp.s tptp.int (tptp.i _let_4 _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mul))) (let ((_let_5 (tptp.s _let_3 tptp.intu_neg))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_2)))) (tptp.s tptp.int (tptp.i _let_5 _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_neg))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul) (tptp.s tptp.int X))))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_sub))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_neg) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (= (not (= _let_1 _let_2)) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_1)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_1)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_add) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (= (= (tptp.s tptp.int (tptp.i _let_3 _let_2)) (tptp.s tptp.int (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_ge) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.g_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_gt) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.g_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_le) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_lt) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_max) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.max) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_min) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.min) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_mul) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s _let_4 tptp.intu_ofu_num))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow) (tptp.s tptp.int (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0) _let_2)) _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) _let_1)) _let_2))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_sub) (tptp.s tptp.int (tptp.i _let_4 _let_2)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.m_) _let_2)) _let_1))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_add) (tptp.s tptp.int (tptp.i _let_3 _let_1)))) (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i _let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.int (tptp.i _let_1 (tptp.s tptp.num N0))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt) _let_1)) _let_2))) (not (= _let_2 _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) _let_3)))) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s _let_4 tptp.intu_ofu_num))) (let ((_let_6 (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_7 (tptp.s tptp.int X))) (let ((_let_8 (tptp.fun tptp.int tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.int _let_8) tptp.intu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_7)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow) _let_7)) (tptp.s tptp.num N0))))) _let_6)))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s _let_4 tptp.intu_ofu_num))) (let ((_let_6 (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_7 (tptp.s tptp.num N0))) (let ((_let_8 (tptp.s tptp.int X))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.fun tptp.int _let_9))) (let ((_let_11 (tptp.s _let_10 tptp.intu_lt))) (let ((_let_12 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (=> (and (not (= _let_7 _let_12)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.intu_le) (tptp.s tptp.int (tptp.i _let_5 _let_12)))) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_8)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow) _let_8)) _let_7)))) _let_6))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul) _let_1)) _let_1)))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.int))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_pow) (tptp.s tptp.int X))))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.p_) _let_4)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_mul) (tptp.s tptp.int (tptp.i _let_3 _let_4)))) (tptp.s tptp.int (tptp.i _let_3 _let_1)))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s _let_4 tptp.intu_ofu_num) _let_6)))))) (=> (and (not (= _let_3 _let_6)) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_1))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_3)))) (= _let_2 _let_1))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_ofu_num) _let_1)))) (let ((_let_5 (tptp.s tptp.int X))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow) _let_5)) _let_2)) _let_4) (and (= _let_5 _let_4) (not (= _let_2 _let_1)))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num tptp.int))) (let ((_let_6 (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_pow))) (=> (and (not (= _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) _let_4)))) (= (tptp.s tptp.int (tptp.i _let_2 _let_3)) (tptp.s tptp.int (tptp.i _let_2 _let_1))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.num tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_pow) _let_1)) (tptp.s tptp.num N0)))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.odd) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.int))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_pow))) (let ((_let_8 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (=> (and (not (= _let_5 _let_8)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 tptp.intu_ofu_num) _let_8)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.num tptp.int))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_pow) _let_1)) (tptp.s tptp.num N0))))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.num tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_pow) _let_1)) (tptp.s tptp.num N0)))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.s _let_7 tptp.intu_lt))) (let ((_let_9 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (=> (and (not (= _let_1 _let_9)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_ofu_num) _let_9)))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_5)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.intu_lt))) (let ((_let_6 (tptp.s tptp.num N0))) (let ((_let_7 (tptp.fun tptp.num tptp.int))) (let ((_let_8 (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_pow))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s _let_7 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6)))) (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s tptp.num tptp.u_0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 tptp.numeral))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.int _let_7) tptp.intu_lt) (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_4)))))))))) (=> (and (not (= _let_1 (tptp.s tptp.num (tptp.i _let_6 _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow) _let_2)) _let_1))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow) _let_2)))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i _let_4 _let_5)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow) _let_2)))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i _let_4 _let_5)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow))) (let ((_let_5 (tptp.s tptp.int X))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_mul))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow))) (let ((_let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.s _let_6 tptp.intu_neg))) (let ((_let_8 (tptp.fun tptp.int _let_6))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_7 _let_2)))) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) _let_1)))) _let_5)) (tptp.s tptp.int (tptp.i _let_7 _let_5)))))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.int))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s _let_1 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s tptp.int X))) (=> (not (= _let_3 _let_2)) (not (= (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.int _let_1) tptp.intu_pow) _let_3)) (tptp.s tptp.num N0))) _let_2))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.int))) (let ((_let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_pow) _let_3)) (tptp.s tptp.num N0))) _let_3))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int X))))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_6 _let_2)))) _let_1)) (tptp.s tptp.int (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1)))))))))))) (forall ((N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (let ((_let_5 (tptp.fun tptp.num tptp.int))) (let ((_let_6 (tptp.s _let_5 tptp.intu_ofu_num))) (let ((_let_7 (tptp.s tptp.int (tptp.i _let_6 _let_4)))) (let ((_let_8 (tptp.s tptp.bool V))) (let ((_let_9 (tptp.fun tptp.int tptp.int))) (let ((_let_10 (tptp.fun tptp.int _let_9))) (let ((_let_11 (tptp.s tptp.num N0))) (and (= (tptp.p _let_8) (= _let_11 _let_4)) (= (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_pow) _let_7)) _let_11)) (tptp.s tptp.int (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) _let_8)) (tptp.s tptp.int (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) _let_7))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s tptp.int Y))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_add) _let_1)) _let_3)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (let ((_let_6 (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (let ((_let_8 (tptp.s tptp.int X))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.int _let_9) tptp.intu_lt))) (let ((_let_11 (tptp.fun tptp.int _let_7))) (let ((_let_12 (tptp.s (tptp.fun tptp.bool _let_11) tptp.cond))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_7 tptp.intu_sgn) _let_8)) (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_5)) _let_8)))) _let_6)) (tptp.s tptp.int (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_8)) _let_5)))) (tptp.s tptp.int (tptp.i (tptp.s _let_7 tptp.intu_neg) _let_6)))) _let_5)))))))))))))))))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_84 tptp.intu_sgn) _let_83)) _let_83) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_sgn) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_abs) _let_1)))) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_6 tptp.intu_sgn) (tptp.s tptp.int X))))) (or (= _let_7 (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1))))) (= _let_7 _let_5) (= _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_6 tptp.intu_neg) _let_5)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.int X))) (= (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_sgn) _let_2)) _let_1) (= _let_2 _let_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_sgn) _let_6)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_gt) _let_6)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_5 (tptp.s (tptp.fun tptp.int tptp.real) tptp.realu_ofu_int))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_sgn) _let_6)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_neg) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt) _let_6)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_sgn))) (let ((_let_4 (tptp.s tptp.int X))) (let ((_let_5 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_mul))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.int (tptp.i _let_3 _let_4)))) (tptp.s tptp.int (tptp.i _let_3 _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 tptp.intu_sgn))) (let ((_let_4 (tptp.s _let_2 tptp.intu_neg))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i _let_4 _let_1)))) (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_3 _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.int))) (let ((_let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_4 tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (let ((_let_6 (tptp.s tptp.int Y))) (let ((_let_7 (tptp.s tptp.int X))) (let ((_let_8 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_9 (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_pow))) (let ((_let_10 (tptp.fun tptp.int tptp.int))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.int _let_10) tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_9 _let_7)) _let_8)))) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_9 _let_6)) _let_8)))) _let_5) (and (= _let_7 _let_5) (= _let_6 _let_5)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_sub) _let_2)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_2 _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_sub))) (let ((_let_5 (tptp.s _let_3 tptp.intu_abs))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_2)))) (tptp.s tptp.int (tptp.i _let_5 _let_1)))))) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_1)) _let_2)))) _let_2)) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_1)) _let_2)))) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_mul) (tptp.s tptp.int X))))) (let ((_let_5 (tptp.s tptp.int Y))) (let ((_let_6 (tptp.s _let_3 tptp.intu_sub))) (= (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.int (tptp.i _let_4 _let_5)))) (tptp.s tptp.int (tptp.i _let_4 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_sub) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_3 tptp.intu_neg))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) (tptp.s tptp.int (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_sub) _let_1)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_sub) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_sub))) (let ((_let_5 (tptp.s _let_3 tptp.intu_neg))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.int (tptp.i _let_5 _let_1)))) (tptp.s tptp.int (tptp.i _let_5 _let_2)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int Z0))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.intu_mul))) (let ((_let_6 (tptp.s tptp.int X))) (let ((_let_7 (tptp.s _let_4 tptp.intu_sub))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_sub) _let_1)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 tptp.intu_neg) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_2)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_sub) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_sub))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_3)) _let_1)))) _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_sub) (tptp.s tptp.int X))))) (= (tptp.s tptp.int (tptp.i _let_3 (tptp.s tptp.int (tptp.i _let_3 _let_1)))) _let_1))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int C0))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.intu_sub))) (let ((_let_5 (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.int A5))))) (let ((_let_6 (tptp.s tptp.int B0))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_add) (tptp.s tptp.int (tptp.i _let_5 _let_6)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_6)) _let_1)))) (tptp.s tptp.int (tptp.i _let_5 _let_1)))))))))) (forall ((P0 $$unsorted)) (= (forall ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.int tptp.bool) P0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num N0))))))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int I0))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))) (forall ((P0 $$unsorted)) (= (exists ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.int tptp.bool) P0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num N0))))))) (exists ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int I0))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))) (forall ((P0 $$unsorted)) (= (forall ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.int tptp.bool) P0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num N0))))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.int tptp.bool) P0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) (tptp.s tptp.int X))))))))) (forall ((P0 $$unsorted)) (= (exists ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.int tptp.bool) P0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num N0))))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.int tptp.bool) P0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.int tptp.int) tptp.intu_abs) (tptp.s tptp.int X))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.int Y))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.s _let_4 tptp.intu_abs))) (let ((_let_6 (tptp.s tptp.int X))) (= (= (tptp.s tptp.int (tptp.i _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_mul) _let_6)) _let_3)))) _let_2) (and (= (tptp.s tptp.int (tptp.i _let_5 _let_6)) _let_2) (= (tptp.s tptp.int (tptp.i _let_5 _let_3)) _let_2)))))))))) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.int X))) _let_1))))))))))))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_79 (tptp.i (tptp.s (tptp.fun tptp.int _let_79) tptp.intu_pow) _let_82)) _let_51)) _let_81) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.int tptp.x))) (let ((_let_3 (tptp.fun tptp.num tptp.int))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_pow) _let_2)))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.intu_mul) _let_2)) (tptp.s tptp.int (tptp.i _let_4 _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_2))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_abs) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.bool _let_4) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_ge) _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_gt) _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_lt) _let_1)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.intu_le) _let_2)) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s tptp.int X))) (let ((_let_4 (tptp.fun tptp.int _let_2))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.intu_sub) _let_3)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.intu_add) _let_3)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_neg) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.int Y))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_max) _let_1)) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le) _let_1)) _let_2)))) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_min) _let_2)) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le) _let_2)) _let_1)))) _let_2)) _let_1))))))))) (forall ((X $$unsorted) (D0 $$unsorted)) (=> (not (= (tptp.s tptp.int D0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (exists ((C0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_lt) (tptp.s tptp.int X))) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.int _let_1) tptp.intu_mul) (tptp.s tptp.int C0))) (tptp.s tptp.int D0))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (exists ((Q0 $$unsorted) (R0 $$unsorted) (V $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool V)) (and (= (tptp.s tptp.int Q0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= (tptp.s tptp.int R0) (tptp.s tptp.int M0)))) (exists ((VI_ $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool VI_)) (= (tptp.s tptp.int N0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (exists ((VI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_I_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.s tptp.int R0))) (let ((_let_5 (tptp.s tptp.int N0))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.fun tptp.int tptp.bool))) (let ((_let_9 (tptp.fun tptp.int _let_8))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.intu_lt) _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_6 tptp.intu_abs) _let_5))))) (= (tptp.s tptp.int M0) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_mul) (tptp.s tptp.int Q0))) _let_5)))) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) (tptp.s tptp.bool VI_))) (tptp.s tptp.bool V))) _let_1))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.int M0))) (let ((_let_2 (tptp.s tptp.int N0))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (and (= (tptp.p (tptp.s tptp.bool V)) (and (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.div0) _let_1)) _let_2)) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.rem) _let_1)) _let_2)) _let_1))) (exists ((VI_ $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool VI_)) (= (tptp.s tptp.int N0) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (exists ((VI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_I_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.s tptp.int N0))) (let ((_let_5 (tptp.s tptp.int M0))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.rem) _let_5)) _let_4)))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.fun tptp.int _let_9))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.intu_lt) _let_8)) (tptp.s tptp.int (tptp.i (tptp.s _let_6 tptp.intu_abs) _let_4))))) (= _let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_mul) (tptp.s tptp.int (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.div0) _let_5)) _let_4)))) _let_4)))) _let_8))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) (tptp.s tptp.bool VI_))) (tptp.s tptp.bool V))) _let_1)))))))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int N0))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.s tptp.int M0))) (let ((_let_4 (tptp.fun tptp.int _let_2))) (let ((_let_5 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.rem) _let_3)) _let_1)))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (=> (not (= _let_1 _let_8)) (and (= _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.intu_mul) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.div0) _let_3)) _let_1)))) _let_1)))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_le) _let_8)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_lt) _let_5)) (tptp.s tptp.int (tptp.i (tptp.s _let_2 tptp.intu_abs) _let_1)))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (Q0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int R0))) (let ((_let_2 (tptp.s tptp.int N0))) (let ((_let_3 (tptp.s tptp.int M0))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.s tptp.int Q0))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (=> (and (= _let_3 (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.intu_mul) _let_6)) _let_2)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.intu_lt) _let_1)) (tptp.s tptp.int (tptp.i (tptp.s _let_4 tptp.intu_abs) _let_2)))))) (and (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.div0) _let_3)) _let_2)) _let_6) (= (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.rem) _let_3)) _let_2)) _let_1)))))))))))) (forall ((A $$unsorted) (REL $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 REL))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun A _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.a_a_) _let_2)) _let_1)) _let_5)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mod) (tptp.s tptp.real N0))) (tptp.s tptp.real X))) (tptp.s tptp.real Y)))) (exists ((Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Q0))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) tptp.integer) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_sub) (tptp.s tptp.real X))) (tptp.s tptp.real Y))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_mul) _let_1)) (tptp.s tptp.real N0))))))))))))) (forall ((B0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.int _let_1) tptp.intu_divides) (tptp.s tptp.int A5))) (tptp.s tptp.int B0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.s tptp.int B0) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.int _let_1) tptp.intu_mul) (tptp.s tptp.int A5))) (tptp.s tptp.int X))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int Y))) (let ((_let_2 (tptp.s tptp.int X))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.s tptp.int N0))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_mod) _let_4)) _let_2)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.intu_divides) _let_4)) (tptp.s tptp.int (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_sub) _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int (tptp.fun tptp.int tptp.bool)))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.a_a_) (tptp.s tptp.int X))) (tptp.s tptp.int Y))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.int _let_1) tptp.intu_mod) (tptp.s tptp.int N0)))))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.intu_sub) (tptp.s tptp.int X))) (tptp.s tptp.int Y))) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.intu_mul) (tptp.s tptp.int N0))) (tptp.s tptp.int D0)))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.intu_coprime) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.c_) (tptp.s tptp.int A5))) (tptp.s tptp.int B0)))))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.intu_mul))) (= (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.int A5))) (tptp.s tptp.int X))))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.int B0))) (tptp.s tptp.int Y))))) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (M0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.int _let_1) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun A tptp.int) M0) (tptp.s A X)))))))) (forall ((X $$unsorted)) (=> (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s (tptp.fun A tptp.int) M0))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_lt) (tptp.s tptp.int (tptp.i _let_2 _let_1)))) (tptp.s tptp.int (tptp.i _let_2 (tptp.s A X)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))))) (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X))))))) (forall ((A $$unsorted) (B $$unsorted) (P0 $$unsorted) (M0 $$unsorted)) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) M0) (tptp.s A X))) (tptp.s B Y))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (=> (forall ((XI_ $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.s B YI_))) (let ((_let_2 (tptp.s A XI_))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun B tptp.int))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) M0))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_lt) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A X))) (tptp.s B Y)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) P0) _let_2)) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) P0) (tptp.s A X))) (tptp.s B Y)))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.int _let_1) tptp.intu_divides) (tptp.s tptp.int D0))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.int A5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s tptp.int B0)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.s _let_2 tptp.intu_mul))) (= (tptp.s tptp.int D0) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i _let_3 (tptp.s tptp.int A5))) (tptp.s tptp.int X))))) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i _let_3 (tptp.s tptp.int B0))) (tptp.s tptp.int Y))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int D0))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_divides) _let_1)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.int A5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.int B0)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.s _let_2 tptp.intu_mul))) (= (tptp.s tptp.int D0) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i _let_3 (tptp.s tptp.int A5))) (tptp.s tptp.int X))))) (tptp.s tptp.int (tptp.i (tptp.s _let_1 (tptp.i _let_3 (tptp.s tptp.int B0))) (tptp.s tptp.int Y))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int B0))) (let ((_let_2 (tptp.s tptp.int A5))) (let ((_let_3 (tptp.prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun _let_3 tptp.int) tptp.intu_gcd) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.c_) _let_2)) _let_1)))))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_divides) _let_5)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.intu_le) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_1))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.int B0))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.intu_mul))) (let ((_let_5 (tptp.s tptp.int A5))) (let ((_let_6 (tptp.prod tptp.int tptp.int))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun _let_6 tptp.int) tptp.intu_gcd) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.int _let_7) tptp.c_) _let_5)) _let_1)))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.intu_add) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_5)) (tptp.s tptp.int X))))) (tptp.s tptp.int (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) (tptp.s tptp.int Y)))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) U_0) _let_1)) _let_2))) (= (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) _let_2)) _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.int tptp.num) tptp.numu_ofu_int) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.h_) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.int _let_2) U_0) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.int tptp.num) tptp.numu_ofu_int) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num) _let_1)))) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le) (tptp.s tptp.int (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (= (tptp.s tptp.int (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.int tptp.num) tptp.numu_ofu_int) _let_1)))) _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.int X))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_le) (tptp.s tptp.int (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (= (tptp.s tptp.int (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.int tptp.num) tptp.numu_ofu_int) _let_1)))) _let_1)))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num B0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_3 (tptp.s tptp.num A5))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.numu_divides) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.int _let_4) tptp.intu_divides) (tptp.s tptp.int (tptp.i _let_2 _let_3)))) (tptp.s tptp.int (tptp.i _let_2 _let_1))))))))))) (forall ((N0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_3 (tptp.s tptp.num X))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.numu_mod) _let_4)) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.int _let_6) tptp.intu_mod) (tptp.s tptp.int (tptp.i _let_2 _let_4)))) (tptp.s tptp.int (tptp.i _let_2 _let_3)))) (tptp.s tptp.int (tptp.i _let_2 _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_3 (tptp.fun tptp.int (tptp.fun tptp.int tptp.bool)))) (let ((_let_4 (tptp.s tptp.num Y))) (let ((_let_5 (tptp.s tptp.num X))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.fun tptp.num (tptp.fun tptp.num tptp.bool)))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.a_a_) _let_5)) _let_4)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.numu_mod) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.int _let_7) tptp.a_a_) (tptp.s tptp.int (tptp.i _let_2 _let_5)))) (tptp.s tptp.int (tptp.i _let_2 _let_4)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.int _let_3) tptp.intu_mod) (tptp.s tptp.int (tptp.i _let_2 _let_1)))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num B0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_3 (tptp.s tptp.num A5))) (let ((_let_4 (tptp.prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.prod tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.numu_coprime) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.c_) _let_3)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.intu_coprime) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.c_) (tptp.s tptp.int (tptp.i _let_2 _let_3)))) (tptp.s tptp.int (tptp.i _let_2 _let_1))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num B0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_3 (tptp.s tptp.num A5))) (let ((_let_4 (tptp.prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.prod tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.numu_gcd) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.c_) _let_3)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.int tptp.num) tptp.numu_ofu_int) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun _let_4 tptp.int) tptp.intu_gcd) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.c_) (tptp.s tptp.int (tptp.i _let_2 _let_3)))) (tptp.s tptp.int (tptp.i _let_2 _let_1))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num B0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.int) tptp.intu_ofu_num))) (let ((_let_3 (tptp.s tptp.num A5))) (let ((_let_4 (tptp.prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.prod tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (= (tptp.s tptp.int (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.numu_gcd) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.c_) _let_3)) _let_1)))))) (tptp.s tptp.int (tptp.i (tptp.s (tptp.fun _let_4 tptp.int) tptp.intu_gcd) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.int _let_5) tptp.c_) (tptp.s tptp.int (tptp.i _let_2 _let_3)))) (tptp.s tptp.int (tptp.i _let_2 _let_1))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) _let_3)) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (= (tptp.s _let_1 S0) (tptp.s _let_1 T0)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 S0))) (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 T0))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) _let_2)) _let_2)))) (forall ((Q44069 $$unsorted) (P0 $$unsorted) (V $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.s Q44069 T0))) (let ((_let_2 (tptp.s Q44069 V))) (let ((_let_3 (tptp.s tptp.bool P0))) (let ((_let_4 (tptp.fun Q44069 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q44069 _let_5) tptp.setspec) _let_2)) _let_3)) _let_1))) (and (tptp.p _let_3) (= _let_2 _let_1))))))))) (forall ((Q44207 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q44207 Y))) (let ((_let_2 (tptp.fun Q44207 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))) (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q44207 X))) (let ((_let_2 (tptp.fun Q44207 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q44207 _let_4) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)))) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))) (forall ((Q44190 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun Q44190 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) (tptp.s _let_1 P0))) (tptp.s Q44190 V)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s Q44190 Y))) (let ((_let_2 (tptp.fun Q44190 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q44190 _let_3) tptp.setspec) (tptp.s Q44190 V))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))) _let_1)))))))))) (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q44190 X))) (let ((_let_2 (tptp.fun Q44190 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_4 U_0) _let_3)))) _let_1)) (tptp.s tptp.bool (tptp.i _let_3 _let_1)))))))))) (forall ((Q44161 $$unsorted) (U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.s Q44161 T0))) (let ((_let_2 (tptp.s Q44161 X))) (let ((_let_3 (tptp.s tptp.bool P0))) (let ((_let_4 (tptp.fun Q44161 tptp.bool))) (let ((_let_5 (tptp.fun Q44161 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) U_2) _let_3)) _let_2)) _let_1))) (and (tptp.p _let_3) (= _let_2 _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((X $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s Q44161 X))) (let ((_let_2 (tptp.s tptp.bool P0))) (let ((_let_3 (tptp.fun Q44161 tptp.bool))) (let ((_let_4 (tptp.fun Q44161 _let_3))) (let ((_let_5 (tptp.fun tptp.bool _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q44161 _let_5) U_1) _let_1)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.bool _let_4) U_2) _let_2)) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q44161 V))) (let ((_let_2 (tptp.fun Q44161 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) U_0) _let_5)) _let_1)) (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q44161 _let_3) tptp.setspec) _let_1))))))))))) (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q44161 X))) (let ((_let_2 (tptp.fun Q44161 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) U_0) _let_5)))) _let_1)) (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q44161 _let_3) U_1) _let_1))))))))))))))))) (forall ((Q44133 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun Q44133 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) (tptp.s _let_1 P0))) (tptp.s Q44133 V)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s Q44133 Y))) (let ((_let_2 (tptp.fun Q44133 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q44133 _let_3) tptp.setspec) (tptp.s Q44133 V))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))) _let_1)))))))))) (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q44133 X))) (let ((_let_2 (tptp.fun Q44133 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q44133 _let_5) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_4 U_0) _let_3)))))) (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((Q44102 $$unsorted) (U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.s Q44102 T0))) (let ((_let_2 (tptp.s Q44102 X))) (let ((_let_3 (tptp.s tptp.bool P0))) (let ((_let_4 (tptp.fun Q44102 tptp.bool))) (let ((_let_5 (tptp.fun Q44102 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) U_2) _let_3)) _let_2)) _let_1))) (and (tptp.p _let_3) (= _let_2 _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((X $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s Q44102 X))) (let ((_let_2 (tptp.s tptp.bool P0))) (let ((_let_3 (tptp.fun Q44102 tptp.bool))) (let ((_let_4 (tptp.fun Q44102 _let_3))) (let ((_let_5 (tptp.fun tptp.bool _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q44102 _let_5) U_1) _let_1)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.bool _let_4) U_2) _let_2)) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q44102 V))) (let ((_let_2 (tptp.fun Q44102 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) U_0) _let_5)) _let_1)) (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q44102 _let_3) tptp.setspec) _let_1))))))))))) (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q44102 X))) (let ((_let_2 (tptp.fun Q44102 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q44102 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) U_0) _let_5)))))) (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q44102 _let_3) U_1) _let_1)))))))))))))))))) (forall ((A $$unsorted) (X $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) tptp.empty) (tptp.s A X))) (tptp.s tptp.bool tptp.f0))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A XI_))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.insert) _let_1)) _let_4)) _let_2))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) _let_4))) (= _let_2 _let_1)))))))))) (forall ((A $$unsorted) (X $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) tptp.univ) (tptp.s A X))) (tptp.s tptp.bool tptp.t))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 T0))) (tptp.s A GENR_PVARR_0)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)))) (and (= (tptp.p _let_2) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_0))) _let_2)) _let_1))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.union) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_2))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_1 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_0) (tptp.s _let_2 S0))) (tptp.s A GENR_PVARR_1)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (exists ((U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A X))) _let_2)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.setspec) (tptp.s A GENR_PVARR_1))) _let_1)) (tptp.s A X))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.unions) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_4 U_0) _let_3)))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_2 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 T0))) (tptp.s A GENR_PVARR_2)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_2))) _let_2)) _let_1))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.inter) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_2))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_3 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_0) (tptp.s _let_2 S0))) (tptp.s A GENR_PVARR_3)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (forall ((U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A X))) _let_2)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.setspec) (tptp.s A GENR_PVARR_3))) _let_1)) (tptp.s A X))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.inters) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_4 U_0) _let_3)))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_4 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 T0))) (tptp.s A GENR_PVARR_4)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 S0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 T0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_4))) _let_2)) _let_1))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.diff) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_2))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (forall ((GENR_PVARR_5 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) U_0) (tptp.s A GENR_PVARR_5)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 tptp.s0)))) (= _let_1 (tptp.s A tptp.x)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_5))) _let_2)) _let_1)))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.insert) (tptp.s A tptp.x))) (tptp.s _let_1 tptp.s0))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.gspec) (tptp.s _let_1 U_0)))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (X $$unsorted) (GENR_PVARR_6 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s A X))) (tptp.s A GENR_PVARR_6)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (not (= _let_1 (tptp.s A X))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_6))) _let_2)) _let_1)))))))))))))) (forall ((S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.delete) _let_3)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_1))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 S0))) (tptp.s _let_1 T0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 T0))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.psubset) _let_3)) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.subset) _let_3)) _let_2))) (not (= _let_3 _let_2)))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.disjoint) _let_3)) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inter) _let_3)) _let_2)) (tptp.s _let_1 tptp.empty))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.sing) (tptp.s _let_1 S0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 S0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.insert) (tptp.s A X))) (tptp.s _let_1 tptp.empty)))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 tptp.empty)))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.insert) (tptp.s A X))) _let_2))))))))))) (forall ((A $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 A5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (or (= _let_2 (tptp.s _let_1 tptp.empty)) (exists ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (and (= (tptp.s _let_1 A5) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.insert) (tptp.s A X))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))))))))))))) (forall ((A $$unsorted) (FINITEI_ $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) FINITEI_) (tptp.s _let_1 tptp.empty)))) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) FINITEI_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.insert) (tptp.s A X))) _let_2)))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 FINITEI_) _let_2))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.infinite) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_7 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B GENR_PVARR_7)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B Y) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.setspec) (tptp.s B GENR_PVARR_7))) _let_1)) (tptp.s B Y))))))))))))))) (forall ((S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.image) _let_2)) _let_4)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_2))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (T0 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.inj) (tptp.s _let_3 F0))) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (T0 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.surj) (tptp.s _let_3 F0))) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B X))) (tptp.s _let_1 T0)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B X))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun A B))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_5 _let_8))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.bij) _let_6)) _let_4)) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.inj) _let_6)) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.surj) _let_6)) _let_4)) _let_2))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_3)) _let_2)))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 A))) (= (tptp.s A (tptp.i (tptp.s _let_3 tptp.choice0) _let_2)) (tptp.s A (tptp.i (tptp.s _let_3 tptp.h_) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.rest) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.delete) _let_2)) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.choice0) _let_2))))))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 tptp.empty)))))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 tptp.univ))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A X))))) (let ((_let_5 (tptp.s _let_1 S0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.union) _let_5)) _let_2))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 S0)))))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A X))) _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A X))))) (let ((_let_5 (tptp.s _let_1 S0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.inter) _let_5)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 S0)))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A X))) _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A X))))) (let ((_let_5 (tptp.s _let_1 S0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.diff) _let_5)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_3)))) (let ((_let_6 (tptp.s A Y))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.insert) _let_6)) _let_2))))) (or (= _let_3 _let_6) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)))) (let ((_let_7 (tptp.fun A _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.delete) _let_4)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_4))) (not (= _let_2 _let_1)))))))))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) _let_1)) (tptp.s _let_3 tptp.empty)))))) (= _let_2 _let_1)))))))) (forall ((B $$unsorted) (A $$unsorted) (Y $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) (tptp.s B Y))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 S0)))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (and (= (tptp.s B Y) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_2)) (tptp.s _let_1 S0)))))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_3)))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.rest) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (not (= _let_3 (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.choice0) _let_2)))))))))))) (forall ((Q45021 $$unsorted) (P0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q45021 X))) (let ((_let_2 (tptp.fun Q45021 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q45021 _let_4) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q45021 _let_3) tptp.insert) (tptp.s Q45021 A5))) (tptp.s _let_2 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q45021 tptp.bool) P0) (tptp.s Q45021 A5)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q45021 X))) (let ((_let_2 (tptp.fun Q45021 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q45021 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))))) (forall ((Q45062 $$unsorted) (P0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q45062 X))) (let ((_let_2 (tptp.fun Q45062 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q45062 _let_4) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q45062 _let_3) tptp.insert) (tptp.s Q45062 A5))) (tptp.s _let_2 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q45062 tptp.bool) P0) (tptp.s Q45062 A5)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q45062 X))) (let ((_let_2 (tptp.fun Q45062 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q45062 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (not (= _let_2 (tptp.s _let_1 tptp.empty))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_1 A) tptp.choice0) _let_2)))) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (not (= (tptp.s _let_1 S0) (tptp.s _let_1 T0))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 T0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 S0))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 S0))))))) (not (= (tptp.s _let_1 S0) (tptp.s _let_1 tptp.empty)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (not (= (tptp.s _let_1 tptp.univ) (tptp.s _let_1 tptp.empty))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (not (= (tptp.s _let_1 tptp.empty) (tptp.s _let_1 tptp.univ))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 tptp.s0))))))) (= (tptp.s _let_1 tptp.s0) (tptp.s _let_1 tptp.univ))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.subset))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 S0))))) (let ((_let_6 (tptp.s _let_1 T0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) _let_2))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)))) (= _let_3 _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)))) (= _let_3 _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 tptp.empty))) (tptp.s _let_1 S0))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)) _let_2))) (= _let_3 _let_2))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.univ))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.univ))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) _let_3))) (= _let_3 _let_2))))))) (forall ((Q45300 $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q45300 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s Q45300 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q45300 _let_5) tptp.insert) _let_3)) (tptp.s _let_1 tptp.empty))))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q45300 _let_4) tptp.in) _let_3)) _let_2))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.psubset))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 S0))))) (let ((_let_6 (tptp.s _let_1 T0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.psubset) (tptp.s _let_1 S0))))) (let ((_let_6 (tptp.s _let_1 T0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.subset) _let_6)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.psubset))) (let ((_let_7 (tptp.s _let_1 T0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.subset) _let_3)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.psubset) _let_2)) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.psubset) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.empty)))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.psubset) (tptp.s _let_1 tptp.univ))) (tptp.s _let_1 S0)))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.psubset) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.univ)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 S0)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.psubset) _let_3)) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.subset) _let_3)) _let_2))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A A5))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 T0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 S0)))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.union))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 S0))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) _let_2)) _let_2)) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.union))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) _let_2)) (tptp.s _let_1 T0))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) (tptp.s _let_1 T0))) _let_2)))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) _let_3)) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.union) _let_3)) _let_2)) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) (tptp.s _let_1 tptp.empty))) _let_2)) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) _let_2)) (tptp.s _let_1 tptp.empty))) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.univ))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) _let_2)) (tptp.s _let_1 S0))) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.univ))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) (tptp.s _let_1 S0))) _let_2)) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.union) _let_4)) _let_3)) _let_2) (and (= _let_4 _let_2) (= _let_3 _let_2))))))))) (forall ((Q45668 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun Q45668 tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.s _let_1 S0))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.union) _let_6)) _let_3)))) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.inter))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 S0))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) _let_2)) _let_2)) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.inter))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) _let_2)) (tptp.s _let_1 T0))))) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) (tptp.s _let_1 T0))) _let_2)))) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) _let_2)) _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inter) _let_2)) _let_3)) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) _let_2)) (tptp.s _let_1 S0))) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) (tptp.s _let_1 S0))) _let_2)) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) (tptp.s _let_1 tptp.univ))) _let_2)) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) _let_2)) (tptp.s _let_1 tptp.univ))) _let_2))))) (forall ((Q45857 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun Q45857 tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) (tptp.s _let_1 S0))))) (let ((_let_5 (tptp.s _let_1 T0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.inter) _let_5)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.inter) (tptp.s _let_1 S0))))) (let ((_let_6 (tptp.s _let_1 T0))) (let ((_let_7 (tptp.s _let_4 tptp.union))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_5 _let_6)))) (tptp.s _let_1 (tptp.i _let_5 _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.union) (tptp.s _let_1 S0))))) (let ((_let_6 (tptp.s _let_1 T0))) (let ((_let_7 (tptp.s _let_4 tptp.inter))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_5 _let_6)))) (tptp.s _let_1 (tptp.i _let_5 _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.disjoint) (tptp.s _let_1 S0))) (tptp.s _let_1 T0)))) (not (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 T0)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.disjoint))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.disjoint))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (= _let_2 (tptp.s _let_1 tptp.empty)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.disjoint) _let_2)) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.disjoint))) (let ((_let_6 (tptp.s _let_1 S0))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.union) _let_6)) _let_3)))) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) _let_2)) (tptp.s _let_1 tptp.empty))) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) _let_2)) (tptp.s _let_1 S0))) _let_2))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.diff) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.univ))) (tptp.s _let_1 tptp.empty))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.diff))) (let ((_let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 S0))) _let_2)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_2)) _let_5))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) _let_2)) _let_2)) (tptp.s _let_1 tptp.empty)))))) (forall ((Q46115 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q46115 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) _let_2)) (tptp.s _let_1 T0))))) _let_2)))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.insert) _let_2)) (tptp.s _let_1 S0))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 S0)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (and (= (tptp.s _let_1 S0) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.insert) _let_3)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_3)) _let_2))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (or (= (tptp.s _let_1 S0) (tptp.s _let_1 tptp.empty)) (exists ((X $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (and (= (tptp.s _let_1 S0) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.insert) _let_3)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_3)) _let_2)))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_3)) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) _let_3)) _let_2)) _let_2)))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.insert) (tptp.s A X))))) (let ((_let_4 (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 S0))))) (= (tptp.s _let_1 (tptp.i _let_3 _let_4)) _let_4)))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.insert))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A X))))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A Y))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.univ))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.insert) (tptp.s A X))) _let_2)) _let_2))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (not (= (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.insert) (tptp.s A X))) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.empty)))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (not (= (tptp.s _let_1 tptp.empty) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.insert) (tptp.s A X))) (tptp.s _let_1 S0)))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.union))) (let ((_let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))) (let ((_let_8 (tptp.s A X))) (let ((_let_9 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) _let_8)))) (let ((_let_10 (tptp.fun _let_1 tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_9 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun A _let_10) tptp.in) _let_8)) _let_2)))) _let_7)) (tptp.s _let_1 (tptp.i _let_9 _let_7)))))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.union))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) (tptp.s A X))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.inter))) (let ((_let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))) (let ((_let_8 (tptp.s A X))) (let ((_let_9 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) _let_8)))) (let ((_let_10 (tptp.fun _let_1 tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_9 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun A _let_10) tptp.in) _let_8)) _let_2)))) (tptp.s _let_1 (tptp.i _let_9 _let_7)))) _let_7)))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_1 S0))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_4) tptp.disjoint))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.insert) _let_3)) _let_5)))) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_5)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_3)) _let_2)))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.s A X))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.insert) _let_6)) _let_3)))) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 S0))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) (tptp.s _let_1 S0))))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.insert) (tptp.s A X))) _let_2)))) (tptp.s tptp.bool (tptp.i _let_4 _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.diff))) (let ((_let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))) (let ((_let_8 (tptp.s A X))) (let ((_let_9 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) _let_8)))) (let ((_let_10 (tptp.fun _let_1 tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_9 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun A _let_10) tptp.in) _let_8)) _let_2)))) _let_7)) (tptp.s _let_1 (tptp.i _let_9 _let_7)))))))))))))))) (forall ((Q46571 $$unsorted)) (let ((_let_1 (tptp.fun Q46571 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun Q46571 _let_3) tptp.insert))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s Q46571 tptp.x))))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 (tptp.s Q46571 tptp.y))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))) (forall ((Q46571 $$unsorted)) (let ((_let_1 (tptp.fun Q46571 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q46571 _let_2) tptp.insert) (tptp.s Q46571 tptp.x))))) (let ((_let_4 (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 tptp.s0))))) (= (tptp.s _let_1 (tptp.i _let_3 _let_4)) _let_4)))))) (forall ((Q46638 $$unsorted)) (let ((_let_1 (tptp.fun Q46638 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.p1))) (let ((_let_3 (tptp.s _let_1 tptp.q))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.inter))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q46638 $$unsorted)) (let ((_let_1 (tptp.fun Q46638 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.r0))) (let ((_let_3 (tptp.s _let_1 tptp.q))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.inter))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 tptp.p1))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((Q46638 $$unsorted)) (let ((_let_1 (tptp.fun Q46638 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.r0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.inter))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 tptp.p1))))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 tptp.q))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))) (forall ((Q46638 $$unsorted)) (let ((_let_1 (tptp.fun Q46638 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.p1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) _let_2)) _let_2)) _let_2))))) (forall ((Q46638 $$unsorted)) (let ((_let_1 (tptp.fun Q46638 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.inter) (tptp.s _let_1 tptp.p1))))) (let ((_let_4 (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 tptp.q))))) (= (tptp.s _let_1 (tptp.i _let_3 _let_4)) _let_4)))))) (forall ((Q46704 $$unsorted)) (let ((_let_1 (tptp.fun Q46704 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.p1))) (let ((_let_3 (tptp.s _let_1 tptp.q))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.union))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q46704 $$unsorted)) (let ((_let_1 (tptp.fun Q46704 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.r0))) (let ((_let_3 (tptp.s _let_1 tptp.q))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.union))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 tptp.p1))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((Q46704 $$unsorted)) (let ((_let_1 (tptp.fun Q46704 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.r0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.union))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 tptp.p1))))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 tptp.q))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))) (forall ((Q46704 $$unsorted)) (let ((_let_1 (tptp.fun Q46704 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.p1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) _let_2)) _let_2)) _let_2))))) (forall ((Q46704 $$unsorted)) (let ((_let_1 (tptp.fun Q46704 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.union) (tptp.s _let_1 tptp.p1))))) (let ((_let_4 (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 tptp.q))))) (= (tptp.s _let_1 (tptp.i _let_3 _let_4)) _let_4)))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun A _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_3)) _let_2)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.delete) _let_2)) _let_3)) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.delete) _let_3)))) (let ((_let_6 (tptp.s A XI_))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 _let_6)))) (let ((_let_10 (tptp.s _let_7 (tptp.i _let_8 _let_1)))) (= (= (tptp.s tptp.bool (tptp.i _let_10 _let_3)) (tptp.s tptp.bool (tptp.i _let_9 _let_3))) (= (tptp.s tptp.bool (tptp.i _let_10 (tptp.s _let_2 (tptp.i _let_5 _let_6)))) (tptp.s tptp.bool (tptp.i _let_9 (tptp.s _let_2 (tptp.i _let_5 _let_1))))))))))))))))) (forall ((A $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.fun A _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.delete) _let_2)) (tptp.s A X))) _let_2))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_3) tptp.delete))) (let ((_let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 S0))) _let_1)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1)) _let_5))))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun _let_3 _let_4) tptp.delete))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 S0))))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 (tptp.i _let_6 _let_1)))) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 (tptp.i _let_6 _let_2)))) _let_1)))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.delete) _let_2)) (tptp.s A X))))) _let_2)))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)))) (let ((_let_6 (tptp.s A X))) (let ((_let_7 (tptp.fun A _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.delete) _let_2)) _let_6))))) (and (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_6)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun A _let_1))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.subset))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) tptp.insert) _let_3)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.delete) _let_4)) _let_3)))) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun A _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.diff))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.insert) _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.delete) _let_4)) _let_3)))) _let_2))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.psubset) (tptp.s _let_1 S0))) (tptp.s _let_1 T0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (and (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_3)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) _let_3)) _let_2)))) (tptp.s _let_1 T0))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.psubset) _let_3)) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.subset) _let_3)) _let_2))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A Y))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 T0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 S0)))))))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.delete))) (let ((_let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)))) (let ((_let_7 (tptp.s A X))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) tptp.insert) _let_7)))) (let ((_let_10 (tptp.s tptp.bool V))) (let ((_let_11 (tptp.fun _let_2 _let_8))) (and (= (tptp.p _let_10) (= _let_7 _let_1)) (= (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_2 (tptp.i _let_9 _let_3)))) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.bool _let_11) tptp.cond) _let_10)) _let_6)) (tptp.s _let_2 (tptp.i _let_9 _let_6))))))))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun A _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_3)) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.insert) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.delete) _let_2)) _let_3)))) _let_2))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.s _let_2 S0))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_2 _let_5) tptp.inter))) (let ((_let_7 (tptp.fun A _let_2))) (let ((_let_8 (tptp.s (tptp.fun _let_2 _let_7) tptp.delete))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_1)))) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3)))) _let_1)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.s _let_1 T0))) (let ((_let_5 (tptp.fun A _let_1))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.delete))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.disjoint))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_3)))) _let_4)) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3)))) _let_2)))))))))))) (forall ((Q47111 $$unsorted)) (let ((_let_1 (tptp.fun Q47111 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 tptp.empty))) (tptp.s _let_1 tptp.empty))))) (forall ((Q47117 $$unsorted)) (let ((_let_1 (tptp.fun Q47117 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.unions) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) _let_2)) (tptp.s _let_3 tptp.empty))))) _let_2)))))) (forall ((Q47137 $$unsorted)) (let ((_let_1 (tptp.fun Q47137 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.s _let_1 tptp.s0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.insert))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_5 _let_1) tptp.unions) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s _let_5 tptp.empty))))))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.union) _let_3)) _let_2))))))))))) (forall ((Q47151 $$unsorted)) (let ((_let_1 (tptp.fun Q47151 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.u))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_1) tptp.unions))) (let ((_let_5 (tptp.s _let_1 tptp.s0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.insert) _let_5)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.union) _let_5)) (tptp.s _let_1 (tptp.i _let_4 _let_3))))))))))))) (forall ((Q47193 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q47193 X))) (let ((_let_2 (tptp.fun Q47193 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q47193 _let_3) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.unions) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))) (forall ((T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q47193 X))) (let ((_let_2 (tptp.fun Q47193 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q47193 _let_4) tptp.in) _let_1)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))))))) (forall ((Q47235 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q47235 X))) (let ((_let_2 (tptp.fun Q47235 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q47235 _let_3) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.unions) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))) (exists ((T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q47235 X))) (let ((_let_2 (tptp.fun Q47235 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q47235 _let_4) tptp.in) _let_1)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))))))) (forall ((Q47261 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q47261 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 S0))) (tptp.s _let_1 tptp.empty)) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47261 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= _let_2 (tptp.s _let_1 tptp.empty)))))))))))) (forall ((Q47300 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_8 $$unsorted)) (let ((_let_1 (tptp.fun Q47300 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_8)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun Q47300 tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.setspec) (tptp.s _let_1 GENR_PVARR_8))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) _let_2)) (tptp.s _let_1 T0)))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47300 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_1) tptp.unions))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.inter) (tptp.s _let_1 (tptp.i _let_6 _let_4)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2))))))))))))))))) (forall ((Q47336 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_9 $$unsorted)) (let ((_let_1 (tptp.fun Q47336 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_9)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun Q47336 tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.setspec) (tptp.s _let_1 GENR_PVARR_9))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inter) (tptp.s _let_1 T0))) _let_2))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47336 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_1) tptp.unions))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.inter) _let_2)) (tptp.s _let_1 (tptp.i _let_6 _let_4)))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2))))))))))))))))) (forall ((Q47352 $$unsorted) (F0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47352 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 F0))))) (tptp.s _let_1 T0)))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q47352 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 T0)))))))))))))) (forall ((Q47385 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun Q47385 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_1) tptp.unions))) (let ((_let_5 (tptp.s _let_2 F0))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.subset) _let_5)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_3))))))))))))) (forall ((Q47409 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47409 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_1) tptp.unions))) (let ((_let_5 (tptp.s _let_2 S0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.union) _let_5)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.union) (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_3))))))))))))) (forall ((Q47433 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47433 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_1) tptp.inters))) (let ((_let_5 (tptp.s _let_2 S0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.union) _let_5)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.inter) (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_3))))))))))))) (forall ((Q47464 $$unsorted)) (let ((_let_1 (tptp.fun Q47464 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun _let_2 _let_1) tptp.unions))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q47464 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.in) (tptp.s _let_1 X))) (tptp.s _let_2 tptp.s0)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q47464 tptp.bool))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 tptp.t0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) (tptp.s _let_1 X))) _let_2)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_2 tptp.s0))))) (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_2 tptp.t0))))))))))) (forall ((Q47492 $$unsorted) (Q47481 $$unsorted)) (let ((_let_1 (tptp.fun Q47481 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun Q47492 tptp.bool))) (let ((_let_4 (tptp.fun Q47481 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.image))) (let ((_let_8 (tptp.s (tptp.fun _let_5 _let_3) tptp.unions))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q47481 X))) (let ((_let_2 (tptp.fun Q47492 tptp.bool))) (let ((_let_3 (tptp.fun Q47481 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun Q47481 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q47481 _let_6) tptp.in) _let_1)) (tptp.s _let_5 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.subset) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.f) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.g) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.subset) (tptp.s _let_3 (tptp.i _let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 tptp.f))) _let_2)))))) (tptp.s _let_3 (tptp.i _let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 tptp.g))) _let_2))))))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 tptp.empty))) (tptp.s _let_1 tptp.univ))))) (forall ((Q47510 $$unsorted)) (let ((_let_1 (tptp.fun Q47510 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.inters) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) _let_2)) (tptp.s _let_3 tptp.empty))))) _let_2)))))) (forall ((Q47530 $$unsorted)) (let ((_let_1 (tptp.fun Q47530 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.s _let_1 tptp.s0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.insert))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_5 _let_1) tptp.inters) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s _let_5 tptp.empty))))))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inter) _let_3)) _let_2))))))))))) (forall ((Q47544 $$unsorted)) (let ((_let_1 (tptp.fun Q47544 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.u))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_1) tptp.inters))) (let ((_let_5 (tptp.s _let_1 tptp.s0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.insert) _let_5)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.inter) _let_5)) (tptp.s _let_1 (tptp.i _let_4 _let_3))))))))))))) (forall ((Q47560 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q47560 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 S0))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 F0)))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47560 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) (tptp.s _let_1 S0))) _let_2))))))))))))) (forall ((Q47598 $$unsorted) (Q47602 $$unsorted)) (let ((_let_1 (tptp.fun Q47602 tptp.bool))) (let ((_let_2 (tptp.fun Q47598 tptp.bool))) (let ((_let_3 (tptp.fun Q47598 Q47602))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 tptp.f))) (tptp.s _let_2 tptp.empty))) (tptp.s _let_1 tptp.empty))))))) (forall ((Q47602 $$unsorted) (Q47598 $$unsorted)) (let ((_let_1 (tptp.fun Q47598 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun Q47598 Q47602))) (let ((_let_4 (tptp.s _let_3 tptp.f))) (let ((_let_5 (tptp.fun Q47602 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.image) _let_4)))) (let ((_let_8 (tptp.s Q47598 tptp.x))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q47598 _let_10) tptp.insert) _let_8)) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q47602 _let_9) tptp.insert) (tptp.s Q47602 (tptp.i _let_4 _let_8)))) (tptp.s _let_5 (tptp.i _let_7 _let_2)))))))))))))))) (forall ((Q47636 $$unsorted) (Q47625 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47625 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q47625 Q47636))) (let ((_let_4 (tptp.fun Q47636 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))))) (let ((_let_7 (tptp.s _let_1 S0))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.union) _let_7)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.union) (tptp.s _let_4 (tptp.i _let_6 _let_7)))) (tptp.s _let_4 (tptp.i _let_6 _let_2))))))))))))))) (forall ((Q47649 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q47649 X))) (= (tptp.s Q47649 (tptp.i (tptp.s (tptp.fun Q47649 Q47649) U_0) _let_1)) _let_1))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q47649 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q47649 Q47649))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 U_0))) _let_2)) _let_2)))))))) (forall ((Q47663 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q47663 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q47663 Q47663))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 tptp.i1))) _let_2)) _let_2)))))) (forall ((Q47692 $$unsorted) (Q47696 $$unsorted) (Q47687 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q47687 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q47687 Q47696))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun Q47696 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun Q47696 Q47692))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun Q47692 tptp.bool))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.fun Q47687 Q47692))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun _let_1 _let_9))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.image) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_7 _let_12) tptp.o) _let_8)) _let_4)))) _let_2)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.image) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.image) _let_4)) _let_2))))))))))))))))))) (forall ((Q47725 $$unsorted) (Q47714 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47714 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q47714 Q47725))) (let ((_let_4 (tptp.fun Q47725 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))))) (let ((_let_7 (tptp.s _let_1 S0))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.subset) _let_7)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.subset) (tptp.s _let_4 (tptp.i _let_6 _let_7)))) (tptp.s _let_4 (tptp.i _let_6 _let_2)))))))))))))))) (forall ((Q47779 $$unsorted) (Q47768 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47768 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q47768 Q47779))) (let ((_let_4 (tptp.fun Q47779 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))))) (let ((_let_7 (tptp.s _let_1 S0))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q47768 Y))) (let ((_let_2 (tptp.s Q47768 X))) (let ((_let_3 (tptp.s (tptp.fun Q47768 Q47779) F0))) (=> (= (tptp.s Q47779 (tptp.i _let_3 _let_2)) (tptp.s Q47779 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.inter) _let_7)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.inter) (tptp.s _let_4 (tptp.i _let_6 _let_7)))) (tptp.s _let_4 (tptp.i _let_6 _let_2)))))))))))))))) (forall ((Q47833 $$unsorted) (Q47822 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q47822 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q47822 Q47833))) (let ((_let_4 (tptp.fun Q47833 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))))) (let ((_let_7 (tptp.s _let_1 S0))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q47822 Y))) (let ((_let_2 (tptp.s Q47822 X))) (let ((_let_3 (tptp.s (tptp.fun Q47822 Q47833) F0))) (=> (= (tptp.s Q47833 (tptp.i _let_3 _let_2)) (tptp.s Q47833 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.diff) _let_7)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.diff) (tptp.s _let_4 (tptp.i _let_6 _let_7)))) (tptp.s _let_4 (tptp.i _let_6 _let_2)))))))))))))))) (forall ((Q47879 $$unsorted) (Q47880 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q47880 A5))) (let ((_let_2 (tptp.fun Q47880 Q47879))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q47880 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun Q47879 tptp.bool))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.image) _let_3)))) (let ((_let_9 (tptp.fun Q47879 _let_6))) (let ((_let_10 (tptp.fun Q47880 _let_4))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q47880 A5))) (let ((_let_2 (tptp.s Q47880 X))) (let ((_let_3 (tptp.s (tptp.fun Q47880 Q47879) F0))) (=> (= (tptp.s Q47879 (tptp.i _let_3 _let_2)) (tptp.s Q47879 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (= (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.delete) _let_5)) _let_1)))) (tptp.s _let_6 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.delete) (tptp.s _let_6 (tptp.i _let_8 _let_5)))) (tptp.s Q47879 (tptp.i _let_3 _let_1))))))))))))))))) (forall ((Q47899 $$unsorted) (Q47903 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q47903 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q47899 tptp.bool))) (let ((_let_4 (tptp.fun Q47903 Q47899))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (= (= (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.image) (tptp.s _let_4 F0))) _let_2)) (tptp.s _let_3 tptp.empty)) (= _let_2 (tptp.s _let_1 tptp.empty))))))))) (forall ((Q47938 $$unsorted) (Q47939 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (= (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q47938 Y))) (let ((_let_2 (tptp.fun Q47938 tptp.bool))) (let ((_let_3 (tptp.fun Q47939 tptp.bool))) (let ((_let_4 (tptp.fun Q47939 Q47938))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q47938 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.image) (tptp.s _let_4 F0))) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q47939 X))) (let ((_let_2 (tptp.fun Q47939 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q47939 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q47938 tptp.bool) tptp.p0) (tptp.s Q47938 (tptp.i (tptp.s (tptp.fun Q47939 Q47938) F0) _let_1)))))))))))) (forall ((Q47974 $$unsorted) (Q47975 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (= (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s Q47974 Y))) (let ((_let_2 (tptp.fun Q47974 tptp.bool))) (let ((_let_3 (tptp.fun Q47975 tptp.bool))) (let ((_let_4 (tptp.fun Q47975 Q47974))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q47974 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.image) (tptp.s _let_4 F0))) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1))))))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q47975 X))) (let ((_let_2 (tptp.fun Q47975 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q47975 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q47974 tptp.bool) tptp.p0) (tptp.s Q47974 (tptp.i (tptp.s (tptp.fun Q47975 Q47974) F0) _let_1)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.subset) (tptp.s _let_3 S0))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 T0)))))) (exists ((U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_2)) (tptp.s _let_1 T0)))) (= (tptp.s _let_4 S0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))))))))))))))))) (forall ((Q48078 $$unsorted) (Q48062 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (= (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q48078 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q48062 tptp.bool))) (let ((_let_5 (tptp.fun Q48062 Q48078))) (let ((_let_6 (tptp.fun _let_4 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.image) (tptp.s _let_5 F0))) (tptp.s _let_4 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q48062 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q48062 Q48078))) (let ((_let_4 (tptp.fun Q48078 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2))))))))))))))) (forall ((Q48121 $$unsorted) (Q48105 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (= (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q48121 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q48105 tptp.bool))) (let ((_let_5 (tptp.fun Q48105 Q48121))) (let ((_let_6 (tptp.fun _let_4 _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.image) (tptp.s _let_5 F0))) (tptp.s _let_4 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q48105 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q48105 Q48121))) (let ((_let_4 (tptp.fun Q48121 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2))))))))))))))) (forall ((Q48147 $$unsorted) (Q48152 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q48152 C0))) (let ((_let_2 (tptp.fun Q48147 Q48152))) (= (tptp.s Q48152 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q48152 _let_2) U_0) _let_1)) (tptp.s Q48147 X))) _let_1)))) (forall ((S0 $$unsorted) (C0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q48152 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.s Q48152 C0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_1 _let_4))) (let ((_let_7 (tptp.fun Q48147 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun Q48147 Q48152))) (let ((_let_10 (tptp.fun _let_7 _let_1))) (and (= (tptp.p _let_5) (= _let_8 (tptp.s _let_7 tptp.empty))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_9 _let_10) tptp.image) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q48152 _let_9) U_0) _let_3)))) _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_5)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q48152 _let_4) tptp.insert) _let_3)) _let_2)))))))))))))))))))) (forall ((Q48184 $$unsorted) (Q48180 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_11 $$unsorted)) (let ((_let_1 (tptp.fun Q48180 Q48184))) (let ((_let_2 (tptp.fun Q48180 tptp.bool))) (let ((_let_3 (tptp.fun Q48184 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s Q48184 GENR_PVARR_11)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q48180 X))) (let ((_let_2 (tptp.fun Q48180 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun Q48184 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48184 _let_5) tptp.setspec) (tptp.s Q48184 GENR_PVARR_11))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48180 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0))))) (tptp.s Q48184 (tptp.i (tptp.s (tptp.fun Q48180 Q48184) F0) _let_1))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q48180 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q48180 Q48184))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q48184 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) U_0) _let_2)) _let_4)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.image) _let_4)) _let_2))))))))))))) (forall ((Q48214 $$unsorted) (Q48227 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_13 $$unsorted)) (let ((_let_1 (tptp.fun Q48227 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_1) (tptp.s _let_1 P0))) (tptp.s Q48227 GENR_PVARR_13)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q48227 X))) (let ((_let_2 (tptp.fun Q48227 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48227 _let_3) tptp.setspec) (tptp.s Q48227 GENR_PVARR_13))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))) _let_1)))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_12 $$unsorted)) (let ((_let_1 (tptp.fun Q48227 Q48214))) (let ((_let_2 (tptp.fun Q48227 tptp.bool))) (let ((_let_3 (tptp.fun Q48214 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0))) (tptp.s Q48214 GENR_PVARR_12)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q48227 X))) (let ((_let_2 (tptp.fun Q48214 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48214 _let_3) tptp.setspec) (tptp.s Q48214 GENR_PVARR_12))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48227 tptp.bool) P0) _let_1)))) (tptp.s Q48214 (tptp.i (tptp.s (tptp.fun Q48227 Q48214) F0) _let_1))))))))))))))) (forall ((F0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun Q48227 tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun Q48227 Q48214))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q48214 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_6))) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) U_0) _let_2)) _let_5)))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.image) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_3 U_1) _let_2)))))))))))))))))))) (forall ((Q48254 $$unsorted) (Q48245 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q48245 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun Q48245 Q48254))) (let ((_let_5 (tptp.fun Q48254 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) (tptp.s _let_4 F0))))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (= (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) _let_3)))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_8 _let_5) tptp.unions) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.image) _let_7)) _let_3))))))))))))))) (forall ((Q48280 $$unsorted) (Q48276 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q48276 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q48276 Q48280))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q48280 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s Q48276 X))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q48276 _let_9) tptp.in) _let_7)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q48280 _let_8) tptp.in) (tptp.s Q48280 (tptp.i _let_4 _let_7)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.image) _let_4)) _let_2)))))))))))))))) (forall ((Q48322 $$unsorted) (Q48318 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q48318 tptp.bool))) (let ((_let_2 (tptp.fun Q48322 tptp.bool))) (let ((_let_3 (tptp.fun Q48322 Q48318))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q48318 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q48318 _let_2) tptp.in) (tptp.s Q48318 Y))) (tptp.s _let_1 T0)))) (exists ((X $$unsorted)) (= (tptp.s Q48318 (tptp.i (tptp.s (tptp.fun Q48322 Q48318) tptp.f) (tptp.s Q48322 X))) (tptp.s Q48318 Y))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q48322 tptp.bool))) (let ((_let_2 (tptp.s Q48322 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q48318 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48318 _let_5) tptp.in) (tptp.s Q48318 (tptp.i (tptp.s (tptp.fun Q48322 Q48318) tptp.f) _let_2)))) (tptp.s _let_4 T0))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48322 _let_3) tptp.in) _let_2)) (tptp.s _let_1 S0))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 tptp.f))) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))))))) (forall ((Q48347 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun Q48347 tptp.bool))) (=> (forall ((GENR_PVARR_14 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48347 tptp.bool) U_0) (tptp.s Q48347 GENR_PVARR_14)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun Q48347 tptp.bool))) (let ((_let_2 (tptp.fun tptp.bool _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q48347 _let_2) tptp.setspec) (tptp.s Q48347 GENR_PVARR_14))) (tptp.s tptp.bool tptp.f0))) (tptp.s Q48347 X))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 U_0))) (tptp.s _let_1 tptp.empty))))) (forall ((Q48364 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun Q48364 tptp.bool))) (=> (forall ((GENR_PVARR_15 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48364 tptp.bool) U_0) (tptp.s Q48364 GENR_PVARR_15)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun Q48364 tptp.bool))) (let ((_let_2 (tptp.fun tptp.bool _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q48364 _let_2) tptp.setspec) (tptp.s Q48364 GENR_PVARR_15))) (tptp.s tptp.bool tptp.t))) (tptp.s Q48364 X))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 U_0))) (tptp.s _let_1 tptp.univ))))) (forall ((Q48393 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_16 $$unsorted)) (let ((_let_1 (tptp.fun Q48393 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q48393 _let_1) U_0) (tptp.s Q48393 A5))) (tptp.s Q48393 GENR_PVARR_16)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q48393 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q48393 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (= _let_1 (tptp.s Q48393 A5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q48393 _let_4) tptp.setspec) (tptp.s Q48393 GENR_PVARR_16))) _let_2)) _let_1)))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.fun Q48393 tptp.bool))) (let ((_let_2 (tptp.s Q48393 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q48393 _let_1) U_0) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48393 _let_3) tptp.insert) _let_2)) (tptp.s _let_1 tptp.empty)))))))))) (forall ((Q48419 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_17 $$unsorted)) (let ((_let_1 (tptp.fun Q48419 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q48419 _let_1) U_0) (tptp.s Q48419 A5))) (tptp.s Q48419 GENR_PVARR_17)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q48419 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q48419 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (= (tptp.s Q48419 A5) _let_1)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q48419 _let_4) tptp.setspec) (tptp.s Q48419 GENR_PVARR_17))) _let_2)) _let_1)))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.fun Q48419 tptp.bool))) (let ((_let_2 (tptp.s Q48419 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q48419 _let_1) U_0) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48419 _let_3) tptp.insert) _let_2)) (tptp.s _let_1 tptp.empty)))))))))) (forall ((Q48465 $$unsorted) (Q48464 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_18 $$unsorted)) (let ((_let_1 (tptp.prod Q48465 Q48464))) (let ((_let_2 (tptp.fun Q48465 (tptp.fun Q48464 tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 GENR_PVARR_18)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48464 Y))) (let ((_let_2 (tptp.s Q48465 X))) (let ((_let_3 (tptp.prod Q48465 Q48464))) (let ((_let_4 (tptp.fun Q48464 _let_3))) (let ((_let_5 (tptp.fun Q48464 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_18))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48465 _let_5) P0) _let_2)) _let_1)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q48465 _let_4) tptp.c_) _let_2)) _let_1)))))))))))))))))) (forall ((P0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s Q48464 B0))) (let ((_let_2 (tptp.s Q48465 A5))) (let ((_let_3 (tptp.fun Q48464 tptp.bool))) (let ((_let_4 (tptp.fun Q48465 _let_3))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.prod Q48465 Q48464))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun Q48464 _let_6))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.in) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q48465 _let_8) tptp.c_) _let_2)) _let_1)))) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))))) (forall ((Q48509 $$unsorted) (Q48508 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_20 $$unsorted)) (let ((_let_1 (tptp.prod Q48509 Q48508))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_1) (tptp.s _let_2 P0))) (tptp.s _let_1 GENR_PVARR_20)))) (exists ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.prod Q48509 Q48508))) (let ((_let_2 (tptp.fun Q48508 _let_1))) (let ((_let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q48509 _let_2) tptp.c_) (tptp.s Q48509 A5))) (tptp.s Q48508 B0))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_20))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 P0) _let_3)))) _let_3))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_19 $$unsorted)) (let ((_let_1 (tptp.prod Q48509 Q48508))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 GENR_PVARR_19)))) (exists ((P1 $$unsorted)) (let ((_let_1 (tptp.prod Q48509 Q48508))) (let ((_let_2 (tptp.s _let_1 P1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_19))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2)))) _let_2)))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q48509 Q48508) tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 tptp.gspec))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 U_0) _let_2)))) (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 U_1) _let_2)))))))))))))) (forall ((Q48678 $$unsorted) (Q48557 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_21 $$unsorted)) (let ((_let_1 (tptp.fun Q48557 Q48678))) (let ((_let_2 (tptp.fun Q48557 tptp.bool))) (let ((_let_3 (tptp.fun Q48678 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0))) (tptp.s Q48678 GENR_PVARR_21)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q48557 X))) (let ((_let_2 (tptp.fun Q48678 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48678 _let_3) tptp.setspec) (tptp.s Q48678 GENR_PVARR_21))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48557 tptp.bool) P0) _let_1)))) (tptp.s Q48678 (tptp.i (tptp.s (tptp.fun Q48557 Q48678) F0) _let_1))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (= (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s Q48678 Z0))) (let ((_let_2 (tptp.fun Q48678 tptp.bool))) (let ((_let_3 (tptp.fun Q48557 Q48678))) (let ((_let_4 (tptp.fun Q48557 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q48678 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_0) (tptp.s _let_4 P0))) (tptp.s _let_3 F0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q48557 X))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48557 tptp.bool) P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48678 tptp.bool) tptp.q0) (tptp.s Q48678 (tptp.i (tptp.s (tptp.fun Q48557 Q48678) F0) _let_1)))))))))))) (forall ((Q48678 $$unsorted) (Q48614 $$unsorted) (Q48613 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_22 $$unsorted)) (let ((_let_1 (tptp.fun Q48614 (tptp.fun Q48613 Q48678)))) (let ((_let_2 (tptp.fun Q48614 (tptp.fun Q48613 tptp.bool)))) (let ((_let_3 (tptp.fun Q48678 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0))) (tptp.s Q48678 GENR_PVARR_22)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48613 Y))) (let ((_let_2 (tptp.s Q48614 X))) (let ((_let_3 (tptp.fun Q48613 Q48678))) (let ((_let_4 (tptp.fun Q48613 tptp.bool))) (let ((_let_5 (tptp.fun Q48678 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q48678 _let_6) tptp.setspec) (tptp.s Q48678 GENR_PVARR_22))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q48614 _let_4) P0) _let_2)) _let_1)))) (tptp.s Q48678 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48614 _let_3) F0) _let_2)) _let_1)))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (= (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s Q48678 Z0))) (let ((_let_2 (tptp.fun Q48678 tptp.bool))) (let ((_let_3 (tptp.fun Q48614 (tptp.fun Q48613 Q48678)))) (let ((_let_4 (tptp.fun Q48614 (tptp.fun Q48613 tptp.bool)))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q48678 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_0) (tptp.s _let_4 P0))) (tptp.s _let_3 F0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48613 Y))) (let ((_let_2 (tptp.s Q48614 X))) (let ((_let_3 (tptp.fun Q48613 Q48678))) (let ((_let_4 (tptp.fun Q48613 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q48614 _let_4) P0) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48678 tptp.bool) tptp.q0) (tptp.s Q48678 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48614 _let_3) F0) _let_2)) _let_1))))))))))))))) (forall ((Q48678 $$unsorted) (Q48681 $$unsorted) (Q48680 $$unsorted) (Q48679 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_23 $$unsorted)) (let ((_let_1 (tptp.fun Q48681 (tptp.fun Q48680 (tptp.fun Q48679 Q48678))))) (let ((_let_2 (tptp.fun Q48681 (tptp.fun Q48680 (tptp.fun Q48679 tptp.bool))))) (let ((_let_3 (tptp.fun Q48678 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0))) (tptp.s Q48678 GENR_PVARR_23)))) (exists ((W $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48679 Y))) (let ((_let_2 (tptp.s Q48680 X))) (let ((_let_3 (tptp.s Q48681 W))) (let ((_let_4 (tptp.fun Q48679 Q48678))) (let ((_let_5 (tptp.fun Q48680 _let_4))) (let ((_let_6 (tptp.fun Q48679 tptp.bool))) (let ((_let_7 (tptp.fun Q48680 _let_6))) (let ((_let_8 (tptp.fun Q48678 tptp.bool))) (let ((_let_9 (tptp.fun tptp.bool _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q48678 _let_9) tptp.setspec) (tptp.s Q48678 GENR_PVARR_23))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q48681 _let_7) P0) _let_3)) _let_2)) _let_1)))) (tptp.s Q48678 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48681 _let_5) F0) _let_3)) _let_2)) _let_1))))))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (= (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s Q48678 Z0))) (let ((_let_2 (tptp.fun Q48678 tptp.bool))) (let ((_let_3 (tptp.fun Q48681 (tptp.fun Q48680 (tptp.fun Q48679 Q48678))))) (let ((_let_4 (tptp.fun Q48681 (tptp.fun Q48680 (tptp.fun Q48679 tptp.bool))))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q48678 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_0) (tptp.s _let_4 P0))) (tptp.s _let_3 F0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))))))) (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48679 Y))) (let ((_let_2 (tptp.s Q48680 X))) (let ((_let_3 (tptp.s Q48681 W))) (let ((_let_4 (tptp.fun Q48679 Q48678))) (let ((_let_5 (tptp.fun Q48680 _let_4))) (let ((_let_6 (tptp.fun Q48679 tptp.bool))) (let ((_let_7 (tptp.fun Q48680 _let_6))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q48681 _let_7) P0) _let_3)) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48678 tptp.bool) tptp.q0) (tptp.s Q48678 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48681 _let_5) F0) _let_3)) _let_2)) _let_1)))))))))))))))))) (forall ((Q48848 $$unsorted) (Q48727 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_24 $$unsorted)) (let ((_let_1 (tptp.fun Q48727 Q48848))) (let ((_let_2 (tptp.fun Q48727 tptp.bool))) (let ((_let_3 (tptp.fun Q48848 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0))) (tptp.s Q48848 GENR_PVARR_24)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q48727 X))) (let ((_let_2 (tptp.fun Q48848 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48848 _let_3) tptp.setspec) (tptp.s Q48848 GENR_PVARR_24))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48727 tptp.bool) P0) _let_1)))) (tptp.s Q48848 (tptp.i (tptp.s (tptp.fun Q48727 Q48848) F0) _let_1))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (= (exists ((Z0 $$unsorted)) (let ((_let_1 (tptp.s Q48848 Z0))) (let ((_let_2 (tptp.fun Q48848 tptp.bool))) (let ((_let_3 (tptp.fun Q48727 Q48848))) (let ((_let_4 (tptp.fun Q48727 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q48848 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_0) (tptp.s _let_4 P0))) (tptp.s _let_3 F0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q48727 X))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48727 tptp.bool) P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48848 tptp.bool) tptp.q0) (tptp.s Q48848 (tptp.i (tptp.s (tptp.fun Q48727 Q48848) F0) _let_1)))))))))))) (forall ((Q48848 $$unsorted) (Q48784 $$unsorted) (Q48783 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_25 $$unsorted)) (let ((_let_1 (tptp.fun Q48784 (tptp.fun Q48783 Q48848)))) (let ((_let_2 (tptp.fun Q48784 (tptp.fun Q48783 tptp.bool)))) (let ((_let_3 (tptp.fun Q48848 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0))) (tptp.s Q48848 GENR_PVARR_25)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48783 Y))) (let ((_let_2 (tptp.s Q48784 X))) (let ((_let_3 (tptp.fun Q48783 Q48848))) (let ((_let_4 (tptp.fun Q48783 tptp.bool))) (let ((_let_5 (tptp.fun Q48848 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q48848 _let_6) tptp.setspec) (tptp.s Q48848 GENR_PVARR_25))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q48784 _let_4) P0) _let_2)) _let_1)))) (tptp.s Q48848 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48784 _let_3) F0) _let_2)) _let_1)))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (= (exists ((Z0 $$unsorted)) (let ((_let_1 (tptp.s Q48848 Z0))) (let ((_let_2 (tptp.fun Q48848 tptp.bool))) (let ((_let_3 (tptp.fun Q48784 (tptp.fun Q48783 Q48848)))) (let ((_let_4 (tptp.fun Q48784 (tptp.fun Q48783 tptp.bool)))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q48848 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_0) (tptp.s _let_4 P0))) (tptp.s _let_3 F0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))))))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48783 Y))) (let ((_let_2 (tptp.s Q48784 X))) (let ((_let_3 (tptp.fun Q48783 Q48848))) (let ((_let_4 (tptp.fun Q48783 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q48784 _let_4) P0) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48848 tptp.bool) tptp.q0) (tptp.s Q48848 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48784 _let_3) F0) _let_2)) _let_1))))))))))))))) (forall ((Q48848 $$unsorted) (Q48851 $$unsorted) (Q48850 $$unsorted) (Q48849 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_26 $$unsorted)) (let ((_let_1 (tptp.fun Q48851 (tptp.fun Q48850 (tptp.fun Q48849 Q48848))))) (let ((_let_2 (tptp.fun Q48851 (tptp.fun Q48850 (tptp.fun Q48849 tptp.bool))))) (let ((_let_3 (tptp.fun Q48848 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0))) (tptp.s Q48848 GENR_PVARR_26)))) (exists ((W $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48849 Y))) (let ((_let_2 (tptp.s Q48850 X))) (let ((_let_3 (tptp.s Q48851 W))) (let ((_let_4 (tptp.fun Q48849 Q48848))) (let ((_let_5 (tptp.fun Q48850 _let_4))) (let ((_let_6 (tptp.fun Q48849 tptp.bool))) (let ((_let_7 (tptp.fun Q48850 _let_6))) (let ((_let_8 (tptp.fun Q48848 tptp.bool))) (let ((_let_9 (tptp.fun tptp.bool _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q48848 _let_9) tptp.setspec) (tptp.s Q48848 GENR_PVARR_26))) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q48851 _let_7) P0) _let_3)) _let_2)) _let_1)))) (tptp.s Q48848 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48851 _let_5) F0) _let_3)) _let_2)) _let_1))))))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (= (exists ((Z0 $$unsorted)) (let ((_let_1 (tptp.s Q48848 Z0))) (let ((_let_2 (tptp.fun Q48848 tptp.bool))) (let ((_let_3 (tptp.fun Q48851 (tptp.fun Q48850 (tptp.fun Q48849 Q48848))))) (let ((_let_4 (tptp.fun Q48851 (tptp.fun Q48850 (tptp.fun Q48849 tptp.bool))))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q48848 _let_6) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_0) (tptp.s _let_4 P0))) (tptp.s _let_3 F0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.q0) _let_1))))))))))) (exists ((W $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q48849 Y))) (let ((_let_2 (tptp.s Q48850 X))) (let ((_let_3 (tptp.s Q48851 W))) (let ((_let_4 (tptp.fun Q48849 Q48848))) (let ((_let_5 (tptp.fun Q48850 _let_4))) (let ((_let_6 (tptp.fun Q48849 tptp.bool))) (let ((_let_7 (tptp.fun Q48850 _let_6))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q48851 _let_7) P0) _let_3)) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q48848 tptp.bool) tptp.q0) (tptp.s Q48848 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48851 _let_5) F0) _let_3)) _let_2)) _let_1)))))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 tptp.empty)))) (forall ((A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A A5))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_3)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 P0) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) _let_3)) _let_2))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 S0))))))))) (forall ((Q48928 $$unsorted) (Q48912 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_27 $$unsorted)) (let ((_let_1 (tptp.fun Q48912 tptp.bool))) (let ((_let_2 (tptp.fun Q48928 _let_1))) (let ((_let_3 (tptp.fun Q48928 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) (tptp.s Q48912 GENR_PVARR_27)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q48912 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q48928 X))) (let ((_let_2 (tptp.fun Q48912 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun Q48928 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48928 _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48912 _let_3) tptp.in) (tptp.s Q48912 Y))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q48928 _let_2) F0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48912 _let_3) tptp.setspec) (tptp.s Q48912 GENR_PVARR_27))) _let_1)) (tptp.s Q48912 Y))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q48912 tptp.bool))) (let ((_let_2 (tptp.fun Q48928 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q48928 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.unions) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.image) _let_3)) _let_5)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)) _let_3)))))))))))))))) (forall ((Q48971 $$unsorted) (Q48955 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_28 $$unsorted)) (let ((_let_1 (tptp.fun Q48955 tptp.bool))) (let ((_let_2 (tptp.fun Q48971 _let_1))) (let ((_let_3 (tptp.fun Q48971 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) (tptp.s Q48955 GENR_PVARR_28)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q48955 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q48971 X))) (let ((_let_2 (tptp.fun Q48955 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun Q48971 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q48971 _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48955 _let_3) tptp.in) (tptp.s Q48955 Y))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q48971 _let_2) F0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q48955 _let_3) tptp.setspec) (tptp.s Q48955 GENR_PVARR_28))) _let_1)) (tptp.s Q48955 Y))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q48955 tptp.bool))) (let ((_let_2 (tptp.fun Q48971 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q48971 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.inters) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.image) _let_3)) _let_5)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)) _let_3)))))))))))))))) (forall ((Q49162 $$unsorted) (Q49161 $$unsorted) (Q49160 $$unsorted) (Q49136 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_34 $$unsorted)) (let ((_let_1 (tptp.fun Q49136 tptp.bool))) (let ((_let_2 (tptp.fun Q49162 (tptp.fun Q49161 (tptp.fun Q49160 _let_1))))) (let ((_let_3 (tptp.fun Q49162 (tptp.fun Q49161 (tptp.fun Q49160 tptp.bool))))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_1) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s Q49136 GENR_PVARR_34)))) (exists ((A5 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q49136 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (exists ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s Q49160 Z0))) (let ((_let_2 (tptp.s Q49161 Y))) (let ((_let_3 (tptp.s Q49162 X))) (let ((_let_4 (tptp.fun Q49136 tptp.bool))) (let ((_let_5 (tptp.fun Q49160 _let_4))) (let ((_let_6 (tptp.fun Q49161 _let_5))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun Q49160 tptp.bool))) (let ((_let_9 (tptp.fun Q49161 _let_8))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q49162 _let_9) P0) _let_3)) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q49136 _let_7) tptp.in) (tptp.s Q49136 A5))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q49162 _let_6) F0) _let_3)) _let_2)) _let_1))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49136 _let_3) tptp.setspec) (tptp.s Q49136 GENR_PVARR_34))) _let_1)) (tptp.s Q49136 A5))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_33 $$unsorted)) (let ((_let_1 (tptp.fun Q49136 tptp.bool))) (let ((_let_2 (tptp.fun Q49162 (tptp.fun Q49161 (tptp.fun Q49160 _let_1))))) (let ((_let_3 (tptp.fun Q49162 (tptp.fun Q49161 (tptp.fun Q49160 tptp.bool))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_33)))) (exists ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s Q49160 Z0))) (let ((_let_2 (tptp.s Q49161 Y))) (let ((_let_3 (tptp.s Q49162 X))) (let ((_let_4 (tptp.fun Q49136 tptp.bool))) (let ((_let_5 (tptp.fun Q49160 _let_4))) (let ((_let_6 (tptp.fun Q49161 _let_5))) (let ((_let_7 (tptp.fun Q49160 tptp.bool))) (let ((_let_8 (tptp.fun Q49161 _let_7))) (let ((_let_9 (tptp.fun _let_4 tptp.bool))) (let ((_let_10 (tptp.fun tptp.bool _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.setspec) (tptp.s _let_4 GENR_PVARR_33))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q49162 _let_8) P0) _let_3)) _let_2)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q49162 _let_6) F0) _let_3)) _let_2)) _let_1))))))))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q49136 tptp.bool))) (let ((_let_2 (tptp.fun Q49162 (tptp.fun Q49161 (tptp.fun Q49160 _let_1))))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q49162 (tptp.fun Q49161 (tptp.fun Q49160 tptp.bool))))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.unions) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_3)))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3)))))))))))))))))) (forall ((Q49088 $$unsorted) (Q49087 $$unsorted) (Q49068 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_32 $$unsorted)) (let ((_let_1 (tptp.fun Q49068 tptp.bool))) (let ((_let_2 (tptp.fun Q49088 (tptp.fun Q49087 _let_1)))) (let ((_let_3 (tptp.fun Q49088 (tptp.fun Q49087 tptp.bool)))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_1) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s Q49068 GENR_PVARR_32)))) (exists ((A5 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q49068 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49087 Y))) (let ((_let_2 (tptp.s Q49088 X))) (let ((_let_3 (tptp.fun Q49068 tptp.bool))) (let ((_let_4 (tptp.fun Q49087 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun Q49087 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q49088 _let_6) P0) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q49068 _let_5) tptp.in) (tptp.s Q49068 A5))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q49088 _let_4) F0) _let_2)) _let_1)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49068 _let_3) tptp.setspec) (tptp.s Q49068 GENR_PVARR_32))) _let_1)) (tptp.s Q49068 A5))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_31 $$unsorted)) (let ((_let_1 (tptp.fun Q49068 tptp.bool))) (let ((_let_2 (tptp.fun Q49088 (tptp.fun Q49087 _let_1)))) (let ((_let_3 (tptp.fun Q49088 (tptp.fun Q49087 tptp.bool)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_31)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49087 Y))) (let ((_let_2 (tptp.s Q49088 X))) (let ((_let_3 (tptp.fun Q49068 tptp.bool))) (let ((_let_4 (tptp.fun Q49087 _let_3))) (let ((_let_5 (tptp.fun Q49087 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_31))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q49088 _let_5) P0) _let_2)) _let_1)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q49088 _let_4) F0) _let_2)) _let_1)))))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q49068 tptp.bool))) (let ((_let_2 (tptp.fun Q49088 (tptp.fun Q49087 _let_1)))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q49088 (tptp.fun Q49087 tptp.bool)))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.unions) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_3)))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3)))))))))))))))))) (forall ((Q49024 $$unsorted) (Q49010 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_30 $$unsorted)) (let ((_let_1 (tptp.fun Q49010 tptp.bool))) (let ((_let_2 (tptp.fun Q49024 _let_1))) (let ((_let_3 (tptp.fun Q49024 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_1) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s Q49010 GENR_PVARR_30)))) (exists ((A5 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q49010 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q49024 X))) (let ((_let_2 (tptp.fun Q49010 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q49024 tptp.bool) P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49010 _let_3) tptp.in) (tptp.s Q49010 A5))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q49024 _let_2) F0) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49010 _let_3) tptp.setspec) (tptp.s Q49010 GENR_PVARR_30))) _let_1)) (tptp.s Q49010 A5))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_29 $$unsorted)) (let ((_let_1 (tptp.fun Q49010 tptp.bool))) (let ((_let_2 (tptp.fun Q49024 _let_1))) (let ((_let_3 (tptp.fun Q49024 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_29)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q49024 X))) (let ((_let_2 (tptp.fun Q49010 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.setspec) (tptp.s _let_2 GENR_PVARR_29))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q49024 tptp.bool) P0) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q49024 _let_2) F0) _let_1))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q49010 tptp.bool))) (let ((_let_2 (tptp.fun Q49024 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q49024 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.unions) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_3)))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3)))))))))))))))))) (forall ((Q49353 $$unsorted) (Q49352 $$unsorted) (Q49351 $$unsorted) (Q49327 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_40 $$unsorted)) (let ((_let_1 (tptp.fun Q49327 tptp.bool))) (let ((_let_2 (tptp.fun Q49353 (tptp.fun Q49352 (tptp.fun Q49351 _let_1))))) (let ((_let_3 (tptp.fun Q49353 (tptp.fun Q49352 (tptp.fun Q49351 tptp.bool))))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_1) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s Q49327 GENR_PVARR_40)))) (exists ((A5 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q49327 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s Q49351 Z0))) (let ((_let_2 (tptp.s Q49352 Y))) (let ((_let_3 (tptp.s Q49353 X))) (let ((_let_4 (tptp.fun Q49327 tptp.bool))) (let ((_let_5 (tptp.fun Q49351 _let_4))) (let ((_let_6 (tptp.fun Q49352 _let_5))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun Q49351 tptp.bool))) (let ((_let_9 (tptp.fun Q49352 _let_8))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q49353 _let_9) P0) _let_3)) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q49327 _let_7) tptp.in) (tptp.s Q49327 A5))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q49353 _let_6) F0) _let_3)) _let_2)) _let_1))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49327 _let_3) tptp.setspec) (tptp.s Q49327 GENR_PVARR_40))) _let_1)) (tptp.s Q49327 A5))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_39 $$unsorted)) (let ((_let_1 (tptp.fun Q49327 tptp.bool))) (let ((_let_2 (tptp.fun Q49353 (tptp.fun Q49352 (tptp.fun Q49351 _let_1))))) (let ((_let_3 (tptp.fun Q49353 (tptp.fun Q49352 (tptp.fun Q49351 tptp.bool))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_39)))) (exists ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s Q49351 Z0))) (let ((_let_2 (tptp.s Q49352 Y))) (let ((_let_3 (tptp.s Q49353 X))) (let ((_let_4 (tptp.fun Q49327 tptp.bool))) (let ((_let_5 (tptp.fun Q49351 _let_4))) (let ((_let_6 (tptp.fun Q49352 _let_5))) (let ((_let_7 (tptp.fun Q49351 tptp.bool))) (let ((_let_8 (tptp.fun Q49352 _let_7))) (let ((_let_9 (tptp.fun _let_4 tptp.bool))) (let ((_let_10 (tptp.fun tptp.bool _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.setspec) (tptp.s _let_4 GENR_PVARR_39))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q49353 _let_8) P0) _let_3)) _let_2)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q49353 _let_6) F0) _let_3)) _let_2)) _let_1))))))))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q49327 tptp.bool))) (let ((_let_2 (tptp.fun Q49353 (tptp.fun Q49352 (tptp.fun Q49351 _let_1))))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q49353 (tptp.fun Q49352 (tptp.fun Q49351 tptp.bool))))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.inters) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_3)))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3)))))))))))))))))) (forall ((Q49279 $$unsorted) (Q49278 $$unsorted) (Q49259 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_38 $$unsorted)) (let ((_let_1 (tptp.fun Q49259 tptp.bool))) (let ((_let_2 (tptp.fun Q49279 (tptp.fun Q49278 _let_1)))) (let ((_let_3 (tptp.fun Q49279 (tptp.fun Q49278 tptp.bool)))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_1) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s Q49259 GENR_PVARR_38)))) (exists ((A5 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q49259 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49278 Y))) (let ((_let_2 (tptp.s Q49279 X))) (let ((_let_3 (tptp.fun Q49259 tptp.bool))) (let ((_let_4 (tptp.fun Q49278 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun Q49278 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q49279 _let_6) P0) _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q49259 _let_5) tptp.in) (tptp.s Q49259 A5))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q49279 _let_4) F0) _let_2)) _let_1)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49259 _let_3) tptp.setspec) (tptp.s Q49259 GENR_PVARR_38))) _let_1)) (tptp.s Q49259 A5))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_37 $$unsorted)) (let ((_let_1 (tptp.fun Q49259 tptp.bool))) (let ((_let_2 (tptp.fun Q49279 (tptp.fun Q49278 _let_1)))) (let ((_let_3 (tptp.fun Q49279 (tptp.fun Q49278 tptp.bool)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_37)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49278 Y))) (let ((_let_2 (tptp.s Q49279 X))) (let ((_let_3 (tptp.fun Q49259 tptp.bool))) (let ((_let_4 (tptp.fun Q49278 _let_3))) (let ((_let_5 (tptp.fun Q49278 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_37))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q49279 _let_5) P0) _let_2)) _let_1)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q49279 _let_4) F0) _let_2)) _let_1)))))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q49259 tptp.bool))) (let ((_let_2 (tptp.fun Q49279 (tptp.fun Q49278 _let_1)))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q49279 (tptp.fun Q49278 tptp.bool)))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.inters) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_3)))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3)))))))))))))))))) (forall ((Q49215 $$unsorted) (Q49201 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_36 $$unsorted)) (let ((_let_1 (tptp.fun Q49201 tptp.bool))) (let ((_let_2 (tptp.fun Q49215 _let_1))) (let ((_let_3 (tptp.fun Q49215 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_1) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s Q49201 GENR_PVARR_36)))) (exists ((A5 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q49201 tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q49215 X))) (let ((_let_2 (tptp.fun Q49201 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q49215 tptp.bool) P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49201 _let_3) tptp.in) (tptp.s Q49201 A5))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q49215 _let_2) F0) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49201 _let_3) tptp.setspec) (tptp.s Q49201 GENR_PVARR_36))) _let_1)) (tptp.s Q49201 A5))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_35 $$unsorted)) (let ((_let_1 (tptp.fun Q49201 tptp.bool))) (let ((_let_2 (tptp.fun Q49215 _let_1))) (let ((_let_3 (tptp.fun Q49215 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_35)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q49215 X))) (let ((_let_2 (tptp.fun Q49201 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.setspec) (tptp.s _let_2 GENR_PVARR_35))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q49215 tptp.bool) P0) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q49215 _let_2) F0) _let_1))))))))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q49201 tptp.bool))) (let ((_let_2 (tptp.fun Q49215 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q49215 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.inters) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_3)))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3)))))))))))))))))) (forall ((Q49390 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (U $$unsorted) (GENR_PVARR_41 $$unsorted)) (let ((_let_1 (tptp.fun Q49390 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 U))) (tptp.s _let_1 GENR_PVARR_41)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q49390 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.setspec) (tptp.s _let_1 GENR_PVARR_41))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) (tptp.s _let_1 U))) _let_2))))))))))))))))) (forall ((U $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q49390 tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.diff) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.inters) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.unions) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2))))))))))))))))) (forall ((Q49425 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_42 $$unsorted)) (let ((_let_1 (tptp.fun Q49425 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_42)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q49425 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.setspec) (tptp.s _let_1 GENR_PVARR_42))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) (tptp.s _let_1 tptp.univ))) _let_2)))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q49425 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.inters) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.diff) (tptp.s _let_1 tptp.univ))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.unions) (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_4 U_0) _let_3)))))))))))))))))) (forall ((Q49460 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_43 $$unsorted)) (let ((_let_1 (tptp.fun Q49460 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_43)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q49460 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.setspec) (tptp.s _let_1 GENR_PVARR_43))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) (tptp.s _let_1 tptp.univ))) _let_2)))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q49460 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.unions) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.diff) (tptp.s _let_1 tptp.univ))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.inters) (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_4 U_0) _let_3)))))))))))))))))) (forall ((Q49497 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_44 $$unsorted)) (let ((_let_1 (tptp.fun Q49497 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_44)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun Q49497 tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.setspec) (tptp.s _let_1 GENR_PVARR_44))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) _let_2)) (tptp.s _let_1 T0)))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q49497 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_1) tptp.unions))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.diff) (tptp.s _let_1 (tptp.i _let_6 _let_4)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2))))))))))))))))) (forall ((Q49537 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (U $$unsorted) (GENR_PVARR_45 $$unsorted)) (let ((_let_1 (tptp.fun Q49537 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 U))) (tptp.s _let_1 GENR_PVARR_45)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q49537 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.setspec) (tptp.s _let_1 GENR_PVARR_45))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) (tptp.s _let_1 U))) _let_2))))))))))))))))) (forall ((U $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q49537 tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.diff) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.unions) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.inter) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.inters) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2)))))))))))))))))))) (forall ((Q49581 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (U $$unsorted) (GENR_PVARR_46 $$unsorted)) (let ((_let_1 (tptp.fun Q49581 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 U))) (tptp.s _let_1 GENR_PVARR_46)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q49581 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.setspec) (tptp.s _let_1 GENR_PVARR_46))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) (tptp.s _let_1 U))) _let_2))))))))))))))))) (forall ((U $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q49581 tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (=> (not (= _let_4 (tptp.s _let_3 tptp.empty))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.diff) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.unions) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 tptp.inters) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2)))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (U_2 $$unsorted)) (=> (forall ((S0 $$unsorted) (G0 $$unsorted) (GENR_PVARR_50 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_2) (tptp.s _let_3 S0))) (tptp.s _let_2 G0))) (tptp.s _let_1 GENR_PVARR_50)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.setspec) (tptp.s _let_2 GENR_PVARR_50))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) G0) _let_1))))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (S0 $$unsorted) (GENR_PVARR_51 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_1) (tptp.s _let_4 F0))) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_51)))) (exists ((G0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s tptp.bool V))) (let ((_let_7 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_6) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.in) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) G0) _let_1)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) F0) _let_1)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.setspec) (tptp.s _let_1 GENR_PVARR_51))) _let_6)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.inters) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_2) (tptp.s _let_3 S0))) (tptp.s _let_2 G0)))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_47 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_0) (tptp.s _let_4 S0))) (tptp.s _let_3 F0))) (tptp.s _let_1 GENR_PVARR_47)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.setspec) (tptp.s _let_2 GENR_PVARR_47))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.unions) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) F0) _let_1))))))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_1 _let_4))) (let ((_let_8 (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec))) (let ((_let_9 (tptp.fun _let_4 _let_3))) (let ((_let_10 (tptp.fun _let_5 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_9 tptp.inters) (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_1 _let_10) U_0) _let_2)) _let_6)))))) (tptp.s _let_3 (tptp.i (tptp.s _let_9 tptp.unions) (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) U_1) _let_6)) _let_2)))))))))))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 tptp.empty)))) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_3)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) _let_3)) _let_2)))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))))) (forall ((Q49786 $$unsorted) (Q49791 $$unsorted) (P0 $$unsorted) (F0 $$unsorted)) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49791 Y))) (let ((_let_2 (tptp.s Q49791 X))) (let ((_let_3 (tptp.s (tptp.fun Q49791 Q49786) F0))) (let ((_let_4 (tptp.s (tptp.fun Q49791 tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))) (= (tptp.s Q49786 (tptp.i _let_3 _let_2)) (tptp.s Q49786 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49791 Y))) (let ((_let_2 (tptp.s Q49791 X))) (let ((_let_3 (tptp.s (tptp.fun Q49791 Q49786) F0))) (let ((_let_4 (tptp.s (tptp.fun Q49791 tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))) (= (= (tptp.s Q49786 (tptp.i _let_3 _let_2)) (tptp.s Q49786 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))))))) (forall ((Q49829 $$unsorted) (Q49834 $$unsorted) (F0 $$unsorted)) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49834 Y))) (let ((_let_2 (tptp.s Q49834 X))) (let ((_let_3 (tptp.s (tptp.fun Q49834 Q49829) F0))) (=> (= (tptp.s Q49829 (tptp.i _let_3 _let_2)) (tptp.s Q49829 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49834 Y))) (let ((_let_2 (tptp.s Q49834 X))) (let ((_let_3 (tptp.s (tptp.fun Q49834 Q49829) F0))) (= (= (tptp.s Q49829 (tptp.i _let_3 _let_2)) (tptp.s Q49829 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))))) (forall ((Q49892 $$unsorted) (Q49893 $$unsorted) (F0 $$unsorted) (T0 $$unsorted)) (= (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q49893 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q49893 _let_2) tptp.in) (tptp.s Q49893 Y))) (tptp.s _let_1 T0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q49892 X))) (let ((_let_2 (tptp.fun Q49892 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49892 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (= (tptp.s Q49893 (tptp.i (tptp.s (tptp.fun Q49892 Q49893) F0) _let_1)) (tptp.s Q49893 Y))))))))))) (exists ((G0 $$unsorted)) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q49893 Y))) (let ((_let_2 (tptp.s Q49892 (tptp.i (tptp.s (tptp.fun Q49893 Q49892) G0) _let_1)))) (let ((_let_3 (tptp.fun Q49892 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun Q49893 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q49893 _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q49892 _let_4) tptp.in) _let_2)) (tptp.s _let_3 tptp.s0)))) (= (tptp.s Q49893 (tptp.i (tptp.s (tptp.fun Q49892 Q49893) F0) _let_2)) _let_1))))))))))))) (forall ((Q49989 $$unsorted) (Q49986 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q49986 Y))) (let ((_let_2 (tptp.s Q49986 X))) (let ((_let_3 (tptp.s (tptp.fun Q49986 Q49989) F0))) (let ((_let_4 (tptp.fun Q49986 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q49986 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q49989 (tptp.i _let_3 _let_2)) (tptp.s Q49989 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (exists ((G0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q49986 X))) (let ((_let_2 (tptp.fun Q49986 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q49986 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s Q49986 (tptp.i (tptp.s (tptp.fun Q49989 Q49986) G0) (tptp.s Q49989 (tptp.i (tptp.s (tptp.fun Q49986 Q49989) F0) _let_1)))) _let_1))))))))) (forall ((Q50120 $$unsorted) (Q50121 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q50120 tptp.bool))) (let ((_let_2 (tptp.s Q50121 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q50121 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q50121 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q50120 _let_3) tptp.in) (tptp.s Q50120 (tptp.i (tptp.s (tptp.fun Q50121 Q50120) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (= (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q50121 Y))) (let ((_let_2 (tptp.s Q50121 X))) (let ((_let_3 (tptp.s (tptp.fun Q50121 Q50120) F0))) (let ((_let_4 (tptp.fun Q50121 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q50121 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q50120 (tptp.i _let_3 _let_2)) (tptp.s Q50120 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q50120 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q50120 _let_2) tptp.in) (tptp.s Q50120 Y))) (tptp.s _let_1 T0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q50121 X))) (let ((_let_2 (tptp.fun Q50121 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q50121 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s Q50120 (tptp.i (tptp.s (tptp.fun Q50121 Q50120) F0) _let_1)) (tptp.s Q50120 Y)))))))))))) (exists ((G0 $$unsorted)) (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q50121 tptp.bool))) (let ((_let_2 (tptp.s Q50120 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q50120 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q50120 _let_5) tptp.in) _let_2)) (tptp.s _let_4 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q50121 _let_3) tptp.in) (tptp.s Q50121 (tptp.i (tptp.s (tptp.fun Q50120 Q50121) G0) _let_2)))) (tptp.s _let_1 S0))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q50120 Y))) (let ((_let_2 (tptp.fun Q50120 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q50120 _let_3) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (= (tptp.s Q50120 (tptp.i (tptp.s (tptp.fun Q50121 Q50120) F0) (tptp.s Q50121 (tptp.i (tptp.s (tptp.fun Q50120 Q50121) G0) _let_1)))) _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q50121 X))) (let ((_let_2 (tptp.fun Q50121 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q50121 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s Q50121 (tptp.i (tptp.s (tptp.fun Q50120 Q50121) G0) (tptp.s Q50120 (tptp.i (tptp.s (tptp.fun Q50121 Q50120) F0) _let_1)))) _let_1))))))))))) (forall ((Q50148 $$unsorted) (Q50145 $$unsorted)) (= (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s Q50145 (tptp.i (tptp.s (tptp.fun Q50148 Q50145) tptp.f) (tptp.s Q50148 X))) (tptp.s Q50145 Y)))) (exists ((G0 $$unsorted)) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q50145 Y))) (= (tptp.s Q50145 (tptp.i (tptp.s (tptp.fun Q50148 Q50145) tptp.f) (tptp.s Q50148 (tptp.i (tptp.s (tptp.fun Q50145 Q50148) G0) _let_1)))) _let_1)))))) (forall ((Q50185 $$unsorted) (Q50182 $$unsorted)) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q50182 Y))) (let ((_let_2 (tptp.s Q50182 X))) (let ((_let_3 (tptp.s (tptp.fun Q50182 Q50185) tptp.f))) (=> (= (tptp.s Q50185 (tptp.i _let_3 _let_2)) (tptp.s Q50185 (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (exists ((G0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q50182 X))) (= (tptp.s Q50182 (tptp.i (tptp.s (tptp.fun Q50185 Q50182) G0) (tptp.s Q50185 (tptp.i (tptp.s (tptp.fun Q50182 Q50185) tptp.f) _let_1)))) _let_1)))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted)) (= (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (=> (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))) (tptp.s B Y))))) (exists ((G0 $$unsorted)) (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_1)))) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) _let_1))))))) (forall ((Q50345 $$unsorted) (Q50349 $$unsorted) (Q50350 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q50350 Y))) (let ((_let_2 (tptp.s (tptp.fun Q50350 Q50345) F0))) (let ((_let_3 (tptp.s Q50350 X))) (let ((_let_4 (tptp.s (tptp.fun Q50350 Q50349) G0))) (let ((_let_5 (tptp.s (tptp.fun Q50350 tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1))) (= (tptp.s Q50349 (tptp.i _let_4 _let_3)) (tptp.s Q50349 (tptp.i _let_4 _let_1)))) (= (tptp.s Q50345 (tptp.i _let_2 _let_3)) (tptp.s Q50345 (tptp.i _let_2 _let_1)))))))))) (exists ((H0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q50350 X))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q50350 tptp.bool) P0) _let_1))) (= (tptp.s Q50345 (tptp.i (tptp.s (tptp.fun Q50350 Q50345) F0) _let_1)) (tptp.s Q50345 (tptp.i (tptp.s (tptp.fun Q50349 Q50345) H0) (tptp.s Q50349 (tptp.i (tptp.s (tptp.fun Q50350 Q50349) G0) _let_1))))))))))) (forall ((Q50396 $$unsorted) (Q50395 $$unsorted) (Q50375 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q50395 Y))) (let ((_let_2 (tptp.s (tptp.fun Q50395 Q50396) F0))) (let ((_let_3 (tptp.s Q50395 X))) (let ((_let_4 (tptp.s (tptp.fun Q50395 Q50375) G0))) (=> (= (tptp.s Q50375 (tptp.i _let_4 _let_3)) (tptp.s Q50375 (tptp.i _let_4 _let_1))) (= (tptp.s Q50396 (tptp.i _let_2 _let_3)) (tptp.s Q50396 (tptp.i _let_2 _let_1))))))))) (exists ((H0 $$unsorted)) (let ((_let_1 (tptp.fun Q50395 Q50375))) (let ((_let_2 (tptp.fun Q50375 Q50396))) (let ((_let_3 (tptp.fun Q50395 Q50396))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_3 F0) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.o) (tptp.s _let_2 H0))) (tptp.s _let_1 G0))))))))))) (forall ((Q50439 $$unsorted) (Q50443 $$unsorted) (Q50444 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (= (forall ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q50444 tptp.bool) P0) (tptp.s Q50444 X)))) (exists ((Y $$unsorted)) (= (tptp.s Q50439 (tptp.i (tptp.s (tptp.fun Q50443 Q50439) G0) (tptp.s Q50443 Y))) (tptp.s Q50439 (tptp.i (tptp.s (tptp.fun Q50444 Q50439) F0) (tptp.s Q50444 X))))))) (exists ((H0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q50444 X))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q50444 tptp.bool) P0) _let_1))) (= (tptp.s Q50439 (tptp.i (tptp.s (tptp.fun Q50444 Q50439) F0) _let_1)) (tptp.s Q50439 (tptp.i (tptp.s (tptp.fun Q50443 Q50439) G0) (tptp.s Q50443 (tptp.i (tptp.s (tptp.fun Q50444 Q50443) H0) _let_1))))))))))) (forall ((Q50480 $$unsorted) (Q50479 $$unsorted) (Q50467 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (= (forall ((X $$unsorted)) (exists ((Y $$unsorted)) (= (tptp.s Q50480 (tptp.i (tptp.s (tptp.fun Q50467 Q50480) G0) (tptp.s Q50467 Y))) (tptp.s Q50480 (tptp.i (tptp.s (tptp.fun Q50479 Q50480) F0) (tptp.s Q50479 X)))))) (exists ((H0 $$unsorted)) (let ((_let_1 (tptp.fun Q50479 Q50467))) (let ((_let_2 (tptp.fun Q50467 Q50480))) (let ((_let_3 (tptp.fun Q50479 Q50480))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_3 F0) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.o) (tptp.s _let_2 G0))) (tptp.s _let_1 H0))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted)) (= (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))) (tptp.s B Y)))) (forall ((P0 $$unsorted)) (= (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun B tptp.bool) P0) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))))))) (forall ((Y $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun B tptp.bool) P0) (tptp.s B Y))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted)) (= (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))) (tptp.s B Y)))) (forall ((P0 $$unsorted)) (= (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun B tptp.bool) P0) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))))))) (exists ((Y $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun B tptp.bool) P0) (tptp.s B Y))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_53 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_1) (tptp.s _let_1 P0))) (tptp.s B GENR_PVARR_53)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s B X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.setspec) (tptp.s B GENR_PVARR_53))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))) _let_1)))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_52 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 F0))) (tptp.s A GENR_PVARR_52)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.setspec) (tptp.s A GENR_PVARR_52))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun B tptp.bool) P0) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))))) _let_1))))))))))))) (forall ((F0 $$unsorted)) (= (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))) (tptp.s B Y)))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (let ((_let_8 (tptp.fun _let_6 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.image) _let_5)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) U_0) _let_2)) _let_5)))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_3 U_1) _let_2)))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))))) (let ((_let_7 (tptp.s _let_1 S0))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.subset) _let_2)) _let_7))) (= (tptp.s _let_4 (tptp.i _let_6 _let_7)) (tptp.s _let_4 (tptp.i _let_6 _let_2))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))))))))))))))) (forall ((Q50725 $$unsorted)) (let ((_let_1 (tptp.fun Q50725 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 tptp.empty)))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.finite))) (let ((_let_5 (tptp.s _let_1 T0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.union) _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.union) _let_4)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_2))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (or (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inter) _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.insert) (tptp.s A X))) _let_2)))) (tptp.s tptp.bool (tptp.i _let_3 _let_2)))))))) (forall ((Q50925 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun Q50925 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q50925 _let_2) tptp.insert) (tptp.s Q50925 A5))) (tptp.s _let_1 tptp.empty))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.delete) _let_2)) (tptp.s A X)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (let ((_let_4 (tptp.fun A _let_1))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.delete) _let_2)) (tptp.s A X))))) (tptp.s tptp.bool (tptp.i _let_3 _let_2)))))))) (forall ((Q50997 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q50997 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) _let_3))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q50997 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_56 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B GENR_PVARR_56)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B Y) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.setspec) (tptp.s B GENR_PVARR_56))) _let_1)) (tptp.s B Y))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3)) (tptp.s _let_1 F0))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (A5 $$unsorted) (GENR_PVARR_57 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) (tptp.s _let_1 A5))) (tptp.s A GENR_PVARR_57)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (tptp.s _let_5 A5)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_57))) _let_2)) _let_1))))))))))))))))))) (forall ((F0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 S0))) (tptp.s _let_3 F0))) _let_2))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_61 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) (tptp.s _let_1 T0))) (tptp.s A GENR_PVARR_61)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (tptp.s _let_5 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_61))) _let_2)) _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (Y $$unsorted) (GENR_PVARR_60 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B Y))) (tptp.s A GENR_PVARR_60)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_60))) _let_2)) _let_1)))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun B _let_7) tptp.in) _let_1)) (tptp.s _let_6 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) _let_1))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) (tptp.s _let_4 S0))) (tptp.s _let_3 F0))) _let_2))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_63 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_1) (tptp.s _let_2 F0))) (tptp.s _let_1 T0))) (tptp.s A GENR_PVARR_63)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.setspec) (tptp.s A GENR_PVARR_63))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (tptp.s _let_2 T0))))) _let_1))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (Y $$unsorted) (GENR_PVARR_62 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 F0))) (tptp.s B Y))) (tptp.s A GENR_PVARR_62)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_62))) _let_2)) _let_1)))))))))))))) (forall ((F0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 F0))) _let_1)))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) (tptp.s _let_3 F0))) _let_2)))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (A5 $$unsorted) (GENR_PVARR_64 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 A5))) (tptp.s A GENR_PVARR_64)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.setspec) (tptp.s A GENR_PVARR_64))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (tptp.s _let_2 A5))))) _let_1))))))))))))))) (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (=> (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 F0))) _let_2)))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (=> (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.infinite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.infinite) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))))))))))))) (forall ((Q51578 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q51578 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.infinite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 tptp.infinite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.diff) _let_3)) _let_2))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_3 T0))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.subset) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 S0))))))) (exists ((SI_ $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 SI_))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (= (tptp.s _let_4 T0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2))))))))))))))))))) (forall ((Q51738 $$unsorted) (Q51718 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (= (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q51738 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q51718 tptp.bool))) (let ((_let_5 (tptp.fun Q51718 Q51738))) (let ((_let_6 (tptp.fun _let_4 _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.image) (tptp.s _let_5 F0))) (tptp.s _let_4 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q51718 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q51718 Q51738))) (let ((_let_4 (tptp.fun Q51738 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2))))))))))))))) (forall ((Q51804 $$unsorted) (Q51784 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (= (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q51804 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q51784 tptp.bool))) (let ((_let_5 (tptp.fun Q51784 Q51804))) (let ((_let_6 (tptp.fun _let_4 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.image) (tptp.s _let_5 F0))) (tptp.s _let_4 S0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q51784 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q51784 Q51804))) (let ((_let_4 (tptp.fun Q51804 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_2)) (tptp.s _let_1 S0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_3 T0))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.subset) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 S0))))))) (exists ((SI_ $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 SI_))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.subset) (tptp.s _let_4 T0))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))))))))))))))))))))) (forall ((Q51863 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q51863 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.diff) _let_2)) (tptp.s _let_1 T0)))))))))))) (forall ((Q51883 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q51883 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.infinite))) (let ((_let_5 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_5)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.s B tptp.b0))) (let ((_let_2 (tptp.s B tptp.a0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.s0))) (let ((_let_5 (tptp.fun A (tptp.fun B B)))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun B _let_6))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun B _let_8))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.finrec) (tptp.s _let_5 tptp.f))) _let_1)) _let_4)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (and (= _let_4 (tptp.s _let_3 tptp.empty)) (= _let_2 _let_1))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A (tptp.fun B B)))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun B _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.finrec) (tptp.s _let_2 tptp.f))) (tptp.s B tptp.b0))) (tptp.s _let_1 tptp.s0))) (tptp.s B tptp.a0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) (tptp.s tptp.num tptp.n)))))) (exists ((X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s B C0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.f))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 tptp.s0))) (let ((_let_8 (tptp.fun A _let_6))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun B _let_9))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (let ((_let_12 (tptp.fun B _let_11))) (let ((_let_13 (tptp.fun _let_6 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun A _let_13) tptp.in) _let_2)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.finrec) _let_5)) (tptp.s B tptp.b0))) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.delete) _let_7)) _let_2)))) _let_1)) (tptp.s tptp.num tptp.n)))) (= (tptp.s B tptp.a0) (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))))))))))) (forall ((Q51988 $$unsorted) (Q51987 $$unsorted) (F0 $$unsorted) (B0 $$unsorted) (S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun Q51988 tptp.bool))) (let ((_let_3 (tptp.fun Q51988 (tptp.fun Q51987 Q51987)))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun Q51987 _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun Q51987 _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.finrec) (tptp.s _let_3 F0))) (tptp.s Q51987 B0))) (tptp.s _let_2 S0))) (tptp.s Q51987 A5))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q51988 X))) (let ((_let_2 (tptp.fun Q51987 Q51987))) (let ((_let_3 (tptp.fun Q51988 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (and (= (tptp.s _let_3 S0) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q51988 _let_4) tptp.insert) _let_1)) (tptp.s _let_3 tptp.empty)))) (= (tptp.s Q51987 A5) (tptp.s Q51987 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q51988 _let_2) F0) _let_1)) (tptp.s Q51987 B0))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s B S0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) F0))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s A Y))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_4 _let_6)))) (=> (not (= _let_2 _let_6)) (= (tptp.s B (tptp.i _let_5 (tptp.s B (tptp.i _let_7 _let_1)))) (tptp.s B (tptp.i _let_7 (tptp.s B (tptp.i _let_5 _let_1)))))))))))))) (forall ((N0 $$unsorted) (S0 $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A (tptp.fun B B)))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun B _let_5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.finrec) (tptp.s _let_2 F0))) (tptp.s B B0))) (tptp.s _let_1 S0))) (tptp.s B Z0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) (tptp.s tptp.num N0)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 S0)))) (exists ((W $$unsorted)) (let ((_let_1 (tptp.s B W))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun A _let_6))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun B _let_8))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (let ((_let_11 (tptp.fun B _let_10))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_4 _let_11) tptp.finrec) _let_5)) (tptp.s B B0))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.delete) (tptp.s _let_6 S0))) _let_2)))) _let_1)) (tptp.s tptp.num N0)))) (= (tptp.s B Z0) (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s B S0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) F0))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s A Y))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_4 _let_6)))) (=> (not (= _let_2 _let_6)) (= (tptp.s B (tptp.i _let_5 (tptp.s B (tptp.i _let_7 _let_1)))) (tptp.s B (tptp.i _let_7 (tptp.s B (tptp.i _let_5 _let_1)))))))))))))) (forall ((N1 $$unsorted) (N2 $$unsorted) (S0 $$unsorted) (A10 $$unsorted) (A20 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N2))) (let ((_let_2 (tptp.s tptp.num N1))) (let ((_let_3 (tptp.s B A20))) (let ((_let_4 (tptp.s B A10))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun A (tptp.fun B B)))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun B _let_7))) (let ((_let_9 (tptp.fun _let_5 _let_8))) (let ((_let_10 (tptp.fun B _let_9))) (let ((_let_11 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.finrec) (tptp.s _let_6 F0))) (tptp.s B B0))) (tptp.s _let_5 S0))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_11 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_11 _let_3)) _let_1)))) (and (= _let_4 _let_3) (= _let_2 _let_1))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (B0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((A5 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A (tptp.fun B B)))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun B _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.finrec) (tptp.s _let_2 F0))) (tptp.s B B0))) (tptp.s _let_1 S0))) (tptp.s B A5))) (tptp.s tptp.num N0)))))))))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted) (P0 $$unsorted) (R0 $$unsorted)) (=> (and (forall ((S0 $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A S0)))) (exists ((A5 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.fun B _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) R0) (tptp.s A S0))) (tptp.s B A5))) (tptp.s C N0))))))))) (forall ((N1 $$unsorted) (N2 $$unsorted) (S0 $$unsorted) (A10 $$unsorted) (A20 $$unsorted)) (let ((_let_1 (tptp.s C N2))) (let ((_let_2 (tptp.s C N1))) (let ((_let_3 (tptp.s B A20))) (let ((_let_4 (tptp.s B A10))) (let ((_let_5 (tptp.fun C tptp.bool))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) R0) (tptp.s A S0))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))))) (exists ((F0 $$unsorted)) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s A S0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))) (= (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.fun B _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) R0) (tptp.s A S0))) (tptp.s B A5))) (tptp.s C N0))))))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B A5))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s B S0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) F0))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s A Y))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_4 _let_6)))) (=> (not (= _let_2 _let_6)) (= (tptp.s B (tptp.i _let_5 (tptp.s B (tptp.i _let_7 _let_1)))) (tptp.s B (tptp.i _let_7 (tptp.s B (tptp.i _let_5 _let_1)))))))))))))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (and (= (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) G0) (tptp.s _let_1 tptp.empty))) (tptp.s B B0)) (forall ((S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_2 B) G0))) (let ((_let_6 (tptp.fun B B))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_1)) _let_3)))) (= (tptp.s B (tptp.i _let_5 _let_3)) (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) F0) _let_1)) (tptp.s B (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.delete) _let_3)) _let_1))))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s B S0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) F0))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s A Y))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_4 _let_6)))) (=> (not (= _let_2 _let_6)) (= (tptp.s B (tptp.i _let_5 (tptp.s B (tptp.i _let_7 _let_1)))) (tptp.s B (tptp.i _let_7 (tptp.s B (tptp.i _let_5 _let_1)))))))))))))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (and (= (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) G0) (tptp.s _let_1 tptp.empty))) (tptp.s B B0)) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 B) G0))) (let ((_let_4 (tptp.s B (tptp.i _let_3 _let_2)))) (let ((_let_5 (tptp.s A X))) (let ((_let_6 (tptp.fun B B))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun B _let_6))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_2))) (= (tptp.s B (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun A _let_9) tptp.insert) _let_5)) _let_2)))) (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_5)) _let_2)))) _let_4)) (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) F0) _let_5)) _let_4))))))))))))))))))))) (forall ((Q52643 $$unsorted) (Q52644 $$unsorted) (U_0 $$unsorted)) (=> (forall ((B0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.s Q52643 B0))) (let ((_let_2 (tptp.fun Q52644 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 Q52643))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun Q52644 (tptp.fun Q52643 Q52643)))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun _let_5 _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q52643 _let_7) U_0) _let_1)) (tptp.s _let_5 F0))) _let_4))) (and (= (tptp.s Q52643 (tptp.i _let_4 (tptp.s _let_2 tptp.empty))) _let_1) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q52644 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 Q52643) G0))) (let ((_let_4 (tptp.s Q52643 (tptp.i _let_3 _let_2)))) (let ((_let_5 (tptp.s Q52644 X))) (let ((_let_6 (tptp.fun Q52643 Q52643))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun Q52643 _let_6))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_2))) (= (tptp.s Q52643 (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q52644 _let_9) tptp.insert) _let_5)) _let_2)))) (tptp.s Q52643 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q52644 _let_7) tptp.in) _let_5)) _let_2)))) _let_4)) (tptp.s Q52643 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q52644 _let_6) F0) _let_5)) _let_4)))))))))))))))))))))))))) (forall ((B0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q52644 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q52643 Q52643))) (let ((_let_4 (tptp.fun Q52644 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s Q52643 B0))) (let ((_let_7 (tptp.fun _let_1 Q52643))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_1 _let_3))) (= (tptp.s Q52643 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.itset) _let_5)) _let_2)) _let_6)) (tptp.s Q52643 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_8 _let_7) tptp.h_) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q52643 _let_9) U_0) _let_6)) _let_5)))) _let_2)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s B B0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_3))) (=> (forall ((X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s B S0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) F0))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s A Y))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_4 _let_6)))) (=> (not (= _let_2 _let_6)) (= (tptp.s B (tptp.i _let_5 (tptp.s B (tptp.i _let_7 _let_1)))) (tptp.s B (tptp.i _let_7 (tptp.s B (tptp.i _let_5 _let_1)))))))))))))) (and (= (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.itset) (tptp.s _let_4 F0))) (tptp.s _let_2 tptp.empty))) _let_1)) _let_1) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s B B0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun B B))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_2 _let_4))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.itset) _let_6)))) (let ((_let_9 (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_8 _let_3)) _let_1)))) (let ((_let_10 (tptp.s A X))) (let ((_let_11 (tptp.fun _let_2 tptp.bool))) (let ((_let_12 (tptp.fun B _let_4))) (let ((_let_13 (tptp.fun _let_2 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 tptp.finite) _let_3))) (= (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_2 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun A _let_13) tptp.insert) _let_10)) _let_3)))) _let_1)) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.bool _let_12) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_10)) _let_3)))) _let_9)) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_10)) _let_9)))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s B B0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_3))) (=> (forall ((X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s B S0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) F0))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s A Y))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_4 _let_6)))) (=> (not (= _let_2 _let_6)) (= (tptp.s B (tptp.i _let_5 (tptp.s B (tptp.i _let_7 _let_1)))) (tptp.s B (tptp.i _let_7 (tptp.s B (tptp.i _let_5 _let_1)))))))))))))) (and (= (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.itset) (tptp.s _let_4 F0))) (tptp.s _let_2 tptp.empty))) _let_1)) _let_1) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s B B0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun A _let_3))) (let ((_let_6 (tptp.fun B B))) (let ((_let_7 (tptp.fun A _let_6))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun _let_3 _let_6))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.itset) _let_8)))) (let ((_let_11 (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.delete) _let_4)) _let_2)))) _let_1)))) (let ((_let_12 (tptp.fun _let_3 tptp.bool))) (let ((_let_13 (tptp.fun B _let_6))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 tptp.finite) _let_4))) (= (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i _let_10 _let_4)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.bool _let_13) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun A _let_12) tptp.in) _let_2)) _let_4)))) (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_2)) _let_11)))) _let_11)))))))))))))))))))))))))) (forall ((Q52949 $$unsorted) (Q52950 $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s Q52950 B0))) (let ((_let_2 (tptp.fun Q52949 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun Q52950 Q52950))) (let ((_let_5 (tptp.fun Q52949 _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_4))) (let ((_let_7 (tptp.s (tptp.fun _let_5 _let_6) tptp.itset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q52949 X))) (let ((_let_2 (tptp.fun Q52950 Q52950))) (let ((_let_3 (tptp.fun Q52949 _let_2))) (let ((_let_4 (tptp.fun Q52949 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q52949 _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 F0) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 G0) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (S1 $$unsorted)) (let ((_let_1 (tptp.s Q52950 S1))) (let ((_let_2 (tptp.s Q52949 X))) (let ((_let_3 (tptp.fun Q52950 Q52950))) (let ((_let_4 (tptp.s (tptp.fun Q52949 _let_3) F0))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s Q52949 Y))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_4 _let_6)))) (=> (not (= _let_2 _let_6)) (= (tptp.s Q52950 (tptp.i _let_5 (tptp.s Q52950 (tptp.i _let_7 _let_1)))) (tptp.s Q52950 (tptp.i _let_7 (tptp.s Q52950 (tptp.i _let_5 _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (S1 $$unsorted)) (let ((_let_1 (tptp.s Q52950 S1))) (let ((_let_2 (tptp.s Q52949 X))) (let ((_let_3 (tptp.fun Q52950 Q52950))) (let ((_let_4 (tptp.s (tptp.fun Q52949 _let_3) G0))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s Q52949 Y))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_4 _let_6)))) (=> (not (= _let_2 _let_6)) (= (tptp.s Q52950 (tptp.i _let_5 (tptp.s Q52950 (tptp.i _let_7 _let_1)))) (tptp.s Q52950 (tptp.i _let_7 (tptp.s Q52950 (tptp.i _let_5 _let_1))))))))))))))) (= (tptp.s Q52950 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_5 F0))) _let_3)) _let_1)) (tptp.s Q52950 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_5 G0))) _let_3)) _let_1)))))))))))) (forall ((Q52983 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_66 $$unsorted)) (let ((_let_1 (tptp.fun Q52983 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s Q52983 GENR_PVARR_66)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q52983 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q52983 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q52983 _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q52983 _let_4) tptp.setspec) (tptp.s Q52983 GENR_PVARR_66))) _let_2)) _let_1)))))))))))))) (forall ((S0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun Q52983 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)) (tptp.s _let_1 P0))))))) _let_2)))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_67 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s A GENR_PVARR_67)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_67))) _let_2)) _let_1)))))))))))))) (forall ((S0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)) (tptp.s _let_1 P0)))))))))))))))) (forall ((Q53037 $$unsorted) (U_1 $$unsorted)) (=> (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 U_1) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q53037 _let_1) U_0) (tptp.s Q53037 X))) (tptp.s _let_1 U_1)))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun Q53037 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun Q53037 _let_1))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.itset) (tptp.s _let_4 U_0))) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) (tptp.s _let_1 tptp.empty))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_2)))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s A X))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_5))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_2))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun A _let_9) tptp.insert) _let_6)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_6)) _let_2)))) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.suc) _let_4)))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.inter) _let_4)) _let_2)) (tptp.s _let_1 tptp.empty))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.union) _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_2)))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s A X))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun A _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 tptp.finite) _let_2))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.delete) _let_2)) _let_7)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) tptp.in) _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.m_) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_4)))))))))))))) (forall ((Q53282 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun Q53282 tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s _let_1 T0))) (let ((_let_5 (tptp.s _let_1 S0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.inter) _let_5)) _let_4)) (tptp.s _let_1 tptp.empty)) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.union) _let_5)) _let_4)) _let_2)) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.p_) (tptp.s tptp.num (tptp.i _let_3 _let_5)))) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))) (forall ((Q53339 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q53339 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.subset) _let_2)) _let_4)))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.diff) _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.m_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))))) (forall ((Q53377 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q53377 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (= _let_2 (tptp.s _let_1 tptp.empty))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 tptp.empty)))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.s A X))) (let ((_let_6 (tptp.fun A _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_5)) _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.delete) _let_2)) _let_5))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))))) (forall ((Q53496 $$unsorted) (S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun Q53496 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hasu_size) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)) _let_1)))))))) (forall ((Q53515 $$unsorted) (S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun Q53515 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hasu_size) _let_3)) _let_1))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)) _let_1))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.hasu_size) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_2 (tptp.s _let_1 tptp.empty))))))) (forall ((A $$unsorted) (S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.hasu_size) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) (tptp.s tptp.num N0)))))) (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.hasu_size) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.delete) _let_3)) _let_1)))) (tptp.s tptp.num N0)))))))))))))))))) (forall ((Q53649 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun Q53649 tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.s _let_4 S0))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_4 _let_8) tptp.hasu_size))) (let ((_let_10 (tptp.fun _let_4 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.disjoint) _let_6)) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.union) _let_6)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1))))))))))))))))) (forall ((Q53685 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun Q53685 tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.s _let_4 S0))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_4 _let_8) tptp.hasu_size))) (let ((_let_10 (tptp.fun _let_4 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.subset) _let_5)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.diff) _let_6)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.m_) _let_2)) _let_1))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_70 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_70)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.setspec) (tptp.s _let_2 GENR_PVARR_70))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.hasu_size) _let_6)) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.hasu_size) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))) (tptp.s tptp.num N0))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun A _let_2) T0))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun A _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_4)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) _let_7))) (not (= _let_4 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.disjoint) (tptp.s _let_2 (tptp.i _let_3 _let_4)))) (tptp.s _let_2 (tptp.i _let_3 _let_1))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.hasu_size) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_7 _let_3) tptp.unions) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) _let_6)) (tptp.s _let_4 T0))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_1)) (tptp.s tptp.num N0))))))))))))))))))) (forall ((Q53889 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q53889 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.hasu_size) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))) (forall ((Q53951 $$unsorted)) (let ((_let_1 (tptp.fun Q53951 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.hasu_size) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_2 (tptp.s _let_1 tptp.empty))))))) (forall ((Q53951 $$unsorted)) (let ((_let_1 (tptp.fun Q53951 tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.hasu_size) (tptp.s _let_1 tptp.s0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) (tptp.s tptp.num tptp.n)))))) (exists ((A5 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q53951 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s Q53951 A5))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.hasu_size) _let_2)) (tptp.s tptp.num tptp.n)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q53951 _let_5) tptp.in) _let_3)) _let_2)))) (= (tptp.s _let_1 tptp.s0) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q53951 _let_4) tptp.insert) _let_3)) _let_2))))))))))))))) (forall ((A $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) _let_3)) _let_2))) (= (tptp.s tptp.num (tptp.i _let_4 _let_3)) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) (= _let_3 _let_2)))))))) (forall ((A $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s _let_1 A5))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))) (forall ((A $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) (tptp.s tptp.num (tptp.i _let_4 _let_3)))))) (= _let_3 _let_2))))))))) (forall ((Q54262 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q54262 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) _let_3)) _let_2)))) (= (= (tptp.s tptp.num (tptp.i _let_4 _let_3)) (tptp.s tptp.num (tptp.i _let_4 _let_2))) (= _let_3 _let_2))))))))) (forall ((A $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s _let_1 A5))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.psubset) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.union) _let_4)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_76 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_76)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.setspec) (tptp.s _let_2 GENR_PVARR_76))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.hasu_size) _let_6)) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)))) (tptp.s tptp.num N0)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_7 _let_3) tptp.unions) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) _let_6)) (tptp.s _let_4 T0))))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_1)) (tptp.s tptp.num N0))))))))))))))))))) (forall ((Q54685 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q54685 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_2)))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.union) _let_3)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.p_) (tptp.s tptp.num (tptp.i _let_6 _let_3)))) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.inter) _let_3)) _let_2)))))))))))))))))) (forall ((Q54766 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q54766 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2)))) (= (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.union) _let_3)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.p_) (tptp.s tptp.num (tptp.i _let_6 _let_3)))) (tptp.s tptp.num (tptp.i _let_6 _let_2))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.inter) _let_3)) _let_2)) (tptp.s _let_1 tptp.empty))))))))))))) (forall ((Q54808 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q54808 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_) (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.union) _let_3)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.p_) (tptp.s tptp.num (tptp.i _let_6 _let_3)))) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))) (not (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.inter) _let_3)) _let_2)) (tptp.s _let_1 tptp.empty)))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.hasu_size) _let_3)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.hasu_size) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) (tptp.s _let_4 F0))) _let_3)))) _let_1)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 T0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.s (tptp.fun A B) F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) (tptp.s _let_3 T0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))) (forall ((Q55049 $$unsorted) (Q55042 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q55042 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q55049 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun Q55042 Q55049))) (let ((_let_7 (tptp.fun _let_1 _let_3))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.subset) _let_4)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.image) (tptp.s _let_6 F0))) _let_2)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))))))) (forall ((Q55109 $$unsorted) (Q55114 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun Q55114 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun Q55114 Q55109))) (let ((_let_6 (tptp.fun Q55109 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q55114 Y))) (let ((_let_2 (tptp.s Q55114 X))) (let ((_let_3 (tptp.s (tptp.fun Q55114 Q55109) F0))) (let ((_let_4 (tptp.fun Q55114 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q55114 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q55109 (tptp.i _let_3 _let_2)) (tptp.s Q55109 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.hasu_size) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) (tptp.s _let_5 F0))) _let_3)))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hasu_size) _let_3)) _let_1)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))))))))) (forall ((A $$unsorted) (N0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num N0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.hasu_size) _let_2)) (tptp.s tptp.num N0))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num N0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) (tptp.s _let_1 S0)))))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.hasu_size) _let_2)) (tptp.s tptp.num N0))))))))))))))))) (forall ((A $$unsorted) (N0 $$unsorted) (S0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.s _let_7 tptp.finite))) (let ((_let_9 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.subset) _let_9)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_3 _let_9)))) _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 S0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) (tptp.s _let_1 U)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.hasu_size) _let_2)) (tptp.s tptp.num N0)))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_79 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_79)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.in) _let_1)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) T0) _let_2))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_79))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((S0 $$unsorted) (M0 $$unsorted) (T0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.hasu_size) _let_5)) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.hasu_size) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))) (tptp.s tptp.num N0)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.hasu_size) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)) (tptp.s _let_3 T0))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.t_) _let_1)) (tptp.s tptp.num N0)))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_84 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B C)))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun C tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 F0))) (tptp.s C GENR_PVARR_84)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun C tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun B tptp.bool))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (and (= (tptp.p _let_4) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun A _let_10) tptp.in) _let_2)) (tptp.s _let_9 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun B _let_8) tptp.in) _let_1)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) T0) _let_2))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun C _let_6) tptp.setspec) (tptp.s C GENR_PVARR_84))) _let_4)) (tptp.s C (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) F0) _let_2)) _let_1))))))))))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B C)))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun C tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_4)) (tptp.s _let_2 T0))) (tptp.s _let_1 F0))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_85 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_85)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.in) _let_1)) (tptp.s _let_8 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_85))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_2))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_86 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_86)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.in) _let_1)) (tptp.s _let_8 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_86))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.card) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_4)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_87 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_87)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.in) _let_1)) (tptp.s _let_8 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_87))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((S0 $$unsorted) (M0 $$unsorted) (T0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.hasu_size) _let_7)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.hasu_size) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.hasu_size) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_8 _let_8) tptp.gspec) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_0) _let_7)) _let_5)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1))))))))))))))))))) (forall ((Q56069 $$unsorted) (Q56068 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_88 $$unsorted)) (let ((_let_1 (tptp.prod Q56069 Q56068))) (let ((_let_2 (tptp.fun Q56068 tptp.bool))) (let ((_let_3 (tptp.fun Q56069 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_88)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q56068 Y))) (let ((_let_2 (tptp.s Q56069 X))) (let ((_let_3 (tptp.prod Q56069 Q56068))) (let ((_let_4 (tptp.fun Q56068 _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun Q56068 tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun Q56069 tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q56069 _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q56068 _let_9) tptp.in) _let_1)) (tptp.s _let_8 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_88))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q56069 _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q56068 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q56069 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.prod Q56069 Q56068) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.cross0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2))))))))))))))) (forall ((Q56105 $$unsorted) (Q56108 $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q56108 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s Q56108 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun Q56105 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.s Q56105 X))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.prod Q56105 Q56108))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun Q56108 _let_9))) (let ((_let_13 (tptp.fun _let_10 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_9 _let_13) tptp.in) (tptp.s _let_9 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun Q56105 _let_12) tptp.c_) _let_7)) _let_3)))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_5 _let_11) tptp.cross0) _let_6)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q56105 _let_8) tptp.in) _let_7)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q56108 _let_4) tptp.in) _let_3)) _let_2))))))))))))))))))) (forall ((Q56133 $$unsorted) (Q56136 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun Q56136 tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun Q56133 tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun (tptp.prod Q56133 Q56136) tptp.bool))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.hasu_size) _let_7)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.hasu_size) _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.hasu_size) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.cross0) _let_7)) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) _let_2)) _let_1))))))))))))))))) (forall ((Q56161 $$unsorted) (Q56163 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q56163 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q56161 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.prod Q56161 Q56163) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.cross0) _let_4)) _let_2))))))))))))) (forall ((Q56184 $$unsorted) (Q56186 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q56186 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q56184 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun (tptp.prod Q56184 Q56186) tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.card) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.cross0) _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))) (forall ((Q56227 $$unsorted) (Q56231 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q56231 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q56227 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.prod Q56227 Q56231) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (= (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.cross0) _let_4)) _let_2)) (tptp.s _let_5 tptp.empty)) (or (= _let_4 (tptp.s _let_3 tptp.empty)) (= _let_2 (tptp.s _let_1 tptp.empty))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (S0 $$unsorted) (D0 $$unsorted) (GENR_PVARR_92 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) (tptp.s _let_3 T0))) (tptp.s _let_2 S0))) (tptp.s B D0))) (tptp.s _let_1 GENR_PVARR_92)))) (exists ((F0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0))))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B D0))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_92))) _let_2)) (tptp.s _let_1 F0)))))))))))))))))) (forall ((D0 $$unsorted) (N0 $$unsorted) (T0 $$unsorted) (M0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun (tptp.fun A B) tptp.bool))) (let ((_let_9 (tptp.fun B _let_8))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_4 _let_11) tptp.hasu_size) _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_6 _let_11) tptp.hasu_size) _let_7)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.hasu_size) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_8 _let_8) tptp.gspec) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_5)) (tptp.s B D0))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0) _let_2)) _let_1)))))))))))))))))))) (forall ((Q56534 $$unsorted) (Q56537 $$unsorted) (U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (S0 $$unsorted) (GENR_PVARR_93 $$unsorted)) (let ((_let_1 (tptp.fun Q56537 Q56534))) (let ((_let_2 (tptp.fun Q56537 tptp.bool))) (let ((_let_3 (tptp.fun Q56534 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 T0))) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_93)))) (exists ((F0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun Q56537 Q56534))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q56534 tptp.bool))) (let ((_let_2 (tptp.s Q56537 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q56537 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q56537 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q56534 _let_3) tptp.in) (tptp.s Q56534 (tptp.i (tptp.s (tptp.fun Q56537 Q56534) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q56537 X))) (let ((_let_2 (tptp.fun Q56537 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q56537 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0))))) (= (tptp.s Q56534 (tptp.i (tptp.s (tptp.fun Q56537 Q56534) F0) _let_1)) (tptp.s Q56534 tptp.d))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_93))) _let_2)) (tptp.s _let_1 F0))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q56537 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q56534 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun (tptp.fun Q56537 Q56534) tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.card) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_4)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.exp0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))))) (forall ((Q56600 $$unsorted) (Q56603 $$unsorted) (U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (S0 $$unsorted) (GENR_PVARR_94 $$unsorted)) (let ((_let_1 (tptp.fun Q56603 Q56600))) (let ((_let_2 (tptp.fun Q56603 tptp.bool))) (let ((_let_3 (tptp.fun Q56600 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 T0))) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_94)))) (exists ((F0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun Q56603 Q56600))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q56600 tptp.bool))) (let ((_let_2 (tptp.s Q56603 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q56603 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q56603 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q56600 _let_3) tptp.in) (tptp.s Q56600 (tptp.i (tptp.s (tptp.fun Q56603 Q56600) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q56603 X))) (let ((_let_2 (tptp.fun Q56603 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q56603 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0))))) (= (tptp.s Q56600 (tptp.i (tptp.s (tptp.fun Q56603 Q56600) F0) _let_1)) (tptp.s Q56600 tptp.d))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_94))) _let_2)) (tptp.s _let_1 F0))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q56603 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q56600 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun (tptp.fun Q56603 Q56600) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_2))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun (tptp.fun A B) tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.fun A tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_7 _let_5) tptp.hasu_size) (tptp.s _let_7 tptp.univ))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.hasu_size) (tptp.s _let_6 tptp.univ))) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.hasu_size) (tptp.s _let_4 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0) _let_2)) _let_1)))))))))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.univ))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.univ))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun (tptp.fun A B) tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.card) (tptp.s _let_6 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.exp0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun A B) tptp.bool))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 tptp.univ)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 tptp.univ))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 tptp.univ))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_77 _let_18) tptp.hasu_size) _let_78)) _let_33))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_77 tptp.num) tptp.card) _let_78)) _let_33) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_77 tptp.bool) tptp.finite) _let_78))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_97 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_97)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_97))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 S0))))) _let_2)))))))))))) (forall ((S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.hasu_size) _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.hasu_size) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.exp0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_98 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_98)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_98))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 S0))))) _let_2)))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_99 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_99)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_99))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 S0))))) _let_2)))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) _let_3))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))))))))))))))) (forall ((Q56919 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun Q56919 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (forall ((GENR_PVARR_100 $$unsorted)) (let ((_let_1 (tptp.fun Q56919 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 GENR_PVARR_100)))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q56919 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_100))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 tptp.empty))))) _let_2))))))))))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_2 U_0))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.insert) (tptp.s _let_1 tptp.empty))) (tptp.s _let_2 tptp.empty))))))))) (forall ((A $$unsorted) (U_2 $$unsorted)) (=> (forall ((A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A A5))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun A _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_2) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.insert) _let_3)) _let_2))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (GENR_PVARR_102 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_102)))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_102))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 T0))))) _let_2)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (T0 $$unsorted) (GENR_PVARR_101 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) U_0) (tptp.s A A5))) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_101)))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_101))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.insert) (tptp.s A A5))) (tptp.s _let_1 T0))))))) _let_2)))))))))))))) (forall ((A5 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (let ((_let_6 (tptp.s _let_5 tptp.gspec))) (let ((_let_7 (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_1) _let_2)))))) (let ((_let_8 (tptp.s A A5))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) U_0) _let_8)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.union) _let_7)) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_9 _let_5) tptp.image) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun A _let_9) U_2) _let_8)))) _let_7))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_107 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_107)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_107))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num N0))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.hasu_size) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) _let_1)))))) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_108 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_108)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_108))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num N0))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) _let_1)))))) _let_1)))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_109 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_109)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_109))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num N0))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_110 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_110)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_110))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_1)) (tptp.s tptp.num N0))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.hasu_size) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) U_0) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_111 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_111)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_111))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_1)) (tptp.s tptp.num N0))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_112 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_112)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_112))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_1)) (tptp.s tptp.num N0))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) U_0) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((A5 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_1)) (tptp.s tptp.num A5))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.in) (tptp.s tptp.num A5))) (tptp.s _let_1 S0))))))))))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_58 tptp.finite) _let_50)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_58 tptp.infinite) _let_50))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_76 tptp.bool) tptp.infinite) (tptp.s _let_76 tptp.univ)))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_122 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real A5))) (tptp.s tptp.real GENR_PVARR_122)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.setspec) (tptp.s tptp.real GENR_PVARR_122))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real A5))) _let_1)))) _let_1)))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real A5))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_123 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real A5))) (tptp.s tptp.real GENR_PVARR_123)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.setspec) (tptp.s tptp.real GENR_PVARR_123))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real A5))) _let_1)))) _let_1)))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real A5))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((B0 $$unsorted) (GENR_PVARR_124 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real B0))) (tptp.s tptp.real GENR_PVARR_124)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.setspec) (tptp.s tptp.real GENR_PVARR_124))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) _let_1)) (tptp.s tptp.real B0))))) _let_1)))))))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real B0))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((B0 $$unsorted) (GENR_PVARR_125 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real B0))) (tptp.s tptp.real GENR_PVARR_125)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.setspec) (tptp.s tptp.real GENR_PVARR_125))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))) _let_1)))))))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real B0))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (GENR_PVARR_126 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) (tptp.s tptp.real A5))) (tptp.s tptp.real B0))) (tptp.s tptp.real GENR_PVARR_126)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real A5))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.real B0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.setspec) (tptp.s tptp.real GENR_PVARR_126))) _let_2)) _let_1)))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real A5))) (let ((_let_2 (tptp.s tptp.real B0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) U_0) _let_1)) _let_2)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1)))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (GENR_PVARR_127 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) (tptp.s tptp.real A5))) (tptp.s tptp.real B0))) (tptp.s tptp.real GENR_PVARR_127)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun tptp.real _let_3))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.realu_le) (tptp.s tptp.real A5))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.realu_lt) _let_1)) (tptp.s tptp.real B0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.setspec) (tptp.s tptp.real GENR_PVARR_127))) _let_2)) _let_1)))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real A5))) (let ((_let_2 (tptp.s tptp.real B0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) U_0) _let_1)) _let_2)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1)))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (GENR_PVARR_128 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) (tptp.s tptp.real A5))) (tptp.s tptp.real B0))) (tptp.s tptp.real GENR_PVARR_128)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun tptp.real _let_3))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.realu_lt) (tptp.s tptp.real A5))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.realu_le) _let_1)) (tptp.s tptp.real B0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.setspec) (tptp.s tptp.real GENR_PVARR_128))) _let_2)) _let_1)))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real A5))) (let ((_let_2 (tptp.s tptp.real B0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) U_0) _let_1)) _let_2)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1)))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (GENR_PVARR_129 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) (tptp.s tptp.real A5))) (tptp.s tptp.real B0))) (tptp.s tptp.real GENR_PVARR_129)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real A5))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.real B0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.setspec) (tptp.s tptp.real GENR_PVARR_129))) _let_2)) _let_1)))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real A5))) (let ((_let_2 (tptp.s tptp.real B0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) U_0) _let_1)) _let_2)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_57 tptp.infinite) _let_4))) (forall ((A $$unsorted) (S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.hasu_size) (tptp.s _let_1 S0))) (tptp.s tptp.num N0)))) (exists ((F0 $$unsorted)) (and (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_) _let_2)) (tptp.s tptp.num N0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) (tptp.s A (tptp.i (tptp.s (tptp.fun tptp.num A) F0) _let_2)))) (tptp.s _let_1 S0)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 S0)))) (and (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num N0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun tptp.num A) F0) _let_1)) (tptp.s A X)))))) (forall ((M0 $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.num XI_))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.s (tptp.fun tptp.num A) F0))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (= (tptp.s A (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s A (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.list A))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.setu_ofu_list) (tptp.s _let_2 tptp.nil))) (tptp.s _let_1 tptp.empty))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.setu_ofu_list))) (let ((_let_5 (tptp.s A tptp.h0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.cons) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.insert) _let_5)) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((Q58114 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun Q58114 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.list Q58114))) (let ((_let_4 (tptp.s _let_3 L))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_2)) _let_4))) (and (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.setu_ofu_list) _let_4)) _let_2) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.length) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q58114 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.list Q58114))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.listu_ofu_set) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.h_) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.list A))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.listu_ofu_set) _let_2)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (and (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.setu_ofu_list) _let_4)) _let_2) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.length) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))) (forall ((Q58163 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q58163 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.list Q58163))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.setu_ofu_list) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.listu_ofu_set) _let_2)))) _let_2)))))) (forall ((Q58179 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q58179 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.list Q58179))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.length) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.listu_ofu_set) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.list A))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.mem) _let_3)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.listu_ofu_set) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_3)) _let_2))))))))))))) (forall ((Q58224 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q58224))) (let ((_let_2 (tptp.fun Q58224 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.setu_ofu_list) (tptp.s _let_1 L))))))))) (forall ((Q58242 $$unsorted) (X $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q58242))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s Q58242 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun Q58242 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q58242 _let_6) tptp.in) _let_3)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setu_ofu_list) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q58242 _let_4) tptp.mem) _let_3)) _let_2)))))))))) (forall ((Q58267 $$unsorted) (L1 $$unsorted) (L2 $$unsorted)) (let ((_let_1 (tptp.list Q58267))) (let ((_let_2 (tptp.s _let_1 L2))) (let ((_let_3 (tptp.fun Q58267 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.setu_ofu_list))) (let ((_let_5 (tptp.s _let_1 L1))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.append) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.union) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((Q58289 $$unsorted) (Q58291 $$unsorted) (F0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q58291))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q58291 tptp.bool))) (let ((_let_4 (tptp.fun Q58291 Q58289))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q58289 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.list Q58289))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_8 _let_6) tptp.setu_ofu_list) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.map0) _let_5)) _let_2)))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.image) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.setu_ofu_list) _let_2))))))))))))))) (forall ((Q58308 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q58308))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q58308 tptp.bool))) (= (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.setu_ofu_list) _let_2)) (tptp.s _let_3 tptp.empty)) (= _let_2 (tptp.s _let_1 tptp.nil))))))) (forall ((Q58342 $$unsorted) (S0 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun Q58342 tptp.bool))) (let ((_let_2 (tptp.fun Q58342 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.pairwise) (tptp.s _let_2 R0))) (tptp.s _let_1 S0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q58342 Y))) (let ((_let_2 (tptp.s Q58342 X))) (let ((_let_3 (tptp.fun Q58342 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun Q58342 _let_5) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) _let_4))) (not (= _let_2 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q58342 _let_3) R0) _let_2)) _let_1)))))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.pairwise0) (tptp.s _let_2 tptp.r0))) (tptp.s _let_1 tptp.nil))) (tptp.s tptp.bool tptp.t)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.r0))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.pairwise0) _let_5)))) (let ((_let_8 (tptp.s A tptp.h0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun A _let_9) tptp.cons) _let_8)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.all0) (tptp.s _let_3 (tptp.i _let_5 _let_8)))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))))))))))))))) (forall ((Q58377 $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun Q58377 tptp.bool))) (let ((_let_2 (tptp.fun Q58377 _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.pairwise) (tptp.s _let_2 R0))) (tptp.s _let_1 tptp.empty))) (tptp.s tptp.bool tptp.t)))))) (forall ((Q58395 $$unsorted) (R0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q58395 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun Q58395 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.pairwise) (tptp.s _let_3 R0))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q58395 _let_2) tptp.insert) (tptp.s Q58395 X))) (tptp.s _let_1 tptp.empty))))) (tptp.s tptp.bool tptp.t))))))) (forall ((Q58415 $$unsorted) (R0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q58415 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q58415 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.pairwise) (tptp.s _let_3 R0))))) (let ((_let_6 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))) (forall ((Q58464 $$unsorted) (R0 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q58464 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q58464 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.pairwise) (tptp.s _let_3 R0))))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q58464 _let_6) tptp.insert) (tptp.s Q58464 X))) _let_2))))) (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q58464 X))) (let ((_let_2 (tptp.s Q58464 Y))) (let ((_let_3 (tptp.fun Q58464 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun Q58464 _let_3) R0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q58464 _let_5) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (not (= _let_2 _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))))))))))) (forall ((Q58502 $$unsorted) (Q58505 $$unsorted) (U_1 $$unsorted)) (=> (forall ((R0 $$unsorted) (X $$unsorted) (F0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q58505 Y))) (let ((_let_2 (tptp.fun Q58505 Q58502))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s Q58502 (tptp.i _let_3 _let_1)))) (let ((_let_5 (tptp.s Q58505 X))) (let ((_let_6 (tptp.s Q58502 (tptp.i _let_3 _let_5)))) (let ((_let_7 (tptp.fun Q58502 tptp.bool))) (let ((_let_8 (tptp.fun Q58502 _let_7))) (let ((_let_9 (tptp.s _let_8 R0))) (let ((_let_10 (tptp.fun Q58505 tptp.bool))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun Q58505 _let_11))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_8 _let_12) U_1) _let_9)) _let_5)) _let_3)) _let_1))) (=> (not (= _let_6 _let_4)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_6)) _let_4)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((R0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q58505 Q58502))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s Q58505 X))) (let ((_let_4 (tptp.fun Q58502 (tptp.fun Q58502 tptp.bool)))) (let ((_let_5 (tptp.s _let_4 R0))) (let ((_let_6 (tptp.fun Q58505 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun Q58505 _let_7))) (let ((_let_9 (tptp.fun Q58505 _let_6))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) U_0) _let_5)) _let_2)) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) _let_5)) _let_3)) _let_2)))))))))))))) (forall ((R0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q58505 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun Q58505 Q58502))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q58502 tptp.bool))) (let ((_let_6 (tptp.fun Q58502 _let_5))) (let ((_let_7 (tptp.s _let_6 R0))) (let ((_let_8 (tptp.fun Q58505 _let_1))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_1 tptp.bool))) (let ((_let_11 (tptp.fun _let_1 _let_5))) (let ((_let_12 (tptp.fun _let_5 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_6 _let_12) tptp.pairwise) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.image) _let_4)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.pairwise) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_0) _let_7)) _let_4)))) _let_2)))))))))))))))))))) (forall ((Q58517 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.list Q58517))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q58517 tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.setu_ofu_list) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2)))))))))) (forall ((Q58537 $$unsorted) (U_1 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q58537 Y))) (let ((_let_2 (tptp.s Q58537 X))) (let ((_let_3 (tptp.fun Q58537 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q58537 _let_3) U_1) _let_2)) _let_1))) (not (= _let_2 _let_1))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q58537 X))) (let ((_let_2 (tptp.fun Q58537 tptp.bool))) (let ((_let_3 (tptp.fun Q58537 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_0) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_1) _let_1))))))) (forall ((L $$unsorted)) (let ((_let_1 (tptp.list Q58537))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun Q58537 tptp.bool))) (let ((_let_4 (tptp.fun Q58537 _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.hasu_size) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.setu_ofu_list) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.length) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.pairwise0) (tptp.s _let_4 U_0))) _let_2)))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun A B))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.image) (tptp.s _let_5 F0))) _let_4)))) _let_2)))) (= (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 T0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A A))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 F0))) _let_2)))) _let_2)))) (= (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A Y))) (tptp.s _let_1 S0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) F0) _let_1)) (tptp.s A Y))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A A) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s A (tptp.i _let_3 _let_2)) (tptp.s A (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun A B))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.image) (tptp.s _let_5 F0))) _let_4)) _let_2)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))))))))) (forall ((Q58875 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q58875 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q58875 Q58875))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 F0))) _let_2)) _let_2)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q58875 Y))) (let ((_let_2 (tptp.s Q58875 X))) (let ((_let_3 (tptp.s (tptp.fun Q58875 Q58875) F0))) (let ((_let_4 (tptp.fun Q58875 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q58875 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q58875 (tptp.i _let_3 _let_2)) (tptp.s Q58875 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 F0))) (tptp.s _let_2 S0))))) (tptp.s _let_1 T0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))))))))))))))) (forall ((Q58981 $$unsorted) (P0 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q58981 X))) (let ((_let_2 (tptp.fun Q58981 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q58981 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.empty)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))) (tptp.p (tptp.s tptp.bool tptp.t)))) (forall ((Q59021 $$unsorted) (P0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q59021 X))) (let ((_let_2 (tptp.fun Q59021 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q59021 _let_4) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q59021 _let_3) tptp.insert) (tptp.s Q59021 A5))) (tptp.s _let_2 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q59021 tptp.bool) P0) (tptp.s Q59021 A5)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q59021 X))) (let ((_let_2 (tptp.fun Q59021 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q59021 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))))) (forall ((Q59041 $$unsorted) (P0 $$unsorted)) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q59041 X))) (let ((_let_2 (tptp.fun Q59041 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q59041 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.empty)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))) (tptp.p (tptp.s tptp.bool tptp.f0)))) (forall ((Q59081 $$unsorted) (P0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q59081 X))) (let ((_let_2 (tptp.fun Q59081 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q59081 _let_4) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q59081 _let_3) tptp.insert) (tptp.s Q59081 A5))) (tptp.s _let_2 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q59081 tptp.bool) P0) (tptp.s Q59081 A5)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q59081 X))) (let ((_let_2 (tptp.fun Q59081 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q59081 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (U $$unsorted)) (= (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) (tptp.s _let_4 F0))))) (let ((_let_8 (tptp.s _let_1 U))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_1 _let_9) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_2)) _let_8))) (= (tptp.s _let_5 (tptp.i _let_7 _let_3)) (tptp.s _let_5 (tptp.i _let_7 _let_2)))) (= _let_3 _let_2))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 U))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted)) (= (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) (tptp.s _let_4 F0))))) (=> (= (tptp.s _let_5 (tptp.i _let_7 _let_3)) (tptp.s _let_5 (tptp.i _let_7 _let_2))) (= _let_3 _let_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (=> (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (= (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 T0))) (tptp.s _let_1 V)))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.subset) _let_3)) (tptp.s _let_2 U)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.image) (tptp.s _let_4 F0))) _let_3)) (tptp.s _let_1 T0)))))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 V)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 U)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted)) (= (forall ((T0 $$unsorted)) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 F0))) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))))))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A X))) (tptp.s B Y)))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))) (exists ((F0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 T0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))) (exists ((F0 $$unsorted) (G0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_2)) _let_1)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) _let_1)))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.n))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_2)) _let_1)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.hasu_size) (tptp.s _let_4 S0))) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.hasu_size) (tptp.s _let_2 T0))) _let_1))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_2)) _let_1)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.hasu_size) (tptp.s _let_4 S0))) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.hasu_size) (tptp.s _let_2 T0))) _let_1)))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (=> (and (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_2)) _let_1)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) _let_1))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L_L_ $$unsorted) (X $$unsorted) (GENR_PVARR_133 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 L_L_))) (tptp.s A X))) (tptp.s A GENR_PVARR_133)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.setspec) (tptp.s A GENR_PVARR_133))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) L_L_) _let_1)) (tptp.s A X))))) _let_1))))))))))) (forall ((L_L_ $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A tptp.bool)))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) L_L_) _let_1)) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun A _let_2) L_L_))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s A X))))) (let ((_let_5 (tptp.s A Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 L_L_))) (tptp.s A X)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 L_L_))))))))) (forall ((Q59915 $$unsorted) (Q59920 $$unsorted) (T0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q59915 tptp.bool))) (let ((_let_2 (tptp.fun Q59920 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.l_a_u_c) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))) (exists ((F0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q59915 tptp.bool))) (let ((_let_2 (tptp.s Q59920 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q59920 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q59920 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q59915 _let_3) tptp.in) (tptp.s Q59915 (tptp.i (tptp.s (tptp.fun Q59920 Q59915) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q59920 Y))) (let ((_let_2 (tptp.s Q59920 X))) (let ((_let_3 (tptp.s (tptp.fun Q59920 Q59915) F0))) (let ((_let_4 (tptp.fun Q59920 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q59920 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q59915 (tptp.i _let_3 _let_2)) (tptp.s Q59915 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))))))))))) (forall ((Q59933 $$unsorted) (Q59932 $$unsorted) (T0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q59932 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q59933 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_u_c) _let_2)) _let_4))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_a_u_c) _let_2)) _let_4))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_a_u_c) _let_4)) _let_2)))))))))))))) (forall ((Q59981 $$unsorted) (Q59984 $$unsorted) (T0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q59981 tptp.bool))) (let ((_let_2 (tptp.fun Q59984 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.a_u_c) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))) (exists ((F0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q59981 tptp.bool))) (let ((_let_2 (tptp.s Q59984 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q59984 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q59984 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q59981 _let_3) tptp.in) (tptp.s Q59981 (tptp.i (tptp.s (tptp.fun Q59984 Q59981) F0) _let_2)))) (tptp.s _let_1 T0))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q59981 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q59981 _let_2) tptp.in) (tptp.s Q59981 Y))) (tptp.s _let_1 T0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q59984 X))) (let ((_let_2 (tptp.fun Q59984 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q59984 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s Q59981 (tptp.i (tptp.s (tptp.fun Q59984 Q59981) F0) _let_1)) (tptp.s Q59981 Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s Q59984 XI_))) (let ((_let_2 (tptp.s Q59984 X))) (let ((_let_3 (tptp.s Q59981 Y))) (let ((_let_4 (tptp.s (tptp.fun Q59984 Q59981) F0))) (let ((_let_5 (tptp.fun Q59984 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun Q59984 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s Q59981 (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s Q59981 (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))))))))) (forall ((Q59992 $$unsorted) (Q59993 $$unsorted) (T0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q59993 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q59992 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.g_a_u_c) _let_2)) _let_4)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_a_u_c) _let_4)) _let_2)))))))))) (forall ((Q60001 $$unsorted) (Q60002 $$unsorted) (T0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q60002 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q60001 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.g_u_c) _let_2)) _let_4)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2)))))))))) (forall ((Q60043 $$unsorted) (Q60040 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q60043 tptp.bool))) (let ((_let_2 (tptp.fun Q60040 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.l_a_u_c) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))) (exists ((G0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q60040 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q60040 _let_2) tptp.in) (tptp.s Q60040 X))) (tptp.s _let_1 S0)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s Q60043 Y))) (let ((_let_2 (tptp.fun Q60043 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q60043 _let_3) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (= (tptp.s Q60040 (tptp.i (tptp.s (tptp.fun Q60043 Q60040) G0) _let_1)) (tptp.s Q60040 X))))))))))))))))) (forall ((Q60081 $$unsorted) (Q60084 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q60081 tptp.bool))) (let ((_let_2 (tptp.fun Q60084 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.g_a_u_c) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))) (exists ((F0 $$unsorted)) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q60081 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q60081 _let_2) tptp.in) (tptp.s Q60081 Y))) (tptp.s _let_1 T0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q60084 X))) (let ((_let_2 (tptp.fun Q60084 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q60084 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s Q60081 Y) (tptp.s Q60081 (tptp.i (tptp.s (tptp.fun Q60084 Q60081) F0) _let_1)))))))))))))))))) (forall ((Q60092 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q60092 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.countable) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.g_a_u_c) (tptp.s _let_3 tptp.univ))) _let_2)))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) (tptp.s _let_1 S0))) (tptp.s tptp.real A5)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real A5))))))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real A5))) (tptp.s tptp.real B0))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.sup) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.h_) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup))) (=> (forall ((B0 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))))))))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s _let_1 S0))) (tptp.s tptp.real (tptp.i _let_2 (tptp.s _let_1 T0)))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= (tptp.s _let_1 S0) (tptp.s _let_1 tptp.empty))) (exists ((B0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))))))))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2))))))))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) (tptp.s _let_1 S0))))) (tptp.s tptp.real B0))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.in) (tptp.s tptp.real B0))) (tptp.s _let_1 S0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2)))) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2))))))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real A5))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real A5))) _let_1))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2)))) (tptp.s tptp.real A5)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real A5)))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real A5))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real A5))) _let_1))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2)))) (tptp.s tptp.real A5)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) _let_1)) (tptp.s tptp.real A5)))))))))))))) (forall ((S0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))))))) (forall ((BI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real BI_))) (tptp.s tptp.real B0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real BI_))) _let_1)))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) (tptp.s _let_1 S0))) (tptp.s tptp.real B0))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2)))) (tptp.s tptp.real B0)))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (and (not (= _let_4 (tptp.s _let_1 tptp.empty))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) _let_4)) _let_2))) (exists ((B0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real B0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2)))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real A5))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_1)) (tptp.s tptp.real B0)))))))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i _let_4 (tptp.s tptp.real A5))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s tptp.real B0))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)))) (tptp.s tptp.real A5)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2)))))) (tptp.s tptp.real A5)))))))) (forall ((S0 $$unsorted) (L $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_sub) _let_1)) (tptp.s tptp.real L))))))) (tptp.s tptp.real E0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2)))) (tptp.s tptp.real L))))))) (tptp.s tptp.real E0))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) (tptp.s _let_1 S0))) (tptp.s tptp.real A5)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real A5))) _let_1)))))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real B0))) _let_1)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real B0))) (tptp.s tptp.real A5))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.inf) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.h_) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf))) (=> (forall ((A5 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real A5))) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real A5))) _let_1)))))))))) (= (tptp.s tptp.real (tptp.i _let_2 (tptp.s _let_1 S0))) (tptp.s tptp.real (tptp.i _let_2 (tptp.s _let_1 T0)))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= (tptp.s _let_1 S0) (tptp.s _let_1 tptp.empty))) (exists ((B0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real B0))) _let_1)))))))))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_1)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.inf) _let_3)))) _let_1))))))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real B0))) _let_1)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) (tptp.s _let_1 S0))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.in) (tptp.s tptp.real B0))) (tptp.s _let_1 S0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real B0))) _let_1)))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2)))) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_1)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.inf) _let_3)))) _let_1))))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real A5))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real A5))) _let_1))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2)))) (tptp.s tptp.real A5)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real A5)))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real A5))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real A5))) _let_1))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2)))) (tptp.s tptp.real A5)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) _let_1)) (tptp.s tptp.real A5)))))))))))))) (forall ((S0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real B0))) _let_1)))))))) (forall ((BI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real B0))) (tptp.s tptp.real BI_)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) _let_1)) (tptp.s tptp.real BI_))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) (tptp.s _let_1 S0))) (tptp.s tptp.real B0))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real B0))) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) _let_2)) _let_4))) (exists ((B0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real B0))) _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2)))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real A5))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_1)) (tptp.s tptp.real B0)))))))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i _let_4 (tptp.s tptp.real A5))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s tptp.real B0))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)))) (tptp.s tptp.real A5)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2)))))) (tptp.s tptp.real A5)))))))) (forall ((S0 $$unsorted) (L $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_sub) _let_1)) (tptp.s tptp.real L))))))) (tptp.s tptp.real E0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2)))) (tptp.s tptp.real L))))))) (tptp.s tptp.real E0))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s tptp.real tptp.a0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) _let_2)) _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_3)) _let_2))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) _let_1)) (tptp.s tptp.real tptp.a0))))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s tptp.real tptp.a0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) _let_2)) _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_3)) _let_2))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real tptp.a0))) _let_1)))))))))))))))) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (and (= (tptp.p _let_7) (= _let_2 (tptp.s _let_1 tptp.empty))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.insert) _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_7)) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_max) _let_4)) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.real A5))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.sup) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.insert) _let_1)) (tptp.s _let_2 tptp.empty))))) _let_1))))) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (and (= (tptp.p _let_7) (= _let_2 (tptp.s _let_1 tptp.empty))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.insert) _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_7)) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_min) _let_4)) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.real A5))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.inf) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.insert) _let_1)) (tptp.s _let_2 tptp.empty))))) _let_1))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (=> (and (not (= _let_2 (tptp.s _let_1 tptp.empty))) (exists ((B0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)))) (tptp.s tptp.real B0))))))))))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.sup) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.inf) _let_2))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 S0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.insert) (tptp.s tptp.real A5))) (tptp.s _let_1 tptp.empty))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((M0 $$unsorted) (N0 $$unsorted) (GENR_PVARR_134 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_134)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_1)) (tptp.s tptp.num N0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.setspec) (tptp.s tptp.num GENR_PVARR_134))) _let_2)) _let_1)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.o_o_) _let_2)) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))))) (forall ((M0 $$unsorted) (P0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.s tptp.num P0))) (let ((_let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.p_) _let_8)) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (let ((_let_11 (tptp.s _let_4 tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_11 _let_2)) _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_11 _let_8)) _let_1)))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.union) (tptp.s _let_3 (tptp.i _let_6 _let_8)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_9)) _let_1)))) (tptp.s _let_3 (tptp.i _let_6 _let_1)))))))))))))))) (forall ((M0 $$unsorted) (P0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s tptp.num P0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_10 (tptp.fun tptp.num _let_8))) (let ((_let_11 (tptp.fun _let_3 _let_3))) (let ((_let_12 (tptp.s _let_4 tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_12 _let_2)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_12 _let_7)) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 tptp.p_) _let_1)) _let_9)))))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.union) (tptp.s _let_3 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 tptp.m_) _let_7)) _let_9)))))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) _let_1)))) (tptp.s _let_3 (tptp.i _let_6 _let_1))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.insert) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) _let_2)))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.insert) _let_1)) (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.m_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s _let_3 (tptp.i _let_5 _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) _let_2)))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_6))) (= (tptp.s _let_3 (tptp.i _let_5 _let_6)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.insert) _let_6)) (tptp.s _let_3 (tptp.i _let_5 _let_1)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.l_a_))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) _let_6)) _let_1))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.num _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) _let_2)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.insert) _let_2)) (tptp.s _let_1 tptp.empty))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) _let_1)) _let_2)) (tptp.s _let_3 tptp.empty)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_1))))))))) (forall ((M0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num D0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_1) tptp.p_))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.card) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_3 _let_4)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_3 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.card) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) _let_1)) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.p_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.hasu_size) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) _let_1)) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.p_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) _let_1)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.hasu_size) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)))) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) _let_2)))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_5 _let_1)))) (let ((_let_7 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_1)))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (= (tptp.s _let_3 (tptp.i _let_5 _let_7)) (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_7)))) (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.insert) _let_7)) _let_6)))) _let_6))))))))))))) (forall ((M0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_1 _let_4))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.fun tptp.num _let_1))) (and (= (tptp.p _let_5) (= _let_7 _let_3)) (= (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.o_o_) _let_7)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.insert) _let_3)) _let_2)))) _let_2)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun tptp.num A))) (let ((_let_7 (tptp.fun _let_4 _let_1))) (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num A) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 S0))))))) (let ((_let_9 (tptp.fun _let_6 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_2)) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_1)) _let_8))) (= (tptp.s A (tptp.i _let_3 _let_2)) (tptp.s A (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))))))) (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.image) (tptp.s _let_6 F0))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((K0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.s _let_1 K0))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (and (forall ((I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num A) F0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s _let_4 K0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s A (tptp.i _let_3 _let_2)) (tptp.s A (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (tptp.s _let_4 S0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num Q0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.l_))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.s tptp.num N0))) (let ((_let_9 (tptp.s _let_3 (tptp.i _let_5 _let_8)))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_))) (let ((_let_11 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.disjoint) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_10 _let_7)) _let_8)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_10 _let_1)) _let_2))))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_1))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_1)))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num P0))))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_))) (let ((_let_9 (tptp.s tptp.num M0))) (let ((_let_10 (tptp.s _let_7 (tptp.i _let_8 _let_9)))) (let ((_let_11 (tptp.fun _let_6 _let_6))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_a_) _let_9)) _let_5))) (= (tptp.s _let_6 (tptp.i _let_10 _let_4)) (tptp.s _let_6 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_6 _let_11) tptp.union) (tptp.s _let_6 (tptp.i _let_10 _let_1)))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_4)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1)))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_))) (let ((_let_6 (tptp.s tptp.num P0))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (let ((_let_10 (tptp.s _let_8 tptp.p_))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i _let_10 _let_2)) _let_6)))) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i _let_10 _let_1)) _let_6)))) (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.image) (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_0) _let_6)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num Q0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.l_a_))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s tptp.num P0))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.subset) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_8 _let_6)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_8 _let_7)) _let_1))))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_6))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_7)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_136 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_136)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_136))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) _let_1)) (tptp.s tptp.num N0))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_0) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_137 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_137)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_137))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) _let_1)) (tptp.s tptp.num N0))))) _let_1)))))))))) (forall ((N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s tptp.bool V))) (let ((_let_9 (tptp.fun _let_6 _let_6))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (and (= (tptp.p _let_8) (= _let_4 _let_5)) (= (tptp.s _let_6 (tptp.i (tptp.s _let_9 tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)))) (tptp.s _let_6 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) _let_8)) (tptp.s _let_6 tptp.empty))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.m_) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))))))))))))))))) (forall ((A $$unsorted) (L_L_ $$unsorted)) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) L_L_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun A _let_2) L_L_))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s A X))))) (let ((_let_5 (tptp.s A Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1))))))))))) (forall ((N0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.hasu_size) (tptp.s _let_1 S0))) (tptp.s tptp.num N0)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun tptp.num A))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (and (= (tptp.s _let_5 S0) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) (tptp.s _let_4 F0))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num N0)))))) (forall ((J0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num A) F0))) (let ((_let_3 (tptp.s tptp.num K0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num N0))))) (let ((_let_9 (tptp.fun _let_5 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_1)) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_) _let_1)) _let_3)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) L_L_) (tptp.s A (tptp.i _let_2 _let_3)))) (tptp.s A (tptp.i _let_2 _let_1)))))))))))))))))))))))))))))))) (forall ((Q63228 $$unsorted) (U_0 $$unsorted)) (=> (forall ((OP $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q63228 (tptp.fun Q63228 Q63228)))) (let ((_let_2 (tptp.fun Q63228 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 OP))) (tptp.s Q63228 X)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q63228 Y))) (let ((_let_2 (tptp.s Q63228 X))) (let ((_let_3 (tptp.fun Q63228 Q63228))) (let ((_let_4 (tptp.s (tptp.fun Q63228 _let_3) OP))) (and (= (tptp.s Q63228 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)) _let_1) (= (tptp.s Q63228 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) _let_1))))))))))) (forall ((OP $$unsorted)) (let ((_let_1 (tptp.fun Q63228 (tptp.fun Q63228 Q63228)))) (let ((_let_2 (tptp.s _let_1 OP))) (let ((_let_3 (tptp.fun Q63228 tptp.bool))) (= (tptp.s Q63228 (tptp.i (tptp.s (tptp.fun _let_1 Q63228) tptp.neutral) _let_2)) (tptp.s Q63228 (tptp.i (tptp.s (tptp.fun _let_3 Q63228) tptp.h_) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))) (forall ((A $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun A A)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.fun A A))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) OP))) (= (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.fun A A))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) OP))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A X))))) (= (tptp.s A (tptp.i _let_5 (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))) (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s A (tptp.i _let_5 _let_2)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 OP))) (= (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s A (tptp.i (tptp.s (tptp.fun _let_3 A) tptp.neutral) _let_4)))) _let_1)) _let_1)))))))))) (forall ((Q63384 $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun Q63384 (tptp.fun Q63384 Q63384)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (and (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s Q63384 A5))) (let ((_let_2 (tptp.fun Q63384 Q63384))) (let ((_let_3 (tptp.fun Q63384 _let_2))) (let ((_let_4 (tptp.s _let_3 OP))) (= (tptp.s Q63384 (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s Q63384 (tptp.i (tptp.s (tptp.fun _let_3 Q63384) tptp.neutral) _let_4)))) _let_1)) _let_1)))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s Q63384 A5))) (let ((_let_2 (tptp.fun Q63384 Q63384))) (let ((_let_3 (tptp.fun Q63384 _let_2))) (let ((_let_4 (tptp.s _let_3 OP))) (= (tptp.s Q63384 (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) (tptp.s Q63384 (tptp.i (tptp.s (tptp.fun _let_3 Q63384) tptp.neutral) _let_4)))) _let_1)))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s Q63384 A5))) (let ((_let_2 (tptp.s Q63384 B0))) (let ((_let_3 (tptp.fun Q63384 Q63384))) (let ((_let_4 (tptp.s (tptp.fun Q63384 _let_3) OP))) (= (tptp.s Q63384 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) _let_2)) (tptp.s Q63384 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s Q63384 C0))) (let ((_let_2 (tptp.s Q63384 B0))) (let ((_let_3 (tptp.fun Q63384 Q63384))) (let ((_let_4 (tptp.s (tptp.fun Q63384 _let_3) OP))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s Q63384 A5))))) (= (tptp.s Q63384 (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s Q63384 (tptp.i _let_5 _let_2)))) _let_1)) (tptp.s Q63384 (tptp.i _let_5 (tptp.s Q63384 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s Q63384 C0))) (let ((_let_2 (tptp.fun Q63384 Q63384))) (let ((_let_3 (tptp.s (tptp.fun Q63384 _let_2) OP))) (let ((_let_4 (tptp.s _let_2 (tptp.i _let_3 (tptp.s Q63384 A5))))) (let ((_let_5 (tptp.s _let_2 (tptp.i _let_3 (tptp.s Q63384 B0))))) (= (tptp.s Q63384 (tptp.i _let_4 (tptp.s Q63384 (tptp.i _let_5 _let_1)))) (tptp.s Q63384 (tptp.i _let_5 (tptp.s Q63384 (tptp.i _let_4 _let_1))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (OP $$unsorted) (GENR_PVARR_142 $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) (tptp.s _let_1 OP))) (tptp.s A GENR_PVARR_142)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun B (tptp.fun B B)))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (not (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_5 B) tptp.neutral) (tptp.s _let_5 OP))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_142))) _let_2)) _let_1)))))))))))))))))) (forall ((S0 $$unsorted) (F0 $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (let ((_let_2 (tptp.s _let_1 OP))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_1 _let_5))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_1 _let_10) tptp.support) _let_2)) _let_4)) _let_6)) (tptp.s _let_5 (tptp.i (tptp.s _let_9 tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) _let_6)) _let_4)) _let_2)))))))))))))))))) (forall ((A $$unsorted) (Q63442 $$unsorted) (U_1 $$unsorted)) (=> (forall ((OP $$unsorted) (F0 $$unsorted) (X $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q63442 A5))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A Q63442))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q63442 Q63442))) (let ((_let_6 (tptp.fun Q63442 _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun A _let_5))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (= (tptp.s Q63442 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_1) _let_7)) _let_4)) _let_2)) _let_1)) (tptp.s Q63442 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s Q63442 (tptp.i _let_4 _let_2)))) _let_1))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((OP $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A Q63442))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q63442 Q63442))) (let ((_let_5 (tptp.fun Q63442 _let_4))) (let ((_let_6 (tptp.s _let_5 OP))) (let ((_let_7 (tptp.fun A _let_4))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_5 _let_8))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 U_0) _let_6)) _let_3)) _let_1)) (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 U_1) _let_6)) _let_3)) _let_1))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun Q63442 Q63442))) (let ((_let_2 (tptp.fun Q63442 _let_1))) (let ((_let_3 (tptp.s _let_2 OP))) (let ((_let_4 (tptp.s Q63442 (tptp.i (tptp.s (tptp.fun _let_2 Q63442) tptp.neutral) _let_3)))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun A Q63442))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_7 _let_9))) (let ((_let_11 (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) tptp.support) _let_3)) _let_8)) _let_6)))) (let ((_let_12 (tptp.fun A _let_1))) (let ((_let_13 (tptp.fun _let_7 _let_12))) (let ((_let_14 (tptp.fun _let_5 _let_1))) (let ((_let_15 (tptp.fun _let_7 Q63442))) (let ((_let_16 (tptp.fun _let_5 _let_15))) (= (tptp.s Q63442 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_2 _let_16) tptp.iterate) _let_3)) _let_6)) _let_8)) (tptp.s Q63442 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.bool _let_2) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_11)))) (tptp.s Q63442 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_12 _let_14) tptp.itset) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_2 _let_13) U_0) _let_3)) _let_8)))) _let_11)) _let_4)))) _let_4)))))))))))))))))))))))) (forall ((Q63492 $$unsorted) (Q63489 $$unsorted) (OP $$unsorted) (F0 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q63489 (tptp.fun Q63489 Q63489)))) (let ((_let_2 (tptp.s _let_1 OP))) (let ((_let_3 (tptp.s Q63492 X))) (let ((_let_4 (tptp.fun Q63492 Q63489))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q63492 tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q63492 _let_8) tptp.in) _let_3)))) (let ((_let_10 (tptp.fun _let_6 _let_6))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_9 (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.support) _let_2)) _let_5)) _let_7))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_7))) (not (= (tptp.s Q63489 (tptp.i _let_5 _let_3)) (tptp.s Q63489 (tptp.i (tptp.s (tptp.fun _let_1 Q63489) tptp.neutral) _let_2)))))))))))))))))) (forall ((Q63514 $$unsorted) (Q63525 $$unsorted) (OP $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q63525 tptp.bool))) (let ((_let_2 (tptp.fun Q63525 Q63514))) (let ((_let_3 (tptp.fun Q63514 (tptp.fun Q63514 Q63514)))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.support) (tptp.s _let_3 OP))) (tptp.s _let_2 F0))))) (let ((_let_7 (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 S0))))) (= (tptp.s _let_1 (tptp.i _let_6 _let_7)) _let_7))))))))) (forall ((Q63550 $$unsorted) (Q63564 $$unsorted) (OP $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q63564 tptp.bool))) (let ((_let_2 (tptp.fun Q63564 Q63550))) (let ((_let_3 (tptp.fun Q63550 (tptp.fun Q63550 Q63550)))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q63550 (tptp.fun Q63550 Q63550)))) (let ((_let_2 (tptp.s Q63564 X))) (let ((_let_3 (tptp.fun Q63564 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q63564 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s Q63550 (tptp.i (tptp.s (tptp.fun Q63564 Q63550) F0) _let_2)) (tptp.s Q63550 (tptp.i (tptp.s (tptp.fun _let_1 Q63550) tptp.neutral) (tptp.s _let_1 OP)))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.support) (tptp.s _let_3 OP))) (tptp.s _let_2 F0))) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.empty))))))))) (forall ((Q63584 $$unsorted) (Q63585 $$unsorted) (OP $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q63585 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q63585 Q63584))) (let ((_let_4 (tptp.fun Q63584 (tptp.fun Q63584 Q63584)))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.support) (tptp.s _let_4 OP))) (tptp.s _let_3 F0))) _let_2)))) _let_2))))))))))) (forall ((Q63608 $$unsorted) (Q63602 $$unsorted) (OP $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q63602 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q63602 Q63608))) (let ((_let_4 (tptp.fun Q63608 (tptp.fun Q63608 Q63608)))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.support) (tptp.s _let_4 OP))) (tptp.s _let_3 F0))) _let_2)))))))))))))) (forall ((Q63859 $$unsorted) (Q63626 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q63626 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.fun Q63626 Q63859))) (let ((_let_4 (tptp.fun Q63859 (tptp.fun Q63859 Q63859)))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.support) (tptp.s _let_4 tptp.op))) (tptp.s _let_3 F0))) _let_2)) _let_2)))))))) (forall ((Q63859 $$unsorted) (Q63674 $$unsorted) (F0 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q63674 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q63674 Q63859))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q63859 (tptp.fun Q63859 Q63859)))) (let ((_let_6 (tptp.s _let_5 tptp.op))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.support) _let_6)) _let_4)))) (let ((_let_10 (tptp.s _let_1 (tptp.i _let_9 _let_2)))) (let ((_let_11 (tptp.s Q63674 X))) (let ((_let_12 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q63674 _let_7) tptp.insert) _let_11)))) (let ((_let_13 (tptp.s tptp.bool V))) (let ((_let_14 (tptp.fun _let_1 _let_7))) (and (= (tptp.p _let_13) (= (tptp.s Q63859 (tptp.i _let_4 _let_11)) (tptp.s Q63859 (tptp.i (tptp.s (tptp.fun _let_5 Q63859) tptp.neutral) _let_6)))) (= (tptp.s _let_1 (tptp.i _let_9 (tptp.s _let_1 (tptp.i _let_12 _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.bool _let_14) tptp.cond) _let_13)) _let_10)) (tptp.s _let_1 (tptp.i _let_12 _let_10)))))))))))))))))))))) (forall ((Q63859 $$unsorted) (Q63707 $$unsorted) (F0 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s Q63707 X))) (let ((_let_2 (tptp.fun Q63707 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun Q63707 Q63859))) (let ((_let_5 (tptp.fun Q63859 (tptp.fun Q63859 Q63859)))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.support) (tptp.s _let_5 tptp.op))) (tptp.s _let_4 F0))))) (let ((_let_9 (tptp.fun Q63707 _let_2))) (let ((_let_10 (tptp.s (tptp.fun _let_2 _let_9) tptp.delete))) (= (tptp.s _let_2 (tptp.i _let_8 (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_2 (tptp.i _let_8 _let_3)))) _let_1)))))))))))))) (forall ((Q63859 $$unsorted) (Q63745 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q63745 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q63745 Q63859))) (let ((_let_4 (tptp.fun Q63859 (tptp.fun Q63859 Q63859)))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.support) (tptp.s _let_4 tptp.op))) (tptp.s _let_3 F0))))) (let ((_let_8 (tptp.s _let_1 S0))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_5) tptp.union))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_9 _let_8)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_9 (tptp.s _let_1 (tptp.i _let_7 _let_8)))) (tptp.s _let_1 (tptp.i _let_7 _let_2))))))))))))))) (forall ((Q63859 $$unsorted) (Q63783 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q63783 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q63783 Q63859))) (let ((_let_4 (tptp.fun Q63859 (tptp.fun Q63859 Q63859)))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.support) (tptp.s _let_4 tptp.op))) (tptp.s _let_3 F0))))) (let ((_let_8 (tptp.s _let_1 S0))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_5) tptp.inter))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_9 _let_8)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_9 (tptp.s _let_1 (tptp.i _let_7 _let_8)))) (tptp.s _let_1 (tptp.i _let_7 _let_2))))))))))))))) (forall ((Q63859 $$unsorted) (Q63821 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q63821 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q63821 Q63859))) (let ((_let_4 (tptp.fun Q63859 (tptp.fun Q63859 Q63859)))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.support) (tptp.s _let_4 tptp.op))) (tptp.s _let_3 F0))))) (let ((_let_8 (tptp.s _let_1 S0))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_5) tptp.diff))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_9 _let_8)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_9 (tptp.s _let_1 (tptp.i _let_7 _let_8)))) (tptp.s _let_1 (tptp.i _let_7 _let_2))))))))))))))) (forall ((Q63859 $$unsorted) (Q63849 $$unsorted) (Q63858 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q63858 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q63858 Q63849))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q63849 Q63859))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun Q63858 Q63859))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun Q63859 (tptp.fun Q63859 Q63859)))) (let ((_let_10 (tptp.s _let_9 tptp.op))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun Q63849 tptp.bool))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (let ((_let_15 (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_3 _let_14) tptp.image) _let_4)))) (let ((_let_16 (tptp.fun _let_13 _let_13))) (let ((_let_17 (tptp.fun _let_5 _let_16))) (= (tptp.s _let_13 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_9 _let_17) tptp.support) _let_10)) _let_6)) (tptp.s _let_13 (tptp.i _let_15 _let_2)))) (tptp.s _let_13 (tptp.i _let_15 (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.support) _let_10)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.o) _let_6)) _let_4)))) _let_2))))))))))))))))))))))) (forall ((Q63885 $$unsorted) (Q63913 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (F0 $$unsorted) (OP $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q63885 Q63885))) (let ((_let_2 (tptp.fun Q63885 _let_1))) (let ((_let_3 (tptp.s _let_2 OP))) (let ((_let_4 (tptp.s Q63913 X))) (let ((_let_5 (tptp.fun Q63913 Q63885))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.s Q63913 A5))) (let ((_let_9 (tptp.fun _let_2 _let_5))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (and (= (tptp.p _let_7) (= _let_4 _let_8)) (= (tptp.s Q63885 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q63913 _let_10) U_0) _let_8)) _let_6)) _let_3)) _let_4)) (tptp.s Q63885 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.bool _let_2) tptp.cond) _let_7)) (tptp.s Q63885 (tptp.i _let_6 _let_4)))) (tptp.s Q63885 (tptp.i (tptp.s (tptp.fun _let_2 Q63885) tptp.neutral) _let_3)))))))))))))))))) (forall ((OP $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun Q63913 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.empty))) (let ((_let_3 (tptp.s Q63913 A5))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun Q63913 Q63885))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun Q63885 (tptp.fun Q63885 Q63885)))) (let ((_let_8 (tptp.s _let_7 OP))) (let ((_let_9 (tptp.fun _let_5 _let_4))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.support) _let_8)))) (let ((_let_11 (tptp.s _let_1 S0))) (let ((_let_12 (tptp.fun _let_1 tptp.bool))) (let ((_let_13 (tptp.fun _let_1 _let_4))) (let ((_let_14 (tptp.fun _let_7 _let_5))) (let ((_let_15 (tptp.fun _let_5 _let_14))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_10 (tptp.s _let_5 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun Q63913 _let_15) U_0) _let_3)) _let_6)) _let_8)))) _let_11)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.bool _let_13) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun Q63913 _let_12) tptp.in) _let_3)) _let_11)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_10 _let_6)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q63913 _let_4) tptp.insert) _let_3)) _let_2)))))) _let_2))))))))))))))))))))) (forall ((Q63934 $$unsorted) (Q63943 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (F0 $$unsorted) (OP $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q63934 Q63934))) (let ((_let_2 (tptp.fun Q63934 _let_1))) (let ((_let_3 (tptp.s _let_2 OP))) (let ((_let_4 (tptp.s Q63943 X))) (let ((_let_5 (tptp.fun Q63943 Q63934))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.s Q63943 A5))) (let ((_let_9 (tptp.fun _let_2 _let_5))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (and (= (tptp.p _let_7) (= _let_4 _let_8)) (= (tptp.s Q63934 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q63943 _let_10) U_0) _let_8)) _let_6)) _let_3)) _let_4)) (tptp.s Q63934 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.bool _let_2) tptp.cond) _let_7)) (tptp.s Q63934 (tptp.i _let_6 _let_4)))) (tptp.s Q63934 (tptp.i (tptp.s (tptp.fun _let_2 Q63934) tptp.neutral) _let_3)))))))))))))))))) (forall ((OP $$unsorted) (F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun Q63943 tptp.bool))) (let ((_let_2 (tptp.fun Q63934 (tptp.fun Q63934 Q63934)))) (let ((_let_3 (tptp.s _let_2 OP))) (let ((_let_4 (tptp.fun Q63943 Q63934))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.support) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q63943 _let_6) U_0) (tptp.s Q63943 A5))) (tptp.s _let_4 F0))) _let_3)))) (tptp.s _let_1 tptp.s0))))))))))))))))) (forall ((Q63971 $$unsorted) (Q63959 $$unsorted) (OP $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q63971 Q63959))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q63971 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun Q63959 (tptp.fun Q63959 Q63959)))) (let ((_let_6 (tptp.s _let_5 OP))) (let ((_let_7 (tptp.fun _let_1 Q63959))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.iterate) _let_6)))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (= (tptp.s Q63959 (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_5 _let_11) tptp.support) _let_6)) _let_2)) _let_4)))) _let_2)) (tptp.s Q63959 (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_4)) _let_2))))))))))))))) (forall ((Q63996 $$unsorted) (Q63990 $$unsorted) (OP $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q63990 Q63990))) (let ((_let_2 (tptp.fun Q63990 _let_1))) (let ((_let_3 (tptp.s _let_2 OP))) (let ((_let_4 (tptp.fun Q63996 Q63990))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q63996 tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 _let_6))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_2 _let_9) tptp.support) _let_3)) _let_5)) _let_7)))) (let ((_let_11 (tptp.fun _let_4 Q63990))) (let ((_let_12 (tptp.fun _let_6 _let_11))) (let ((_let_13 (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_2 _let_12) tptp.iterate) _let_3)))) (= (tptp.s Q63990 (tptp.i (tptp.s _let_11 (tptp.i _let_13 _let_7)) _let_5)) (tptp.s Q63990 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.bool _let_2) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.finite) _let_10)))) (tptp.s Q63990 (tptp.i (tptp.s _let_11 (tptp.i _let_13 _let_10)) _let_5)))) (tptp.s Q63990 (tptp.i (tptp.s (tptp.fun _let_2 Q63990) tptp.neutral) _let_3))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (and (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (let ((_let_2 (tptp.s _let_1 OP))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_3 B))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (= (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.iterate) _let_2)) (tptp.s _let_4 tptp.empty))) (tptp.s _let_3 F0))) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.neutral) _let_2)))))))))) (forall ((F0 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 B))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)))) (let ((_let_11 (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2)))) (let ((_let_12 (tptp.s A X))) (let ((_let_13 (tptp.fun _let_3 tptp.bool))) (let ((_let_14 (tptp.fun _let_3 _let_3))) (let ((_let_15 (tptp.fun _let_1 _let_14))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.monoidal) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_6 _let_15) tptp.support) _let_7)) _let_2)) _let_4)))))) (= (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun A _let_14) tptp.insert) _let_12)) _let_4)))) _let_2)) (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun A _let_13) tptp.in) _let_12)) _let_4)))) _let_11)) (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s B (tptp.i _let_2 _let_12)))) _let_11)))))))))))))))))))))))))) (forall ((Q64144 $$unsorted) (Q64188 $$unsorted) (Q64186 $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun Q64186 (tptp.fun Q64186 Q64186)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (and (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q64186 (tptp.fun Q64186 Q64186)))) (let ((_let_2 (tptp.s _let_1 OP))) (let ((_let_3 (tptp.fun Q64144 Q64186))) (let ((_let_4 (tptp.fun Q64144 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 Q64186))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (= (tptp.s Q64186 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.iterate) _let_2)) (tptp.s _let_4 tptp.empty))) (tptp.s _let_3 F0))) (tptp.s Q64186 (tptp.i (tptp.s (tptp.fun _let_1 Q64186) tptp.neutral) _let_2)))))))))) (forall ((F0 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q64188 Q64186))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q64188 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun Q64186 Q64186))) (let ((_let_6 (tptp.fun Q64186 _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 Q64186))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)))) (let ((_let_11 (tptp.s Q64186 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2)))) (let ((_let_12 (tptp.s Q64188 X))) (let ((_let_13 (tptp.fun _let_3 tptp.bool))) (let ((_let_14 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 tptp.finite) _let_4))) (= (tptp.s Q64186 (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun Q64188 _let_14) tptp.insert) _let_12)) _let_4)))) _let_2)) (tptp.s Q64186 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun Q64188 _let_13) tptp.in) _let_12)) _let_4)))) _let_11)) (tptp.s Q64186 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s Q64186 (tptp.i _let_2 _let_12)))) _let_11))))))))))))))))))))))))) (forall ((Q64259 $$unsorted) (Q64274 $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun Q64274 (tptp.fun Q64274 Q64274)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q64259 Q64274))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q64259 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun Q64274 Q64274))) (let ((_let_6 (tptp.fun Q64274 _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 Q64274))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)))) (let ((_let_11 (tptp.s _let_3 S0))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (let ((_let_13 (tptp.fun _let_3 tptp.bool))) (let ((_let_14 (tptp.s _let_13 tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_11))) (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_3 _let_13) tptp.disjoint) _let_11)) _let_4)))) (= (tptp.s Q64274 (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.union) _let_11)) _let_4)))) _let_2)) (tptp.s Q64274 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s Q64274 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_11)) _let_2)))) (tptp.s Q64274 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2)))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 B))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)))) (let ((_let_11 (tptp.s _let_3 S0))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (let ((_let_13 (tptp.fun _let_1 _let_12))) (let ((_let_14 (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) tptp.support) _let_7)) _let_2)))) (let ((_let_15 (tptp.s _let_3 (tptp.i _let_14 _let_4)))) (let ((_let_16 (tptp.s _let_3 (tptp.i _let_14 _let_11)))) (let ((_let_17 (tptp.fun _let_3 tptp.bool))) (let ((_let_18 (tptp.s _let_17 tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_18 _let_16))) (tptp.p (tptp.s tptp.bool (tptp.i _let_18 _let_15))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_3 _let_17) tptp.disjoint) _let_16)) _let_15)))) (= (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.union) _let_11)) _let_4)))) _let_2)) (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_11)) _let_2)))) (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2)))))))))))))))))))))))))))) (forall ((Q64412 $$unsorted) (Q64416 $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun Q64416 (tptp.fun Q64416 Q64416)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q64412 Q64416))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q64412 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun Q64416 Q64416))) (let ((_let_6 (tptp.fun Q64416 _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 Q64416))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)))) (let ((_let_11 (tptp.s _let_3 T0))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (let ((_let_13 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_3 _let_13) tptp.subset) _let_11)) _let_4)))) (= (tptp.s Q64416 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s Q64416 (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.diff) _let_4)) _let_11)))) _let_2)))) (tptp.s Q64416 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_11)) _let_2)))) (tptp.s Q64416 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 B))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)))) (let ((_let_11 (tptp.s _let_3 T0))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (let ((_let_13 (tptp.fun _let_1 _let_12))) (let ((_let_14 (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) tptp.support) _let_7)) _let_2)))) (let ((_let_15 (tptp.s _let_3 (tptp.i _let_14 _let_4)))) (let ((_let_16 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_16 tptp.finite) _let_15))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_3 _let_16) tptp.subset) (tptp.s _let_3 (tptp.i _let_14 _let_11)))) _let_15)))) (= (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.diff) _let_4)) _let_11)))) _let_2)))) (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_11)) _let_2)))) (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2)))))))))))))))))))))))) (forall ((Q64627 $$unsorted) (Q64645 $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun Q64645 (tptp.fun Q64645 Q64645)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q64627 Q64645))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q64627 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.s _let_3 S0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun Q64645 Q64645))) (let ((_let_9 (tptp.fun Q64645 _let_8))) (let ((_let_10 (tptp.s _let_9 OP))) (let ((_let_11 (tptp.fun _let_1 Q64645))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.iterate) _let_10)))) (let ((_let_14 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_4)))) (= (tptp.s Q64645 (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s Q64645 (tptp.i (tptp.s _let_11 (tptp.i _let_13 _let_5)) _let_2)))) (tptp.s Q64645 (tptp.i (tptp.s _let_11 (tptp.i _let_13 _let_4)) _let_2)))) (tptp.s Q64645 (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s Q64645 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.union) _let_5)) _let_4)))) _let_2)))) (tptp.s Q64645 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.inter) _let_5)) _let_4)))) _let_2)))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun B tptp.bool) P0) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.neutral) (tptp.s _let_1 OP)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s B X))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.s (tptp.fun B tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) OP) _let_2)) _let_1)))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B (tptp.fun B B)))) (let ((_let_4 (tptp.fun _let_1 B))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (let ((_let_3 (tptp.fun B (tptp.fun B B)))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (not (= _let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun _let_3 B) tptp.neutral) (tptp.s _let_3 OP)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun B tptp.bool) P0) _let_2)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun B tptp.bool) P0) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.iterate) (tptp.s _let_3 OP))) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((R0 $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.neutral) (tptp.s _let_1 OP))))) (let ((_let_3 (tptp.fun B tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) R0) _let_2)) _let_2))) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.s B Y2))) (let ((_let_2 (tptp.s B X2))) (let ((_let_3 (tptp.fun B B))) (let ((_let_4 (tptp.s (tptp.fun B _let_3) OP))) (let ((_let_5 (tptp.s B Y1))) (let ((_let_6 (tptp.s B X1))) (let ((_let_7 (tptp.fun B tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun B _let_7) R0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_6)) _let_5)))) (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1)))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun B (tptp.fun B B)))) (let ((_let_5 (tptp.fun _let_1 B))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.iterate) (tptp.s _let_4 OP))) _let_3)))) (let ((_let_8 (tptp.fun B tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) R0) (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s B (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun B _let_8) R0) (tptp.s B (tptp.i _let_7 (tptp.s _let_1 F0))))) (tptp.s B (tptp.i _let_7 (tptp.s _let_1 G0)))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (let ((_let_2 (tptp.s _let_1 OP))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_3 B))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.neutral) (tptp.s _let_1 OP)))))))))) (= (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.iterate) _let_2)) (tptp.s _let_4 S0))) (tptp.s _let_3 F0))) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.neutral) _let_2)))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.fun B (tptp.fun B B)))) (let ((_let_7 (tptp.fun _let_2 B))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.s B (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.iterate) (tptp.s _let_6 OP))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.insert) _let_1)) (tptp.s _let_4 tptp.empty))))) _let_3)) (tptp.s B (tptp.i _let_3 _let_1))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 B))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)))) (let ((_let_11 (tptp.s A A5))) (let ((_let_12 (tptp.fun A _let_3))) (let ((_let_13 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun A _let_13) tptp.in) _let_11)) _let_4)))) (= (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s B (tptp.i _let_2 _let_11)))) (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.delete) _let_4)) _let_11)))) _let_2)))) (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2))))))))))))))))))))) (forall ((Q65020 $$unsorted) (Q65001 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (F0 $$unsorted) (OP $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q65001 Q65001))) (let ((_let_2 (tptp.fun Q65001 _let_1))) (let ((_let_3 (tptp.s _let_2 OP))) (let ((_let_4 (tptp.s Q65020 X))) (let ((_let_5 (tptp.fun Q65020 Q65001))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.s Q65020 A5))) (let ((_let_9 (tptp.fun _let_2 _let_5))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (and (= (tptp.p _let_7) (= _let_4 _let_8)) (= (tptp.s Q65001 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q65020 _let_10) U_0) _let_8)) _let_6)) _let_3)) _let_4)) (tptp.s Q65001 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.bool _let_2) tptp.cond) _let_7)) (tptp.s Q65001 (tptp.i _let_6 _let_4)))) (tptp.s Q65001 (tptp.i (tptp.s (tptp.fun _let_2 Q65001) tptp.neutral) _let_3)))))))))))))))))) (forall ((OP $$unsorted)) (let ((_let_1 (tptp.fun Q65001 (tptp.fun Q65001 Q65001)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q65001 Q65001))) (let ((_let_2 (tptp.fun Q65001 _let_1))) (let ((_let_3 (tptp.s _let_2 OP))) (let ((_let_4 (tptp.s Q65020 A5))) (let ((_let_5 (tptp.fun Q65020 Q65001))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun Q65020 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (let ((_let_10 (tptp.fun _let_2 _let_5))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_5 Q65001))) (let ((_let_13 (tptp.fun _let_7 _let_12))) (= (tptp.s Q65001 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_2 _let_13) tptp.iterate) _let_3)) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q65020 _let_11) U_0) _let_4)) _let_6)) _let_3)))) (tptp.s Q65001 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.bool _let_2) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q65020 _let_9) tptp.in) _let_4)) _let_8)))) (tptp.s Q65001 (tptp.i _let_6 _let_4)))) (tptp.s Q65001 (tptp.i (tptp.s (tptp.fun _let_2 Q65001) tptp.neutral) _let_3)))))))))))))))))))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun C (tptp.fun C C)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun A C))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun C (tptp.fun C C)))) (let ((_let_10 (tptp.s _let_9 OP))) (let ((_let_11 (tptp.fun _let_5 C))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun B tptp.bool))) (let ((_let_14 (tptp.fun _let_7 _let_13))) (let ((_let_15 (tptp.fun _let_3 C))) (let ((_let_16 (tptp.fun _let_13 _let_15))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (= (tptp.s C (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_9 _let_16) tptp.iterate) _let_10)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_1 _let_14) tptp.image) _let_2)) _let_8)))) _let_4)) (tptp.s C (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.iterate) _let_10)) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.o) _let_4)) _let_2)))))))))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A A))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun B (tptp.fun B B)))) (let ((_let_7 (tptp.fun _let_2 B))) (let ((_let_8 (tptp.fun _let_5 _let_7))) (let ((_let_9 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.iterate) (tptp.s _let_6 OP))) (tptp.s _let_5 S0))))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_3)))) _let_2)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A Y))) (tptp.s _let_1 S0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_1)) (tptp.s A Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s A Y))) (let ((_let_4 (tptp.s (tptp.fun A A) P0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s A (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s A (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))) (= (tptp.s B (tptp.i _let_9 _let_3)) (tptp.s B (tptp.i _let_9 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.o) _let_3)) (tptp.s _let_1 P0)))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (U_2 $$unsorted)) (=> (forall ((X $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) C))) (let ((_let_2 (tptp.fun A (tptp.fun B C)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_2) (tptp.s _let_2 X))) (tptp.s _let_1 F0)))) (forall ((I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun C tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun C _let_6) tptp.geq) (tptp.s C (tptp.i (tptp.s (tptp.fun _let_4 C) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s C (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) X) _let_2)) _let_1))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_146 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_146)))) (exists ((I0 $$unsorted) (J0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.in) _let_1)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) T0) _let_2))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_146))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((OP $$unsorted) (T0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B C))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun A _let_5))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun C (tptp.fun C C)))) (let ((_let_9 (tptp.s _let_8 OP))) (let ((_let_10 (tptp.fun _let_2 C))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun A C))) (let ((_let_13 (tptp.fun _let_3 _let_12))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (= (tptp.s C (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_8 _let_14) U_0) _let_9)) _let_7)) _let_4)) _let_1)) (tptp.s C (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.iterate) _let_9)) (tptp.s _let_5 (tptp.i _let_7 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))))))))) (forall ((OP $$unsorted)) (let ((_let_1 (tptp.fun C (tptp.fun C C)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B C)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun _let_3 C))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (let ((_let_12 (tptp.fun C (tptp.fun C C)))) (let ((_let_13 (tptp.s _let_12 OP))) (let ((_let_14 (tptp.fun _let_4 C))) (let ((_let_15 (tptp.fun _let_10 _let_14))) (let ((_let_16 (tptp.fun A C))) (let ((_let_17 (tptp.fun _let_1 _let_16))) (let ((_let_18 (tptp.fun _let_6 _let_17))) (let ((_let_19 (tptp.fun _let_16 C))) (let ((_let_20 (tptp.fun _let_8 _let_19))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))))))))))) (= (tptp.s C (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_12 _let_20) tptp.iterate) _let_13)) _let_9)) (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_12 _let_18) U_0) _let_13)) _let_7)) _let_2)))) (tptp.s C (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_12 _let_15) tptp.iterate) _let_13)) (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_10 _let_10) tptp.gspec) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) U_1) _let_9)) _let_7)))))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_2) _let_2)))))))))))))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B (tptp.fun B B)))) (let ((_let_4 (tptp.fun _let_1 B))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.iterate) (tptp.s _let_3 OP))) (tptp.s _let_2 S0))))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G0) _let_1))))))))) (= (tptp.s B (tptp.i _let_6 (tptp.s _let_1 F0))) (tptp.s B (tptp.i _let_6 (tptp.s _let_1 G0))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun C (tptp.fun C C)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun C (tptp.fun C C)))) (let ((_let_4 (tptp.s _let_3 OP))) (let ((_let_5 (tptp.fun _let_1 C))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun A C))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.fun _let_7 C))) (let ((_let_10 (tptp.fun _let_8 _let_9))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 T0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)) (tptp.s B Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.s (tptp.fun A B) H0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s C (tptp.i (tptp.s (tptp.fun B C) G0) _let_2)) (tptp.s C (tptp.i (tptp.s (tptp.fun A C) F0) _let_1))))))))))))) (= (tptp.s C (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.iterate) _let_4)) (tptp.s _let_8 S0))) (tptp.s _let_7 F0))) (tptp.s C (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.iterate) _let_4)) (tptp.s _let_2 T0))) (tptp.s _let_1 G0))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun C (tptp.fun C C)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun C (tptp.fun C C)))) (let ((_let_4 (tptp.s _let_3 OP))) (let ((_let_5 (tptp.fun _let_1 C))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun A C))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.fun _let_7 C))) (let ((_let_10 (tptp.fun _let_8 _let_9))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) K0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_2)) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) K0) _let_2)) _let_1) (= (tptp.s C (tptp.i (tptp.s (tptp.fun B C) G0) _let_2)) (tptp.s C (tptp.i (tptp.s (tptp.fun A C) F0) _let_1))))))))))))) (= (tptp.s C (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.iterate) _let_4)) (tptp.s _let_8 S0))) (tptp.s _let_7 F0))) (tptp.s C (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.iterate) _let_4)) (tptp.s _let_2 T0))) (tptp.s _let_1 G0))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun B (tptp.fun B B)))) (let ((_let_6 (tptp.fun _let_1 B))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.iterate) (tptp.s _let_5 OP))) _let_4)))) (let ((_let_9 (tptp.fun A A))) (let ((_let_10 (tptp.fun _let_9 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_3)))) _let_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A A) P0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s A (tptp.i _let_3 _let_2)) (tptp.s A (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))))) (= (tptp.s B (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_1 _let_10) tptp.o) _let_2)) (tptp.s _let_9 P0))))) (tptp.s B (tptp.i _let_8 _let_2)))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 B))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)))) (let ((_let_11 (tptp.s _let_3 S0))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (let ((_let_13 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_13 _let_11))) (tptp.p (tptp.s tptp.bool (tptp.i _let_13 _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.inter) (tptp.s _let_3 S0))) (tptp.s _let_3 T0)))))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.neutral) (tptp.s _let_1 OP)))))))))))) (= (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.union) _let_11)) _let_4)))) _let_2)) (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_11)) _let_2)))) (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_4)) _let_2))))))))))))))))))))))) (forall ((Q65977 $$unsorted) (Q65978 $$unsorted) (U_0 $$unsorted)) (=> (forall ((OP $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q65977 X))) (let ((_let_2 (tptp.fun Q65977 Q65978))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun Q65978 Q65978))) (let ((_let_6 (tptp.fun Q65978 _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (= (tptp.s Q65978 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_0) _let_7)) _let_4)) _let_3)) _let_1)) (tptp.s Q65978 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s Q65978 (tptp.i _let_4 _let_1)))) (tptp.s Q65978 (tptp.i _let_3 _let_1))))))))))))))) (forall ((OP $$unsorted)) (let ((_let_1 (tptp.fun Q65978 (tptp.fun Q65978 Q65978)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q65977 Q65978))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun Q65977 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun Q65978 Q65978))) (let ((_let_6 (tptp.fun Q65978 _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 Q65978))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)) _let_4)))) (let ((_let_11 (tptp.s _let_1 F0))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (let ((_let_13 (tptp.fun _let_1 _let_12))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s Q65978 (tptp.i _let_10 (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) U_0) _let_7)) _let_11)) _let_2)))) (tptp.s Q65978 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s Q65978 (tptp.i _let_10 _let_11)))) (tptp.s Q65978 (tptp.i _let_10 _let_2))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun B (tptp.fun B B)))) (let ((_let_6 (tptp.fun _let_1 B))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.iterate) (tptp.s _let_5 OP))))) (let ((_let_9 (tptp.s _let_3 V))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.subset) _let_4)) _let_9))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 V)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 U)))))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) (tptp.s B (tptp.i (tptp.s (tptp.fun _let_1 B) tptp.neutral) (tptp.s _let_1 OP)))))))))))) (= (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_9)) _let_2)) (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_4)) _let_2)))))))))))))))))) (forall ((C $$unsorted) (A $$unsorted) (B $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun C (tptp.fun C C)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((G0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun A C))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun C (tptp.fun C C)))) (let ((_let_10 (tptp.s _let_9 OP))) (let ((_let_11 (tptp.fun _let_5 C))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun B tptp.bool))) (let ((_let_14 (tptp.fun _let_7 _let_13))) (let ((_let_15 (tptp.fun _let_3 C))) (let ((_let_16 (tptp.fun _let_13 _let_15))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun C (tptp.fun C C)))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.s B (tptp.i _let_3 _let_2)))) (let ((_let_5 (tptp.s A Y))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun A _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_7))) (not (= _let_2 _let_5)) (= _let_4 (tptp.s B (tptp.i _let_3 _let_5)))) (= (tptp.s C (tptp.i (tptp.s (tptp.fun B C) G0) _let_4)) (tptp.s C (tptp.i (tptp.s (tptp.fun _let_1 C) tptp.neutral) (tptp.s _let_1 OP)))))))))))))))) (= (tptp.s C (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_9 _let_16) tptp.iterate) _let_10)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_1 _let_14) tptp.image) _let_2)) _let_8)))) _let_4)) (tptp.s C (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.iterate) _let_10)) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.o) _let_4)) _let_2)))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_2) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_149 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s A GENR_PVARR_149)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_149))) _let_2)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun B B))) (let ((_let_8 (tptp.fun B _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_0) _let_6)) _let_4)) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i _let_6 _let_1)))) (tptp.s B (tptp.i _let_4 _let_1)))) (tptp.s B (tptp.i _let_3 _let_1)))))))))))))))) (forall ((OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((S0 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (let ((_let_6 (tptp.s _let_3 S0))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) _let_6)))) (let ((_let_8 (tptp.s _let_5 tptp.gspec))) (let ((_let_9 (tptp.fun B B))) (let ((_let_10 (tptp.fun B _let_9))) (let ((_let_11 (tptp.s _let_10 OP))) (let ((_let_12 (tptp.fun _let_1 B))) (let ((_let_13 (tptp.fun _let_3 _let_12))) (let ((_let_14 (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_10 _let_13) tptp.iterate) _let_11)))) (let ((_let_15 (tptp.s _let_1 F0))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.fun _let_1 _let_16))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_6))) (= (tptp.s B (tptp.i (tptp.s _let_12 (tptp.i _let_14 _let_6)) (tptp.s _let_1 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_3 _let_17) U_0) _let_4)) _let_15)) _let_2)))) (tptp.s B (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s B (tptp.i (tptp.s _let_12 (tptp.i _let_14 (tptp.s _let_3 (tptp.i _let_8 (tptp.s _let_3 (tptp.i _let_7 _let_4)))))) _let_15)))) (tptp.s B (tptp.i (tptp.s _let_12 (tptp.i _let_14 (tptp.s _let_3 (tptp.i _let_8 (tptp.s _let_3 (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_2) _let_4)))))))) _let_2))))))))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((OP $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (= (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_0) _let_7)) _let_4)) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s B (tptp.i _let_4 _let_1)))) (tptp.s B (tptp.i _let_3 _let_1))))))))))))))) (forall ((OP $$unsorted)) (let ((_let_1 (tptp.fun B (tptp.fun B B)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun B B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.s _let_6 OP))) (let ((_let_8 (tptp.fun _let_1 B))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.iterate) _let_7)) _let_4)))) (let ((_let_11 (tptp.s _let_1 F0))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (let ((_let_13 (tptp.fun _let_1 _let_12))) (let ((_let_14 (tptp.fun _let_3 _let_3))) (let ((_let_15 (tptp.fun _let_1 _let_14))) (let ((_let_16 (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_6 _let_15) tptp.support) _let_7)))) (let ((_let_17 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_17 (tptp.s _let_3 (tptp.i (tptp.s _let_14 (tptp.i _let_16 _let_11)) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_17 (tptp.s _let_3 (tptp.i (tptp.s _let_14 (tptp.i _let_16 _let_2)) _let_4)))))) (= (tptp.s B (tptp.i _let_10 (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) U_0) _let_7)) _let_11)) _let_2)))) (tptp.s B (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s B (tptp.i _let_10 _let_11)))) (tptp.s B (tptp.i _let_10 _let_2))))))))))))))))))))))))))))) (forall ((Q66575 $$unsorted) (OP $$unsorted)) (let ((_let_1 (tptp.fun Q66575 (tptp.fun Q66575 Q66575)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (and (forall ((M0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q66575 Q66575))) (let ((_let_2 (tptp.fun Q66575 _let_1))) (let ((_let_3 (tptp.s _let_2 OP))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_5 (tptp.fun tptp.num Q66575))) (let ((_let_6 (tptp.s _let_5 tptp.f))) (let ((_let_7 (tptp.s tptp.bool V))) (let ((_let_8 (tptp.s tptp.num M0))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun _let_5 Q66575))) (let ((_let_12 (tptp.fun _let_9 _let_11))) (and (= (tptp.p _let_7) (= _let_8 _let_4)) (= (tptp.s Q66575 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_2 _let_12) tptp.iterate) _let_3)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_) _let_8)) _let_4)))) _let_6)) (tptp.s Q66575 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.bool _let_2) tptp.cond) _let_7)) (tptp.s Q66575 (tptp.i _let_6 _let_4)))) (tptp.s Q66575 (tptp.i (tptp.s (tptp.fun _let_2 Q66575) tptp.neutral) _let_3)))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num Q66575))) (let ((_let_2 (tptp.s _let_1 tptp.f))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) _let_4)))) (let ((_let_8 (tptp.fun Q66575 Q66575))) (let ((_let_9 (tptp.fun Q66575 _let_8))) (let ((_let_10 (tptp.s _let_9 OP))) (let ((_let_11 (tptp.fun _let_1 Q66575))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (let ((_let_13 (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.iterate) _let_10)))) (let ((_let_14 (tptp.s Q66575 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_5 (tptp.i _let_7 _let_3)))) _let_2)))) (let ((_let_15 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_3)))) (= (tptp.s Q66575 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_5 (tptp.i _let_7 _let_15)))) _let_2)) (tptp.s Q66575 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_) _let_4)) _let_15)))) (tptp.s Q66575 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_14)) (tptp.s Q66575 (tptp.i _let_2 _let_15)))))) _let_14))))))))))))))))))))))) (forall ((Q66750 $$unsorted) (U_0 $$unsorted)) (=> (forall ((OP $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.t_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) _let_4)))) (let ((_let_7 (tptp.fun tptp.num Q66750))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun Q66750 Q66750))) (let ((_let_10 (tptp.fun Q66750 _let_9))) (let ((_let_11 (tptp.s _let_10 OP))) (let ((_let_12 (tptp.fun _let_7 _let_7))) (= (tptp.s Q66750 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) U_0) _let_11)) _let_8)) _let_4)) (tptp.s Q66750 (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s Q66750 (tptp.i _let_8 _let_6)))) (tptp.s Q66750 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.p_) _let_6)) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))))))))))))) (forall ((OP $$unsorted)) (let ((_let_1 (tptp.fun Q66750 (tptp.fun Q66750 Q66750)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.monoidal) (tptp.s _let_1 OP)))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num Q66750))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q66750 (tptp.fun Q66750 Q66750)))) (let ((_let_4 (tptp.s _let_3 OP))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s tptp.num N0))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_))) (let ((_let_11 (tptp.fun _let_1 Q66750))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (let ((_let_13 (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.iterate) _let_4)))) (let ((_let_14 (tptp.fun tptp.num tptp.num))) (let ((_let_15 (tptp.s tptp.num (tptp.i (tptp.s _let_14 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_16 (tptp.s _let_14 tptp.numeral))) (let ((_let_17 (tptp.fun tptp.num _let_14))) (let ((_let_18 (tptp.s _let_14 (tptp.i (tptp.s _let_17 tptp.t_) (tptp.s tptp.num (tptp.i _let_16 (tptp.s tptp.num (tptp.i (tptp.s _let_14 tptp.bit0) _let_15)))))))) (= (tptp.s Q66750 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_18 _let_7)))) (tptp.s tptp.num (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_17 tptp.p_) (tptp.s tptp.num (tptp.i _let_18 _let_6)))) (tptp.s tptp.num (tptp.i _let_16 _let_15)))))))) _let_2)) (tptp.s Q66750 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_7)) _let_6)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2))))))))))))))))))))))))))))) (forall ((Q66768 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun tptp.num tptp.num)))) (let ((_let_2 (tptp.fun (tptp.fun Q66768 tptp.bool) (tptp.fun (tptp.fun Q66768 tptp.num) tptp.num)))) (= (tptp.s _let_2 tptp.nsum) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.iterate) (tptp.s _let_1 tptp.p_))))))) (= (tptp.s tptp.num (tptp.i _let_75 _let_74)) _let_51) (= (tptp.s tptp.num (tptp.i _let_75 _let_72)) _let_17) (tptp.p (tptp.s tptp.bool (tptp.i _let_73 _let_74))) (tptp.p (tptp.s tptp.bool (tptp.i _let_73 _let_72))) (forall ((Q66806 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q66806 tptp.num))) (let ((_let_2 (tptp.fun Q66806 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.nsum) (tptp.s _let_2 tptp.empty))) (tptp.s _let_1 F0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (forall ((Q66845 $$unsorted) (X $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q66845 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q66845 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))) (let ((_let_8 (tptp.s Q66845 X))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun _let_3 tptp.bool))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 tptp.finite) _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun Q66845 _let_12) tptp.insert) _let_8)) _let_4)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q66845 _let_11) tptp.in) _let_8)) _let_4)))) _let_7)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.p_) (tptp.s tptp.num (tptp.i _let_2 _let_8)))) _let_7))))))))))))))))))) (forall ((Q66871 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q66871 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q66871 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s _let_3 S0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.s _let_10 tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.disjoint) _let_7)) _let_4)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.union) _let_7)) _let_4)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))))) (forall ((Q66926 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q66926 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q66926 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s _let_3 S0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 tptp.finite) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.subset) _let_4)) _let_7)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.diff) _let_7)) _let_4)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.s _let_3 S0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_1 tptp.num))) (let ((_let_9 (tptp.s (tptp.fun _let_3 _let_8) tptp.nsum))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.p_))) (let ((_let_12 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_12 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_12 _let_4)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.union) _let_5)) _let_4)))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.inter) _let_5)) _let_4)))) _let_2))))))))))))))))))) (forall ((Q67015 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q67015 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q67015 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.fun tptp.num (tptp.fun tptp.num tptp.num)))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.support) (tptp.s _let_7 tptp.p_))) _let_2)) _let_4)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))) (forall ((Q67049 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q67049 X))) (let ((_let_2 (tptp.fun Q67049 tptp.num))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_4)) _let_3)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q67049 tptp.num))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun Q67049 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum) _let_4)))) (let ((_let_7 (tptp.s _let_1 F0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) U_0) _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.p_) (tptp.s tptp.num (tptp.i _let_6 _let_7)))) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))))))))))))) (forall ((Q67136 $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q67136 X))) (let ((_let_2 (tptp.fun Q67136 tptp.num))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_1) _let_4)) _let_3)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_155 $$unsorted)) (let ((_let_1 (tptp.fun Q67136 tptp.num))) (let ((_let_2 (tptp.fun Q67136 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s Q67136 GENR_PVARR_155)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q67136 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q67136 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q67136 _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (not (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun Q67136 tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q67136 _let_4) tptp.setspec) (tptp.s Q67136 GENR_PVARR_155))) _let_2)) _let_1))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q67136 tptp.num))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun Q67136 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum) _let_4)))) (let ((_let_7 (tptp.s _let_1 F0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_1 _let_3))) (let ((_let_11 (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_4)))) (let ((_let_12 (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec))) (let ((_let_13 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_13 (tptp.s _let_3 (tptp.i _let_12 (tptp.s _let_3 (tptp.i _let_11 _let_7))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_13 (tptp.s _let_3 (tptp.i _let_12 (tptp.s _let_3 (tptp.i _let_11 _let_2)))))))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) U_1) _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.p_) (tptp.s tptp.num (tptp.i _let_6 _let_7)))) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))))))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.nsum) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((N0 $$unsorted)) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) U_0) (tptp.s A N0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.nsum) (tptp.s _let_2 S0))) (tptp.s _let_1 U_0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num C0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) U_0) _let_4)) _let_3)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.t_) _let_4)) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))) (forall ((F0 $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.nsum) (tptp.s _let_3 S0))))) (let ((_let_6 (tptp.s tptp.num C0))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) U_0) _let_6)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.t_) _let_6)) (tptp.s tptp.num (tptp.i _let_5 _let_2)))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num C0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.num))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.t_) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) _let_1)))))))))) (forall ((F0 $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num C0))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.nsum) (tptp.s _let_4 S0))))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_2))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_0) _let_3)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.t_) (tptp.s tptp.num (tptp.i _let_6 _let_3)))) _let_1)))))))))))))) (forall ((Q67326 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q67326 tptp.num))) (let ((_let_2 (tptp.fun Q67326 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q67326 X))) (let ((_let_2 (tptp.fun Q67326 tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun Q67326 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q67326 _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 F0))))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 G0)))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 G0) _let_1)))))))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 F0))))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 G0)))))))))))))) (forall ((Q67448 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q67448 tptp.num))) (let ((_let_2 (tptp.fun Q67448 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (not (= _let_3 (tptp.s _let_2 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q67448 X))) (let ((_let_2 (tptp.fun Q67448 tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun Q67448 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q67448 _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 F0))))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 G0)))))))))))))) (forall ((Q67486 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q67486 tptp.num))) (let ((_let_2 (tptp.fun Q67486 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.nsum) (tptp.s _let_2 S0))))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q67486 X))) (let ((_let_2 (tptp.fun Q67486 tptp.num))) (let ((_let_3 (tptp.fun Q67486 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q67486 _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 G0) _let_1))))))))) (= (tptp.s tptp.num (tptp.i _let_4 (tptp.s _let_1 F0))) (tptp.s tptp.num (tptp.i _let_4 (tptp.s _let_1 G0)))))))))) (forall ((Q67516 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num C0))) (let ((_let_2 (tptp.fun Q67516 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) _let_1)) (tptp.s Q67516 N0))) _let_1)))) (forall ((C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num C0))) (let ((_let_2 (tptp.fun Q67516 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun Q67516 tptp.num))) (let ((_let_6 (tptp.fun _let_5 tptp.num))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.nsum) _let_3)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) U_0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)))) _let_1))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (B0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)) (tptp.s _let_1 F0))))) (tptp.s tptp.num B0))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)))) (tptp.s tptp.num B0))))))))))))))))) (forall ((Q67625 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q67625 tptp.num))) (let ((_let_2 (tptp.fun Q67625 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)) (tptp.s _let_1 tptp.f))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q67625 X))) (let ((_let_2 (tptp.fun Q67625 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q67625 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun Q67625 tptp.num) tptp.f) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))) (forall ((Q67654 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun Q67654 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q67654 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s Q67654 A5))) (let ((_let_8 (tptp.fun Q67654 _let_3))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q67654 _let_10) tptp.in) _let_7)) _let_4)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.p_) (tptp.s tptp.num (tptp.i _let_2 _let_7)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.delete) _let_4)) _let_7)))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))))) (forall ((Q67683 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q67683 X))) (let ((_let_2 (tptp.fun Q67683 tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q67683 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.fun _let_2 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.nsum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q67683 _let_5) tptp.insert) _let_1)) (tptp.s _let_4 tptp.empty))))) _let_3)) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun tptp.num _let_1))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.s A A5))) (let ((_let_6 (tptp.fun A tptp.num))) (and (= (tptp.p _let_2) (= _let_4 _let_5)) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) U_0) _let_5)) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) _let_2)) (tptp.s tptp.num tptp.b0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s A A5))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_1))) (let ((_let_7 (tptp.fun A tptp.num))) (let ((_let_8 (tptp.fun _let_7 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.nsum) _let_3)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) U_0) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_4)) _let_3)))) (tptp.s tptp.num tptp.b0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_2 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.fun B tptp.num))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.num))) (let ((_let_7 (tptp.fun B _let_6))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_2) _let_5)) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.fun B tptp.num))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.num))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.num))) (let ((_let_10 (tptp.fun _let_3 _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) U_1) _let_8)) _let_4)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.nsum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_2) _let_4)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.num))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.s _let_5 T0))) (let ((_let_7 (tptp.fun _let_2 tptp.num))) (let ((_let_8 (tptp.fun A tptp.num))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_0) _let_6)) _let_4)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.nsum) _let_6)) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.num))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun B tptp.bool))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun _let_1 tptp.num))) (let ((_let_10 (tptp.fun A tptp.num))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun _let_10 tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.nsum) _let_5)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) U_0) _let_8)) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.nsum) _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3))))))))))))))))))))))))) (forall ((Q67819 $$unsorted) (Q67795 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q67819 Q67795))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q67795 tptp.num))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun Q67819 tptp.num))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun Q67819 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.num))) (let ((_let_10 (tptp.fun Q67795 tptp.bool))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (let ((_let_12 (tptp.fun _let_3 tptp.num))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q67819 Y))) (let ((_let_2 (tptp.s Q67819 X))) (let ((_let_3 (tptp.s (tptp.fun Q67819 Q67795) F0))) (let ((_let_4 (tptp.fun Q67819 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q67819 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q67795 (tptp.i _let_3 _let_2)) (tptp.s Q67795 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.nsum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.image) _let_2)) _let_8)))) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.nsum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.o) _let_4)) _let_2))))))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s _let_3 V))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.subset) _let_4)) _let_7))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 V)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 U)))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 V)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 U)))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.union) _let_4)) (tptp.s _let_3 V))))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 V))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 U)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 V)))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.union) (tptp.s _let_3 U))) _let_4)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))) (forall ((Q68010 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s Q68010 X))) (let ((_let_3 (tptp.fun Q68010 tptp.num))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q68010 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_1))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_0) _let_6)) _let_4)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q68010 _let_7) tptp.in) _let_2)) _let_6)))) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q68010 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q68010 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum) _let_4)))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun A tptp.num))) (let ((_let_5 (tptp.fun _let_4 tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)))) (tptp.s tptp.num B0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.nsum) _let_2)) (tptp.s _let_4 F0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))) (tptp.s tptp.num B0)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (not (= _let_3 (tptp.s _let_2 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.div) (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)) (tptp.s _let_1 F0))))) (tptp.s tptp.num B0))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun A tptp.num))) (let ((_let_5 (tptp.fun _let_4 tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)))) (tptp.s tptp.num B0)))))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)))) (tptp.s tptp.num B0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.nsum) _let_2)) (tptp.s _let_4 F0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))) (tptp.s tptp.num B0)))))))))))))) (forall ((Q68228 $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun Q68228 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun Q68228 tptp.num))) (let ((_let_5 (tptp.fun _let_4 tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q68228 X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun Q68228 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q68228 _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun Q68228 tptp.num) F0) _let_1)))) (tptp.s tptp.num B0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.nsum) _let_2)) (tptp.s _let_4 F0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))) (tptp.s tptp.num B0)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (not (= _let_3 (tptp.s _let_2 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.div) (tptp.s tptp.num B0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)) (tptp.s _let_1 F0))))) (tptp.s tptp.num B0))))))))))) (forall ((Q68329 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun Q68329 tptp.num))) (let ((_let_2 (tptp.s _let_1 tptp.f))) (let ((_let_3 (tptp.fun Q68329 tptp.bool))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s _let_3 T0))) (let ((_let_8 (tptp.s _let_3 S0))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.inter) _let_8)) _let_7)) (tptp.s _let_3 tptp.empty)) (= (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.union) _let_8)) _let_7)) _let_4)) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_8)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum))) (let ((_let_6 (tptp.s _let_2 S0))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.subset) _let_3)) _let_6))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.g) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 S0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 T0)))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_1 F0))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_1 tptp.g))))))))))))) (forall ((A $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.num))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun tptp.num _let_1))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_6)) _let_4)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_157 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s A GENR_PVARR_157)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_157))) _let_2)) _let_1)))))))))))))) (forall ((P0 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_3 S0))) (let ((_let_7 (tptp.fun _let_1 tptp.num))) (let ((_let_8 (tptp.s (tptp.fun _let_3 _let_7) tptp.nsum))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_9 tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) U_0) _let_6)) _let_4)))))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) _let_4)) _let_2))))))))))))))))))) (forall ((Q68586 $$unsorted) (Q68585 $$unsorted) (U_5 $$unsorted)) (=> (forall ((F0 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q68585 Y))) (let ((_let_2 (tptp.s Q68586 X))) (let ((_let_3 (tptp.fun Q68585 tptp.num))) (let ((_let_4 (tptp.fun Q68586 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q68586 tptp.num))) (let ((_let_7 (tptp.fun Q68585 _let_6))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_5) _let_5)) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((S0 $$unsorted) (R0 $$unsorted) (Y $$unsorted) (GENR_PVARR_159 $$unsorted)) (let ((_let_1 (tptp.fun Q68586 (tptp.fun Q68585 tptp.bool)))) (let ((_let_2 (tptp.fun Q68586 tptp.bool))) (let ((_let_3 (tptp.fun Q68585 _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_4) (tptp.s _let_2 S0))) (tptp.s _let_1 R0))) (tptp.s Q68585 Y))) (tptp.s Q68586 GENR_PVARR_159)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q68586 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q68586 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun Q68585 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q68586 _let_6) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q68586 _let_5) R0) _let_1)) (tptp.s Q68585 Y)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q68586 _let_4) tptp.setspec) (tptp.s Q68586 GENR_PVARR_159))) _let_2)) _let_1))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((S0 $$unsorted) (R0 $$unsorted) (F0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q68585 Y))) (let ((_let_2 (tptp.fun Q68585 tptp.num))) (let ((_let_3 (tptp.fun Q68586 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q68586 tptp.num))) (let ((_let_6 (tptp.fun Q68585 _let_5))) (let ((_let_7 (tptp.fun Q68586 (tptp.fun Q68585 tptp.bool)))) (let ((_let_8 (tptp.s _let_7 R0))) (let ((_let_9 (tptp.fun Q68586 tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun Q68585 _let_9))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun _let_5 tptp.num))) (let ((_let_14 (tptp.fun _let_3 _let_2))) (let ((_let_15 (tptp.fun _let_7 _let_14))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_9 _let_15) U_3) _let_10)) _let_8)) _let_4)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_9 _let_13) tptp.nsum) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_9 _let_9) tptp.gspec) (tptp.s _let_9 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) U_4) _let_10)) _let_8)) _let_1)))))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_5) _let_4)) _let_1))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q68585 Y))) (let ((_let_2 (tptp.s Q68586 X))) (let ((_let_3 (tptp.fun Q68585 tptp.num))) (let ((_let_4 (tptp.fun Q68586 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) U_2) _let_5)) _let_2)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (X $$unsorted) (GENR_PVARR_158 $$unsorted)) (let ((_let_1 (tptp.fun Q68585 tptp.bool))) (let ((_let_2 (tptp.fun Q68586 _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_1) (tptp.s _let_1 T0))) (tptp.s _let_2 R0))) (tptp.s Q68586 X))) (tptp.s Q68585 GENR_PVARR_158)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q68585 Y))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q68585 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q68585 _let_5) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q68586 _let_3) R0) (tptp.s Q68586 X))) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q68585 _let_4) tptp.setspec) (tptp.s Q68585 GENR_PVARR_158))) _let_2)) _let_1))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q68586 X))) (let ((_let_2 (tptp.fun Q68585 tptp.num))) (let ((_let_3 (tptp.fun Q68586 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q68585 tptp.bool))) (let ((_let_6 (tptp.fun Q68586 _let_5))) (let ((_let_7 (tptp.s _let_6 R0))) (let ((_let_8 (tptp.s _let_5 T0))) (let ((_let_9 (tptp.fun _let_6 _let_6))) (let ((_let_10 (tptp.fun _let_2 tptp.num))) (let ((_let_11 (tptp.fun Q68586 tptp.num))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun _let_6 _let_12))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_5 _let_13) U_0) _let_8)) _let_7)) _let_4)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.nsum) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_1) _let_8)) _let_7)) _let_1)))))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_2) _let_4)) _let_1))))))))))))))))))) (forall ((R0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q68585 tptp.num))) (let ((_let_2 (tptp.fun Q68586 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q68585 tptp.bool))) (let ((_let_5 (tptp.fun Q68586 _let_4))) (let ((_let_6 (tptp.s _let_5 R0))) (let ((_let_7 (tptp.fun Q68586 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.s _let_4 T0))) (let ((_let_12 (tptp.fun _let_1 tptp.num))) (let ((_let_13 (tptp.fun Q68586 tptp.num))) (let ((_let_14 (tptp.fun _let_2 _let_13))) (let ((_let_15 (tptp.fun _let_5 _let_14))) (let ((_let_16 (tptp.fun _let_13 tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_11)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_7 _let_16) tptp.nsum) _let_8)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_4 _let_15) U_0) _let_11)) _let_6)) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.nsum) _let_11)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) U_3) _let_8)) _let_6)) _let_3))))))))))))))))))))))))))))))))))) (forall ((Q68605 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun Q68605 tptp.num) U_0) (tptp.s Q68605 X))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q68605 tptp.num))) (let ((_let_2 (tptp.fun Q68605 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)) (tptp.s _let_1 U_0)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_3 $$unsorted)) (=> (forall ((K0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s B I0))) (let ((_let_2 (tptp.fun B tptp.num))) (let ((_let_3 (tptp.s _let_2 K0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_3) _let_3)) _let_1)) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))) (forall ((U_2 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (I0 $$unsorted) (GENR_PVARR_162 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_2) (tptp.s _let_1 T0))) (tptp.s _let_2 R0))) (tptp.s A I0))) (tptp.s B GENR_PVARR_162)))) (exists ((J0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) R0) (tptp.s A I0))) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.setspec) (tptp.s B GENR_PVARR_162))) _let_2)) _let_1))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 R0))) (let ((_let_5 (tptp.s _let_2 T0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun A tptp.num))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_1) _let_5)) _let_4)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_2) _let_5)) _let_4)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (R0 $$unsorted) (J0 $$unsorted) (GENR_PVARR_161 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 R0))) (tptp.s B J0))) (tptp.s A GENR_PVARR_161)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) R0) _let_1)) (tptp.s B J0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_161))) _let_2)) _let_1))))))))))))))))) (forall ((R0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.num))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.fun A _let_2))) (let ((_let_6 (tptp.fun A tptp.num))) (let ((_let_7 (tptp.fun _let_5 _let_6))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_6 tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun B _let_7) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 S0))) (tptp.s _let_3 R0))) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun B tptp.num) K0) _let_1))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.nsum) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) U_1) _let_3)) (tptp.s _let_5 R0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_3) (tptp.s _let_1 K0)))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_2 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (I0 $$unsorted) (GENR_PVARR_164 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_2) (tptp.s _let_1 T0))) (tptp.s _let_2 R0))) (tptp.s A I0))) (tptp.s B GENR_PVARR_164)))) (exists ((J0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) R0) (tptp.s A I0))) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.setspec) (tptp.s B GENR_PVARR_164))) _let_2)) _let_1))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 R0))) (let ((_let_5 (tptp.s _let_2 T0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun A tptp.num))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_1) _let_5)) _let_4)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_2) _let_5)) _let_4)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (R0 $$unsorted) (J0 $$unsorted) (GENR_PVARR_163 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 R0))) (tptp.s B J0))) (tptp.s A GENR_PVARR_163)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) R0) _let_1)) (tptp.s B J0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_163))) _let_2)) _let_1))))))))))))))))) (forall ((R0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun A _let_1))) (let ((_let_5 (tptp.fun A tptp.num))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun B _let_7) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 S0))) (tptp.s _let_3 R0))) _let_1)))))) (tptp.s tptp.num K0)))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.nsum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_1) _let_2)) (tptp.s _let_4 R0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) (tptp.s tptp.num K0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (Y $$unsorted) (GENR_PVARR_167 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_1) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B Y))) (tptp.s A GENR_PVARR_167)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_167))) _let_2)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun B _let_6))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_1 tptp.num))) (let ((_let_11 (tptp.fun B tptp.num))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) U_0) _let_7)) _let_5)) _let_2)) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.nsum) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_1) _let_7)) _let_5)) _let_3)))))) _let_2))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun B tptp.num))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun B tptp.bool))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_7 tptp.num))) (let ((_let_13 (tptp.fun _let_1 tptp.num))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_5 _let_13) tptp.nsum) _let_6)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.nsum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.image) _let_4)) _let_6)))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_0) _let_6)) _let_4)) _let_2)))))))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (Y $$unsorted) (GENR_PVARR_168 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_1) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B Y))) (tptp.s A GENR_PVARR_168)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_168))) _let_2)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun B _let_6))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_1 tptp.num))) (let ((_let_11 (tptp.fun B tptp.num))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) U_0) _let_7)) _let_5)) _let_2)) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.nsum) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_1) _let_7)) _let_5)) _let_3)))))) _let_2))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.fun A B))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun B tptp.num))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (let ((_let_11 (tptp.fun B tptp.bool))) (let ((_let_12 (tptp.s _let_11 T0))) (let ((_let_13 (tptp.fun _let_8 tptp.num))) (let ((_let_14 (tptp.fun _let_3 _let_11))) (let ((_let_15 (tptp.fun _let_11 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_11 _let_15) tptp.subset) (tptp.s _let_11 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_6 _let_14) tptp.image) _let_7)) _let_4)))) _let_12)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.nsum) _let_12)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_4)) _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum) _let_4)) _let_2)))))))))))))))))))))))) (forall ((A $$unsorted) (U $$unsorted) (V $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 V))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s _let_3 U))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.diff) (tptp.s _let_2 U))) (tptp.s _let_2 V)))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))) (forall ((Q69133 $$unsorted) (U $$unsorted) (V $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q69133 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q69133 tptp.bool))) (let ((_let_4 (tptp.s _let_3 V))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s _let_3 U))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.subset) _let_7)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (D0 $$unsorted) (I0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 I0))) (let ((_let_3 (tptp.fun B tptp.num))) (let ((_let_4 (tptp.s _let_3 D0))) (let ((_let_5 (tptp.fun A tptp.num))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.num))) (let ((_let_10 (tptp.fun B tptp.bool))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (let ((_let_12 (tptp.fun _let_3 tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s (tptp.fun A B) I0))) (let ((_let_3 (tptp.s B (tptp.i _let_2 _let_1)))) (let ((_let_4 (tptp.s A Y))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_6))) (not (= _let_1 _let_4)) (= _let_3 (tptp.s B (tptp.i _let_2 _let_4)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun B tptp.num) D0) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.nsum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.image) _let_2)) _let_8)))) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.nsum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.o) _let_4)) _let_2))))))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A A))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_2 tptp.num))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.nsum) (tptp.s _let_5 S0))))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_3)))) _let_2)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A Y))) (tptp.s _let_1 S0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_1)) (tptp.s A Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s A Y))) (let ((_let_4 (tptp.s (tptp.fun A A) P0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s A (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s A (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))) (= (tptp.s tptp.num (tptp.i _let_7 _let_3)) (tptp.s tptp.num (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.o) _let_3)) (tptp.s _let_1 P0))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_2 $$unsorted)) (=> (forall ((X $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) tptp.num))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.num)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_2) (tptp.s _let_2 X))) (tptp.s _let_1 F0)))) (forall ((I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.fun B tptp.num))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.geq) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) X) _let_2)) _let_1))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_169 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_169)))) (exists ((I0 $$unsorted) (J0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.in) _let_1)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) T0) _let_2))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_169))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.num))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun A _let_5))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun _let_2 tptp.num))) (let ((_let_9 (tptp.fun A tptp.num))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_4)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.nsum) (tptp.s _let_5 (tptp.i _let_7 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.num)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun _let_3 tptp.num))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (let ((_let_12 (tptp.fun _let_4 tptp.num))) (let ((_let_13 (tptp.fun A tptp.num))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (let ((_let_15 (tptp.fun _let_13 tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_8 _let_15) tptp.nsum) _let_9)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_6 _let_14) U_0) _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.nsum) (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_10 _let_10) tptp.gspec) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) U_1) _let_9)) _let_7)))))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_2) _let_2)))))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.num))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.fun A tptp.num))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_4 tptp.num))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 T0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)) (tptp.s B Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.s (tptp.fun A B) H0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun B tptp.num) G0) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.nsum) (tptp.s _let_5 S0))) (tptp.s _let_4 F0))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.nsum) (tptp.s _let_2 T0))) (tptp.s _let_1 G0)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.num))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.fun A tptp.num))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_4 tptp.num))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) K0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_2)) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) K0) _let_2)) _let_1) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun B tptp.num) G0) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.nsum) (tptp.s _let_5 S0))) (tptp.s _let_4 F0))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.nsum) (tptp.s _let_2 T0))) (tptp.s _let_1 G0)))))))))))) (forall ((Q69603 $$unsorted) (F0 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q69603 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q69603 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum) _let_4)))) (let ((_let_7 (tptp.fun Q69603 Q69603))) (let ((_let_8 (tptp.fun _let_7 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q69603 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s Q69603 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun Q69603 _let_4) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s Q69603 (tptp.i (tptp.s (tptp.fun Q69603 Q69603) P0) _let_3)))) _let_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q69603 Y))) (let ((_let_2 (tptp.s Q69603 X))) (let ((_let_3 (tptp.s (tptp.fun Q69603 Q69603) P0))) (let ((_let_4 (tptp.fun Q69603 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q69603 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q69603 (tptp.i _let_3 _let_2)) (tptp.s Q69603 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.o) _let_2)) (tptp.s _let_7 P0))))) (tptp.s tptp.num (tptp.i _let_6 _let_2))))))))))))) (forall ((Q69646 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q69646 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q69646 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum))) (let ((_let_7 (tptp.s _let_3 S0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (let ((_let_10 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q69646 X))) (let ((_let_2 (tptp.fun Q69646 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q69646 _let_4) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.inter) (tptp.s _let_2 S0))) (tptp.s _let_2 T0)))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun Q69646 tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.union) _let_7)) _let_4)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.fun _let_3 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_2)) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum) _let_4)) _let_2)))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.num))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_4 tptp.num))) (let ((_let_8 (tptp.fun _let_1 tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))))))))) (forall ((T1 $$unsorted) (T2 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 T2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)))) (let ((_let_6 (tptp.s _let_2 T1))) (let ((_let_7 (tptp.s _let_4 S0))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_2 _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_7))) (not (= _let_6 _let_3)) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.nsum) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_5 _let_3) tptp.unions) _let_6)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.nsum) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2))))))))))))))))) (forall ((A $$unsorted) (U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_2) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_170 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s A GENR_PVARR_170)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_170))) _let_2)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_0) _let_6)) _let_4)) _let_3)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i _let_6 _let_1)))) (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))) (forall ((S0 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (let ((_let_6 (tptp.s _let_3 S0))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) _let_6)))) (let ((_let_8 (tptp.s _let_5 tptp.gspec))) (let ((_let_9 (tptp.fun _let_1 tptp.num))) (let ((_let_10 (tptp.s (tptp.fun _let_3 _let_9) tptp.nsum))) (let ((_let_11 (tptp.s _let_1 F0))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_6))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_6)) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_3 _let_14) U_0) _let_4)) _let_11)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_3 (tptp.i _let_8 (tptp.s _let_3 (tptp.i _let_7 _let_4)))))) _let_11)))) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_3 (tptp.i _let_8 (tptp.s _let_3 (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_2) _let_4)))))))) _let_2))))))))))))))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num Y))) (let ((_let_2 (tptp.s tptp.num X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) P0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.nsum) (tptp.s _let_2 S0))) (tptp.s _let_1 F0)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_4)) _let_3)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) (tptp.s tptp.num (tptp.i _let_4 _let_1)))) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.nsum) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (let ((_let_7 (tptp.s _let_1 F0))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.num (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) U_0) _let_7)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) (tptp.s tptp.num (tptp.i _let_6 _let_7)))) (tptp.s tptp.num (tptp.i _let_6 _let_2)))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.num N0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 G0) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.l_a_) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 F0))))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 G0))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 G0) _let_1))))))))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 F0))) (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_1 G0))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num C0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) _let_1)) (tptp.s tptp.num N0))) _let_1)))) (forall ((C0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num C0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num _let_3))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_3 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.nsum) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) _let_2)) _let_4)))) (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_0) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.t_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.p_) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)))) _let_1)))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 F0) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))) (tptp.s _let_1 F0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (= (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.nsum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))) (tptp.s _let_1 F0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num N0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 F0) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.num))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.l_) _let_2)) _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.nsum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) _let_3)) _let_2)))) (tptp.s _let_1 F0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((F0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_2 tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.nsum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) _let_1)) _let_1)))) _let_3)) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (forall ((M0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.f))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun _let_1 tptp.num))) (and (= (tptp.p _let_4) (= _let_6 _let_2)) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.nsum) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.o_o_) _let_6)) _let_2)))) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) _let_4)) (tptp.s tptp.num (tptp.i _let_3 _let_2)))) _let_2))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 tptp.f))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) _let_4)))) (let ((_let_8 (tptp.fun _let_1 tptp.num))) (let ((_let_9 (tptp.s (tptp.fun _let_5 _let_8) tptp.nsum))) (let ((_let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i _let_7 _let_3)))) _let_2)))) (let ((_let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) _let_3)))) (let ((_let_12 (tptp.fun tptp.num _let_1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i _let_7 _let_11)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.bool _let_12) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_) _let_4)) _let_11)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_12 tptp.p_) _let_10)) (tptp.s tptp.num (tptp.i _let_2 _let_11)))))) _let_10)))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) U_2) _let_5)) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_1) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_2) _let_4)) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (D0 $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.s tptp.num D0))) (let ((_let_6 (tptp.s tptp.num C0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun _let_2 tptp.num))) (let ((_let_10 (tptp.fun _let_3 _let_2))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) U_0) _let_6)) _let_5)) _let_4)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.nsum) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.o_o_) _let_6)) _let_5)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num B0))) (let ((_let_5 (tptp.s tptp.num A5))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) U_0))) (let ((_let_9 (tptp.s tptp.num D0))) (let ((_let_10 (tptp.s tptp.num C0))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_))) (let ((_let_14 (tptp.fun _let_1 tptp.num))) (let ((_let_15 (tptp.s (tptp.fun _let_11 _let_14) tptp.nsum))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_14 (tptp.i _let_15 (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_5)) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_10)) _let_9)) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_14 (tptp.i _let_15 (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_10)) _let_9)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_1) _let_3))))))))))))))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_1) tptp.p_))) (let ((_let_5 (tptp.s _let_1 (tptp.i _let_4 _let_3)))) (let ((_let_6 (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num P0))))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_))) (let ((_let_11 (tptp.fun _let_1 tptp.num))) (let ((_let_12 (tptp.s (tptp.fun _let_8 _let_11) tptp.nsum))) (let ((_let_13 (tptp.s tptp.num M0))) (let ((_let_14 (tptp.s _let_9 (tptp.i _let_10 _let_13)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_a_) _let_13)) _let_7))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_14 _let_6)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_14 _let_3)))) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_7)) _let_6)))) _let_2))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (P0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_3 F0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) _let_5)) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.o_o_))) (let ((_let_10 (tptp.fun _let_2 tptp.num))) (let ((_let_11 (tptp.s (tptp.fun _let_7 _let_10) tptp.nsum))) (let ((_let_12 (tptp.s _let_4 tptp.p_))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_12 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_12 _let_5)) _let_1)))))) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_5)))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1)))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (M0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_3 F0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) _let_5)) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.p_) _let_2)) _let_1))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_))) (let ((_let_9 (tptp.fun _let_2 tptp.num))) (let ((_let_10 (tptp.s (tptp.fun _let_6 _let_9) tptp.nsum))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_a_) _let_1)) _let_5))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_5)))) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.m_) _let_5)) _let_1)))))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1))))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_1) tptp.p_))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_))) (let ((_let_9 (tptp.fun _let_1 tptp.num))) (let ((_let_10 (tptp.s (tptp.fun _let_6 _let_9) tptp.nsum))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_a_) _let_4)) _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_3)))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_2 _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_5 _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_3)))) _let_2))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num tptp.u_0))) (let ((_let_5 (tptp.s _let_2 tptp.numeral))) (let ((_let_6 (tptp.fun tptp.num _let_2))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) _let_7)))) (let ((_let_11 (tptp.fun _let_2 tptp.num))) (let ((_let_12 (tptp.s (tptp.fun _let_8 _let_11) tptp.nsum))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_) (tptp.s tptp.num (tptp.i _let_5 _let_4)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_a_) _let_7)) _let_1)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_10 _let_1)))) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 tptp.m_) _let_1)) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_4)))))))))) _let_3)))) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.t_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) _let_4)))) (let ((_let_7 (tptp.s _let_5 tptp.p_))) (let ((_let_8 (tptp.s _let_1 F0))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_8)) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_8 _let_6)))) (tptp.s tptp.num (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_7 _let_6)) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_))) (let ((_let_8 (tptp.fun _let_1 tptp.num))) (let ((_let_9 (tptp.s (tptp.fun _let_5 _let_8) tptp.nsum))) (let ((_let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_11 (tptp.s _let_1 tptp.numeral))) (let ((_let_12 (tptp.fun tptp.num _let_1))) (let ((_let_13 (tptp.s _let_1 (tptp.i (tptp.s _let_12 tptp.t_) (tptp.s tptp.num (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_10)))))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_13 _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_12 tptp.p_) (tptp.s tptp.num (tptp.i _let_13 _let_3)))) (tptp.s tptp.num (tptp.i _let_11 _let_10)))))))) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2))))))))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (N0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.fun A tptp.num))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.mod) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) _let_1)))))))))) (forall ((F0 $$unsorted) (N0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun A tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_2 tptp.num))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.nsum) _let_6)))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.mod))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_8 _let_3)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_8 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1)))))) _let_1))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (N0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun tptp.num _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_1)) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.mod) (tptp.s tptp.num (tptp.i _let_4 _let_2)))) _let_1))))))))) (forall ((F0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun _let_2 tptp.num))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.nsum) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) (tptp.s tptp.num A5))) (tptp.s tptp.num B0))))))) (let ((_let_9 (tptp.s _let_4 tptp.mod))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_9 (tptp.s tptp.num (tptp.i _let_8 _let_3)))) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_9 (tptp.s tptp.num (tptp.i _let_8 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1)))))) _let_1)))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.card))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))))))))) (forall ((T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (not (= _let_3 _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inter) _let_3)) _let_2)) (tptp.s _let_1 tptp.empty))))))))))))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.unions) _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.nsum) _let_5)) _let_3))))))))))) (forall ((Q70911 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real (tptp.fun tptp.real tptp.real)))) (let ((_let_2 (tptp.fun (tptp.fun Q70911 tptp.bool) (tptp.fun (tptp.fun Q70911 tptp.real) tptp.real)))) (= (tptp.s _let_2 tptp.sum) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.iterate) (tptp.s _let_1 tptp.realu_add))))))) (= (tptp.s tptp.real (tptp.i _let_70 _let_34)) _let_55) (= (tptp.s tptp.real (tptp.i _let_70 _let_31)) _let_53) (tptp.p (tptp.s tptp.bool (tptp.i _let_69 _let_34))) (tptp.p (tptp.s tptp.bool (tptp.i _let_69 _let_31))) (forall ((Q70953 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q70953 tptp.real))) (let ((_let_2 (tptp.fun Q70953 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.sum) (tptp.s _let_2 tptp.empty))) (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((Q70994 $$unsorted) (X $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q70994 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q70994 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))) (let ((_let_8 (tptp.s Q70994 X))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.fun _let_3 tptp.bool))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 tptp.finite) _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun Q70994 _let_12) tptp.insert) _let_8)) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q70994 _let_11) tptp.in) _let_8)) _let_4)))) _let_7)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.realu_add) (tptp.s tptp.real (tptp.i _let_2 _let_8)))) _let_7))))))))))))))))))) (forall ((Q71020 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q71020 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q71020 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s _let_3 S0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.s _let_10 tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.disjoint) _let_7)) _let_4)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.union) _let_7)) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))))) (forall ((Q71060 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q71060 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q71060 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s _let_3 S0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 tptp.finite) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.subset) _let_4)) _let_7)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.diff) _let_7)) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.s _let_3 S0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_1 tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_3 _let_8) tptp.sum))) (let ((_let_10 (tptp.fun tptp.real tptp.real))) (let ((_let_11 (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_add))) (let ((_let_12 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_12 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_12 _let_4)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.union) _let_5)) _let_4)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.inter) _let_5)) _let_4)))) _let_2))))))))))))))))))) (forall ((Q71149 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71149 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q71149 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.fun tptp.real (tptp.fun tptp.real tptp.real)))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.support) (tptp.s _let_7 tptp.realu_add))) _let_2)) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))) (forall ((Q71183 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q71183 X))) (let ((_let_2 (tptp.fun Q71183 tptp.real))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_4)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71183 tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun Q71183 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)))) (let ((_let_7 (tptp.s _let_1 F0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) U_0) _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_6 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 _let_2)))))))))))))))))) (forall ((Q71274 $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q71274 X))) (let ((_let_2 (tptp.fun Q71274 tptp.real))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_1) _let_4)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_174 $$unsorted)) (let ((_let_1 (tptp.fun Q71274 tptp.real))) (let ((_let_2 (tptp.fun Q71274 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s Q71274 GENR_PVARR_174)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q71274 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q71274 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q71274 _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (not (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q71274 tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q71274 _let_4) tptp.setspec) (tptp.s Q71274 GENR_PVARR_174))) _let_2)) _let_1))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71274 tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun Q71274 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)))) (let ((_let_7 (tptp.s _let_1 F0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_1 _let_3))) (let ((_let_11 (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_4)))) (let ((_let_12 (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec))) (let ((_let_13 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_13 (tptp.s _let_3 (tptp.i _let_12 (tptp.s _let_3 (tptp.i _let_11 _let_7))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_13 (tptp.s _let_3 (tptp.i _let_12 (tptp.s _let_3 (tptp.i _let_11 _let_2)))))))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) U_1) _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_6 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 _let_2)))))))))))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.sum) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((N0 $$unsorted)) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) U_0) (tptp.s A N0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.sum) (tptp.s _let_2 S0))) (tptp.s _let_1 U_0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.real C0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) U_0) _let_4)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) _let_4)) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))) (forall ((F0 $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.sum) (tptp.s _let_3 S0))))) (let ((_let_6 (tptp.s tptp.real C0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) U_0) _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_6)) (tptp.s tptp.real (tptp.i _let_5 _let_2)))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.real C0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.real))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_1)))))))))) (forall ((F0 $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real C0))) (let ((_let_2 (tptp.fun A tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.sum) (tptp.s _let_4 S0))))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_2))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_0) _let_3)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_6 _let_3)))) _let_1)))))))))))))) (forall ((Q71474 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q71474 X))) (let ((_let_2 (tptp.fun Q71474 tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71474 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q71474 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.sum) (tptp.s _let_3 S0))))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i _let_5 _let_2))))))))))))) (forall ((Q71509 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q71509 X))) (let ((_let_2 (tptp.fun Q71509 tptp.real))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_4)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71509 tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun Q71509 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)))) (let ((_let_7 (tptp.s _let_1 F0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) U_0) _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_6 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 _let_2)))))))))))))))))) (forall ((Q71551 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71551 tptp.real))) (let ((_let_2 (tptp.fun Q71551 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q71551 X))) (let ((_let_2 (tptp.fun Q71551 tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun Q71551 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q71551 _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 F0))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 G0)))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 G0) _let_1)))))))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 F0))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 G0)))))))))))))) (forall ((Q71673 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71673 tptp.real))) (let ((_let_2 (tptp.fun Q71673 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (not (= _let_3 (tptp.s _let_2 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q71673 X))) (let ((_let_2 (tptp.fun Q71673 tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun Q71673 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q71673 _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 F0))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 G0)))))))))))))) (forall ((Q71711 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71711 tptp.real))) (let ((_let_2 (tptp.fun Q71711 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.sum) (tptp.s _let_2 S0))))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q71711 X))) (let ((_let_2 (tptp.fun Q71711 tptp.real))) (let ((_let_3 (tptp.fun Q71711 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q71711 _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 G0) _let_1))))))))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s _let_1 G0)))))))))) (forall ((Q71770 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q71770 X))) (let ((_let_2 (tptp.fun Q71770 tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71770 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q71770 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i _let_6 _let_2)))))) (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)))))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 F0))))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 G0)))))))))))))) (forall ((Q71846 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real C0))) (let ((_let_2 (tptp.fun Q71846 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) _let_1)) (tptp.s Q71846 N0))) _let_1)))) (forall ((C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real C0))) (let ((_let_2 (tptp.fun Q71846 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun Q71846 tptp.real))) (let ((_let_6 (tptp.fun _let_5 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.sum) _let_3)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) U_0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)))))) _let_1))))))))))))) (forall ((Q71888 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q71888 tptp.real))) (let ((_let_2 (tptp.fun Q71888 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q71888 X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun Q71888 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q71888 _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q71888 tptp.real) F0) _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 F0))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (B0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 F0))))) (tptp.s tptp.real B0))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)))) (tptp.s tptp.real B0))))))))))))))))) (forall ((Q72035 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q72035 tptp.real))) (let ((_let_2 (tptp.fun Q72035 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q72035 X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun Q72035 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q72035 _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q72035 tptp.real) F0) _let_1))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q72035 X))) (let ((_let_2 (tptp.fun Q72035 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q72035 _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q72035 tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((A $$unsorted) (U $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 U))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (or (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) U) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (exists ((J0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s A K0))) (let ((_let_3 (tptp.s (tptp.fun A tptp.real) U))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun A _let_8) tptp.in))) (let ((_let_10 (tptp.s A J0))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_10)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_3 _let_10)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_gt) (tptp.s tptp.real (tptp.i _let_3 _let_2)))) _let_1)))))))))))))))))))))) (forall ((Q72277 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q72277 A5))) (let ((_let_2 (tptp.fun Q72277 tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q72277 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 tptp.real))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.sum))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun Q72277 _let_4))) (let ((_let_10 (tptp.fun _let_4 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q72277 _let_10) tptp.in) _let_1)) _let_5)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.delete) _let_5)) _let_1)))) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))))))))) (forall ((Q72330 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun Q72330 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q72330 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))) (let ((_let_8 (tptp.s Q72330 A5))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.fun _let_3 tptp.bool))) (let ((_let_12 (tptp.fun Q72330 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 tptp.finite) _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.delete) _let_4)) _let_8)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q72330 _let_11) tptp.in) _let_8)) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.realu_sub) _let_7)) (tptp.s tptp.real (tptp.i _let_2 _let_8)))))) _let_7))))))))))))))))) (forall ((Q72353 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q72353 X))) (let ((_let_2 (tptp.fun Q72353 tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q72353 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.fun _let_2 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.sum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q72353 _let_5) tptp.insert) _let_1)) (tptp.s _let_4 tptp.empty))))) _let_3)) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.s A A5))) (let ((_let_6 (tptp.fun A tptp.real))) (and (= (tptp.p _let_1) (= _let_4 _let_5)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) U_0) _let_5)) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) _let_1)) (tptp.s tptp.real tptp.b0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.fun A tptp.real))) (let ((_let_8 (tptp.fun _let_7 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.sum) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) U_0) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_3)) _let_2)))) (tptp.s tptp.real tptp.b0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_2 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.fun B tptp.real))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.real))) (let ((_let_7 (tptp.fun B _let_6))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_2) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.fun B tptp.real))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.real))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (let ((_let_10 (tptp.fun _let_3 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) U_1) _let_8)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_2) _let_4)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.real))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.s _let_5 T0))) (let ((_let_7 (tptp.fun _let_2 tptp.real))) (let ((_let_8 (tptp.fun A tptp.real))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_0) _let_6)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.sum) _let_6)) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.real))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun B tptp.bool))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (let ((_let_10 (tptp.fun A tptp.real))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun _let_10 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.sum) _let_5)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) U_0) _let_8)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3))))))))))))))))))))))))) (forall ((Q72493 $$unsorted) (Q72469 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q72493 Q72469))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q72469 tptp.real))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun Q72493 tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun Q72493 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (let ((_let_10 (tptp.fun Q72469 tptp.bool))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (let ((_let_12 (tptp.fun _let_3 tptp.real))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q72493 Y))) (let ((_let_2 (tptp.s Q72493 X))) (let ((_let_3 (tptp.s (tptp.fun Q72493 Q72469) F0))) (let ((_let_4 (tptp.fun Q72493 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q72493 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q72469 (tptp.i _let_3 _let_2)) (tptp.s Q72469 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.sum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.image) _let_2)) _let_8)))) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.o) _let_4)) _let_2))))))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s _let_3 V))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.subset) _let_4)) _let_7))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 V)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 U)))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 V)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 U)))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.union) _let_4)) (tptp.s _let_3 V))))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 V))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 U)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 V)))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.union) (tptp.s _let_3 U))) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))) (forall ((Q72690 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q72690 X))) (let ((_let_2 (tptp.fun Q72690 tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q72690 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) U_0) _let_5)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q72690 _let_6) tptp.in) _let_1)) _let_5)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q72690 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q72690 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i _let_6 _let_2)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun A tptp.real))) (let ((_let_5 (tptp.fun _let_4 tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)))) (tptp.s tptp.real B0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.sum) _let_2)) (tptp.s _let_4 F0))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))) (tptp.s tptp.real B0)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (not (= _let_3 (tptp.s _let_2 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_div) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 F0))))) (tptp.s tptp.real B0))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun A tptp.real))) (let ((_let_5 (tptp.fun _let_4 tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)))))) (tptp.s tptp.real B0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.sum) _let_2)) (tptp.s _let_4 F0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))) (tptp.s tptp.real B0)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun A tptp.real))) (let ((_let_5 (tptp.fun _let_4 tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)))) (tptp.s tptp.real B0)))))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)))) (tptp.s tptp.real B0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.sum) _let_2)) (tptp.s _let_4 F0))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))) (tptp.s tptp.real B0)))))))))))))) (forall ((Q72954 $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun Q72954 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun Q72954 tptp.real))) (let ((_let_5 (tptp.fun _let_4 tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q72954 X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun Q72954 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q72954 _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q72954 tptp.real) F0) _let_1)))) (tptp.s tptp.real B0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.sum) _let_2)) (tptp.s _let_4 F0))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))) (tptp.s tptp.real B0)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (not (= _let_3 (tptp.s _let_2 tptp.empty))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s A X))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_div) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 F0))))) (tptp.s tptp.real B0))))))))))) (forall ((Q73037 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun Q73037 tptp.real))) (let ((_let_2 (tptp.s _let_1 tptp.f))) (let ((_let_3 (tptp.fun Q73037 tptp.bool))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s _let_3 T0))) (let ((_let_8 (tptp.s _let_3 S0))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.inter) _let_8)) _let_7)) (tptp.s _let_3 tptp.empty)) (= (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.union) _let_8)) _let_7)) _let_4)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_8)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.sum))) (let ((_let_6 (tptp.s _let_2 S0))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.subset) _let_3)) _let_6))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.real))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.g) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 S0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 T0)))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_1 tptp.g))))))))))))) (forall ((Q73206 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q73206 X))) (let ((_let_2 (tptp.fun Q73206 tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q73206 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) _let_5)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_176 $$unsorted)) (let ((_let_1 (tptp.fun Q73206 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s Q73206 GENR_PVARR_176)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q73206 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q73206 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q73206 _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q73206 _let_4) tptp.setspec) (tptp.s Q73206 GENR_PVARR_176))) _let_2)) _let_1)))))))))))))) (forall ((P0 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q73206 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q73206 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_3 S0))) (let ((_let_7 (tptp.fun _let_1 tptp.real))) (let ((_let_8 (tptp.s (tptp.fun _let_3 _let_7) tptp.sum))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_9 tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) U_0) _let_6)) _let_4)))))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) _let_4)) _let_2))))))))))))))))))) (forall ((Q73298 $$unsorted) (Q73297 $$unsorted) (U_5 $$unsorted)) (=> (forall ((F0 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q73297 Y))) (let ((_let_2 (tptp.s Q73298 X))) (let ((_let_3 (tptp.fun Q73297 tptp.real))) (let ((_let_4 (tptp.fun Q73298 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q73298 tptp.real))) (let ((_let_7 (tptp.fun Q73297 _let_6))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_5) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((S0 $$unsorted) (R0 $$unsorted) (Y $$unsorted) (GENR_PVARR_178 $$unsorted)) (let ((_let_1 (tptp.fun Q73298 (tptp.fun Q73297 tptp.bool)))) (let ((_let_2 (tptp.fun Q73298 tptp.bool))) (let ((_let_3 (tptp.fun Q73297 _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_4) (tptp.s _let_2 S0))) (tptp.s _let_1 R0))) (tptp.s Q73297 Y))) (tptp.s Q73298 GENR_PVARR_178)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q73298 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q73298 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun Q73297 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q73298 _let_6) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q73298 _let_5) R0) _let_1)) (tptp.s Q73297 Y)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q73298 _let_4) tptp.setspec) (tptp.s Q73298 GENR_PVARR_178))) _let_2)) _let_1))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((S0 $$unsorted) (R0 $$unsorted) (F0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q73297 Y))) (let ((_let_2 (tptp.fun Q73297 tptp.real))) (let ((_let_3 (tptp.fun Q73298 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q73298 tptp.real))) (let ((_let_6 (tptp.fun Q73297 _let_5))) (let ((_let_7 (tptp.fun Q73298 (tptp.fun Q73297 tptp.bool)))) (let ((_let_8 (tptp.s _let_7 R0))) (let ((_let_9 (tptp.fun Q73298 tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun Q73297 _let_9))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun _let_5 tptp.real))) (let ((_let_14 (tptp.fun _let_3 _let_2))) (let ((_let_15 (tptp.fun _let_7 _let_14))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_9 _let_15) U_3) _let_10)) _let_8)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_9 _let_13) tptp.sum) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_9 _let_9) tptp.gspec) (tptp.s _let_9 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) U_4) _let_10)) _let_8)) _let_1)))))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_5) _let_4)) _let_1))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q73297 Y))) (let ((_let_2 (tptp.s Q73298 X))) (let ((_let_3 (tptp.fun Q73297 tptp.real))) (let ((_let_4 (tptp.fun Q73298 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) U_2) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (X $$unsorted) (GENR_PVARR_177 $$unsorted)) (let ((_let_1 (tptp.fun Q73297 tptp.bool))) (let ((_let_2 (tptp.fun Q73298 _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_1) (tptp.s _let_1 T0))) (tptp.s _let_2 R0))) (tptp.s Q73298 X))) (tptp.s Q73297 GENR_PVARR_177)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q73297 Y))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q73297 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q73297 _let_5) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q73298 _let_3) R0) (tptp.s Q73298 X))) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q73297 _let_4) tptp.setspec) (tptp.s Q73297 GENR_PVARR_177))) _let_2)) _let_1))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q73298 X))) (let ((_let_2 (tptp.fun Q73297 tptp.real))) (let ((_let_3 (tptp.fun Q73298 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q73297 tptp.bool))) (let ((_let_6 (tptp.fun Q73298 _let_5))) (let ((_let_7 (tptp.s _let_6 R0))) (let ((_let_8 (tptp.s _let_5 T0))) (let ((_let_9 (tptp.fun _let_6 _let_6))) (let ((_let_10 (tptp.fun _let_2 tptp.real))) (let ((_let_11 (tptp.fun Q73298 tptp.real))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun _let_6 _let_12))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_5 _let_13) U_0) _let_8)) _let_7)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.sum) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_1) _let_8)) _let_7)) _let_1)))))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_2) _let_4)) _let_1))))))))))))))))))) (forall ((R0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q73297 tptp.real))) (let ((_let_2 (tptp.fun Q73298 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q73297 tptp.bool))) (let ((_let_5 (tptp.fun Q73298 _let_4))) (let ((_let_6 (tptp.s _let_5 R0))) (let ((_let_7 (tptp.fun Q73298 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.s _let_4 T0))) (let ((_let_12 (tptp.fun _let_1 tptp.real))) (let ((_let_13 (tptp.fun Q73298 tptp.real))) (let ((_let_14 (tptp.fun _let_2 _let_13))) (let ((_let_15 (tptp.fun _let_5 _let_14))) (let ((_let_16 (tptp.fun _let_13 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_11)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_7 _let_16) tptp.sum) _let_8)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_4 _let_15) U_0) _let_11)) _let_6)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.sum) _let_11)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) U_3) _let_8)) _let_6)) _let_3))))))))))))))))))))))))))))))))))) (forall ((Q73319 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q73319 tptp.real) U_0) (tptp.s Q73319 X))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q73319 tptp.real))) (let ((_let_2 (tptp.fun Q73319 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 U_0)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_3 $$unsorted)) (=> (forall ((K0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s B I0))) (let ((_let_2 (tptp.fun B tptp.num))) (let ((_let_3 (tptp.s _let_2 K0))) (let ((_let_4 (tptp.fun B tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_3) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (I0 $$unsorted) (GENR_PVARR_181 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_2) (tptp.s _let_1 T0))) (tptp.s _let_2 R0))) (tptp.s A I0))) (tptp.s B GENR_PVARR_181)))) (exists ((J0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) R0) (tptp.s A I0))) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.setspec) (tptp.s B GENR_PVARR_181))) _let_2)) _let_1))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 R0))) (let ((_let_5 (tptp.s _let_2 T0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun A tptp.real))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_1) _let_5)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_2) _let_5)) _let_4)) _let_1)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (R0 $$unsorted) (J0 $$unsorted) (GENR_PVARR_180 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 R0))) (tptp.s B J0))) (tptp.s A GENR_PVARR_180)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) R0) _let_1)) (tptp.s B J0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_180))) _let_2)) _let_1))))))))))))))))) (forall ((R0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.num))) (let ((_let_2 (tptp.fun B tptp.real))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_2 tptp.real))) (let ((_let_6 (tptp.fun A _let_3))) (let ((_let_7 (tptp.fun A tptp.real))) (let ((_let_8 (tptp.fun _let_6 _let_7))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun _let_7 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_9 tptp.bool) tptp.finite) _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun B _let_7) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 S0))) (tptp.s _let_3 R0))) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun B tptp.num) K0) _let_1))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.sum) _let_10)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_1) _let_4)) (tptp.s _let_6 R0))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_3) (tptp.s _let_1 K0))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_2 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (I0 $$unsorted) (GENR_PVARR_183 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_2) (tptp.s _let_1 T0))) (tptp.s _let_2 R0))) (tptp.s A I0))) (tptp.s B GENR_PVARR_183)))) (exists ((J0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) R0) (tptp.s A I0))) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.setspec) (tptp.s B GENR_PVARR_183))) _let_2)) _let_1))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (R0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 R0))) (let ((_let_5 (tptp.s _let_2 T0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun A tptp.real))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_1) _let_5)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_2) _let_5)) _let_4)) _let_1)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (R0 $$unsorted) (J0 $$unsorted) (GENR_PVARR_182 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 R0))) (tptp.s B J0))) (tptp.s A GENR_PVARR_182)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) R0) _let_1)) (tptp.s B J0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_182))) _let_2)) _let_1))))))))))))))))) (forall ((R0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun A _let_1))) (let ((_let_5 (tptp.fun A tptp.real))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun B _let_7) tptp.in) _let_1)) (tptp.s _let_2 T0)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.card) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 S0))) (tptp.s _let_3 R0))) _let_1)))))) (tptp.s tptp.num K0)))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_1) _let_2)) (tptp.s _let_4 R0))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.t_) (tptp.s tptp.num K0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (Y $$unsorted) (GENR_PVARR_186 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_1) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B Y))) (tptp.s A GENR_PVARR_186)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_186))) _let_2)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun B _let_6))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_1 tptp.real))) (let ((_let_11 (tptp.fun B tptp.real))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) U_0) _let_7)) _let_5)) _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.sum) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_1) _let_7)) _let_5)) _let_3)))))) _let_2))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun B tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun B tptp.bool))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_7 tptp.real))) (let ((_let_13 (tptp.fun _let_1 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_5 _let_13) tptp.sum) _let_6)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.sum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.image) _let_4)) _let_6)))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_0) _let_6)) _let_4)) _let_2)))))))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (Y $$unsorted) (GENR_PVARR_187 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_1) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B Y))) (tptp.s A GENR_PVARR_187)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_187))) _let_2)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun B _let_6))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_1 tptp.real))) (let ((_let_11 (tptp.fun B tptp.real))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) U_0) _let_7)) _let_5)) _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.sum) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_1) _let_7)) _let_5)) _let_3)))))) _let_2))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.fun A B))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun B tptp.real))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (let ((_let_11 (tptp.fun B tptp.bool))) (let ((_let_12 (tptp.s _let_11 T0))) (let ((_let_13 (tptp.fun _let_8 tptp.real))) (let ((_let_14 (tptp.fun _let_3 _let_11))) (let ((_let_15 (tptp.fun _let_11 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_11 _let_15) tptp.subset) (tptp.s _let_11 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_6 _let_14) tptp.image) _let_7)) _let_4)))) _let_12)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) _let_12)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_4)) _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)) _let_2)))))))))))))))))))))))) (forall ((Q73784 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q73784 X))) (let ((_let_2 (tptp.fun Q73784 tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q73784 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q73784 tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q73784 tptp.real))) (let ((_let_4 (tptp.fun Q73784 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_3 tptp.real))) (let ((_let_7 (tptp.fun _let_1 tptp.num))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.nsum) _let_5)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.sum) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))))))) (forall ((A $$unsorted) (U $$unsorted) (V $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 V))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s _let_3 U))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.diff) (tptp.s _let_3 U))) (tptp.s _let_3 V)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.diff) (tptp.s _let_3 V))) (tptp.s _let_3 U)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))) (forall ((A $$unsorted) (U $$unsorted) (V $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 V))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s _let_3 U))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.subset) _let_7)) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.diff) (tptp.s _let_3 V))) (tptp.s _let_3 U)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (D0 $$unsorted) (I0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 I0))) (let ((_let_3 (tptp.fun B tptp.real))) (let ((_let_4 (tptp.s _let_3 D0))) (let ((_let_5 (tptp.fun A tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (let ((_let_10 (tptp.fun B tptp.bool))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (let ((_let_12 (tptp.fun _let_3 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s (tptp.fun A B) I0))) (let ((_let_3 (tptp.s B (tptp.i _let_2 _let_1)))) (let ((_let_4 (tptp.s A Y))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_6))) (not (= _let_1 _let_4)) (= _let_3 (tptp.s B (tptp.i _let_2 _let_4)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun B tptp.real) D0) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.sum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.image) _let_2)) _let_8)))) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.o) _let_4)) _let_2))))))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A A))) (let ((_let_2 (tptp.fun A tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_2 tptp.real))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.sum) (tptp.s _let_5 S0))))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_3)))) _let_2)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A Y))) (tptp.s _let_1 S0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_1)) (tptp.s A Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s A Y))) (let ((_let_4 (tptp.s (tptp.fun A A) P0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s A (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s A (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))) (= (tptp.s tptp.real (tptp.i _let_7 _let_3)) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.o) _let_3)) (tptp.s _let_1 P0))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_2 $$unsorted)) (=> (forall ((X $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) tptp.real))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.real)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_2) (tptp.s _let_2 X))) (tptp.s _let_1 F0)))) (forall ((I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.fun B tptp.real))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.geq) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) X) _let_2)) _let_1))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_188 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_188)))) (exists ((I0 $$unsorted) (J0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.in) _let_1)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) T0) _let_2))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_188))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.real))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun A _let_5))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun _let_2 tptp.real))) (let ((_let_9 (tptp.fun A tptp.real))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.sum) (tptp.s _let_5 (tptp.i _let_7 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B tptp.real)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun _let_3 tptp.real))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (let ((_let_12 (tptp.fun _let_4 tptp.real))) (let ((_let_13 (tptp.fun A tptp.real))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (let ((_let_15 (tptp.fun _let_13 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_8 _let_15) tptp.sum) _let_9)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_6 _let_14) U_0) _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.sum) (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_10 _let_10) tptp.gspec) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) U_1) _let_9)) _let_7)))))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_2) _let_2)))))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.real))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun A tptp.real))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_4 tptp.real))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 T0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)) (tptp.s B Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.s (tptp.fun A B) H0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun B tptp.real) G0) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.sum) (tptp.s _let_5 S0))) (tptp.s _let_4 F0))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.sum) (tptp.s _let_2 T0))) (tptp.s _let_1 G0)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.real))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun A tptp.real))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_4 tptp.real))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) K0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_2)) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) K0) _let_2)) _let_1) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun B tptp.real) G0) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.sum) (tptp.s _let_5 S0))) (tptp.s _let_4 F0))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.sum) (tptp.s _let_2 T0))) (tptp.s _let_1 G0)))))))))))) (forall ((Q74430 $$unsorted) (F0 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q74430 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q74430 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)))) (let ((_let_7 (tptp.fun Q74430 Q74430))) (let ((_let_8 (tptp.fun _let_7 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q74430 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s Q74430 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun Q74430 _let_4) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s Q74430 (tptp.i (tptp.s (tptp.fun Q74430 Q74430) P0) _let_3)))) _let_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q74430 Y))) (let ((_let_2 (tptp.s Q74430 X))) (let ((_let_3 (tptp.s (tptp.fun Q74430 Q74430) P0))) (let ((_let_4 (tptp.fun Q74430 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q74430 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q74430 (tptp.i _let_3 _let_2)) (tptp.s Q74430 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.o) _let_2)) (tptp.s _let_7 P0))))) (tptp.s tptp.real (tptp.i _let_6 _let_2))))))))))))) (forall ((Q74473 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q74473 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun Q74473 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.sum))) (let ((_let_7 (tptp.s _let_3 S0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (let ((_let_10 (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q74473 X))) (let ((_let_2 (tptp.fun Q74473 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q74473 _let_4) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.inter) (tptp.s _let_2 S0))) (tptp.s _let_2 T0)))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q74473 tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.union) _let_7)) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.fun _let_3 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_2)) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) _let_4)) _let_2)))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.real))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_4 tptp.real))) (let ((_let_8 (tptp.fun _let_1 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))))))))) (forall ((T1 $$unsorted) (T2 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 T2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)))) (let ((_let_6 (tptp.s _let_2 T1))) (let ((_let_7 (tptp.s _let_4 S0))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_2 _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_7))) (not (= _let_6 _let_3)) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.sum) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_5 _let_3) tptp.unions) _let_6)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.sum) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2))))))))))))))))) (forall ((A $$unsorted) (U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_2) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_189 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s A GENR_PVARR_189)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_189))) _let_2)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.real))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_0) _let_6)) _let_4)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i _let_6 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))))))) (forall ((S0 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (let ((_let_6 (tptp.s _let_3 S0))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) _let_6)))) (let ((_let_8 (tptp.s _let_5 tptp.gspec))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (let ((_let_10 (tptp.s (tptp.fun _let_3 _let_9) tptp.sum))) (let ((_let_11 (tptp.s _let_1 F0))) (let ((_let_12 (tptp.fun tptp.real tptp.real))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_6))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_6)) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_3 _let_14) U_0) _let_4)) _let_11)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.real _let_12) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_3 (tptp.i _let_8 (tptp.s _let_3 (tptp.i _let_7 _let_4)))))) _let_11)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_3 (tptp.i _let_8 (tptp.s _let_3 (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_2) _let_4)))))))) _let_2))))))))))))))))))))))))))) (forall ((Q74742 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s Q74742 X))) (let ((_let_2 (tptp.fun Q74742 tptp.real))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s Q74742 A5))) (and (= (tptp.p _let_3) (= _let_1 _let_6)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q74742 _let_2) U_0) _let_6)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) _let_3)) (tptp.s tptp.real tptp.y))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.f) _let_1)))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q74742 A5))) (let ((_let_2 (tptp.fun Q74742 tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.f))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun Q74742 tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_2 tptp.real))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.sum) _let_7)))) (let ((_let_10 (tptp.fun _let_6 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 tptp.finite) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun Q74742 _let_10) tptp.in) _let_1)) _let_7)))) (= (tptp.s tptp.real (tptp.i _let_9 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q74742 _let_2) U_0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_add) (tptp.s tptp.real (tptp.i _let_9 _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_sub) (tptp.s tptp.real tptp.y))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.real))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun A tptp.real))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_5 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.finite) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_1)) (tptp.s _let_3 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun B tptp.real) G0) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 S0)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) _let_1)) (tptp.s _let_4 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) I0) _let_1)) _let_2) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun B tptp.real) G0) _let_1))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.sum) _let_7)) (tptp.s _let_5 F0))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 G0))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun B tptp.real))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun A tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (let ((_let_10 (tptp.fun B tptp.bool))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (let ((_let_12 (tptp.fun _let_3 tptp.real))) (let ((_let_13 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun B tptp.real) G0) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.real _let_13) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.sum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.image) _let_2)) _let_8)))) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.o) _let_4)) _let_2)))))))))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) _let_2)) _let_1))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) P0) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.sum) (tptp.s _let_2 S0))) (tptp.s _let_1 F0)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_4)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (let ((_let_7 (tptp.s _let_1 F0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) U_0) _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_6 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 _let_2))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_4)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (let ((_let_7 (tptp.s _let_1 F0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) U_0) _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_6 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 _let_2))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s tptp.num N0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 G0) _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 F0))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 G0)))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_1)) (tptp.s tptp.num N0))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 G0) _let_1))))))))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 G0))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i _let_6 _let_2)))))) (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real C0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) _let_1)) (tptp.s tptp.num N0))) _let_1)))) (forall ((C0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real C0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num _let_3))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun _let_6 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.sum) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) _let_2)) _let_4)))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) U_0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.p_) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)))))) _let_1)))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num N0))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_1 F0) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_1 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))) (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i (tptp.s _let_1 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.l_) _let_2)) _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.sum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) _let_3)) _let_2)))) (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i (tptp.s _let_1 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s tptp.num N0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_1 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))) (tptp.s _let_1 F0))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (=> (and (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s tptp.num N0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 F0) _let_1)))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))) (tptp.s _let_1 F0))) (tptp.s tptp.real (tptp.i (tptp.s _let_1 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s tptp.num P0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num M0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num N0))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_1 F0) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_1 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))) (forall ((F0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_2 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.sum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) _let_1)) _let_1)))) _let_3)) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))) (forall ((M0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.f))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun _let_2 tptp.real))) (and (= (tptp.p _let_4) (= _let_7 _let_1)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.sum) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) _let_7)) _let_1)))) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_4)) (tptp.s tptp.real (tptp.i _let_3 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_1)))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 tptp.f))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) _let_4)))) (let ((_let_8 (tptp.fun _let_1 tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_5 _let_8) tptp.sum))) (let ((_let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i _let_7 _let_3)))) _let_2)))) (let ((_let_11 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_3)))) (let ((_let_12 (tptp.fun tptp.real tptp.real))) (let ((_let_13 (tptp.fun tptp.real _let_12))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i _let_7 _let_11)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.bool _let_13) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_) _let_4)) _let_11)))) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.realu_add) _let_10)) (tptp.s tptp.real (tptp.i _let_2 _let_11)))))) _let_10))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) U_2) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_1) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_2) _let_4)) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (D0 $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.s tptp.num D0))) (let ((_let_6 (tptp.s tptp.num C0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun _let_2 tptp.real))) (let ((_let_10 (tptp.fun _let_3 _let_2))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) U_0) _let_6)) _let_5)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.o_o_) _let_6)) _let_5)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num B0))) (let ((_let_5 (tptp.s tptp.num A5))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) U_0))) (let ((_let_9 (tptp.s tptp.num D0))) (let ((_let_10 (tptp.s tptp.num C0))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_))) (let ((_let_14 (tptp.fun _let_1 tptp.real))) (let ((_let_15 (tptp.s (tptp.fun _let_11 _let_14) tptp.sum))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i _let_15 (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_5)) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_10)) _let_9)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i _let_15 (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_10)) _let_9)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_1) _let_3))))))))))))))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.p_) _let_3)))) (let ((_let_6 (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num P0))))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_))) (let ((_let_11 (tptp.fun _let_1 tptp.real))) (let ((_let_12 (tptp.s (tptp.fun _let_8 _let_11) tptp.sum))) (let ((_let_13 (tptp.s tptp.num M0))) (let ((_let_14 (tptp.s _let_9 (tptp.i _let_10 _let_13)))) (let ((_let_15 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_a_) _let_13)) _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_14 _let_6)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun tptp.real _let_15) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_14 _let_3)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_7)) _let_6)))) _let_2)))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (P0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1)))))))))))) (forall ((P0 $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.o_o_))) (let ((_let_10 (tptp.fun _let_2 tptp.real))) (let ((_let_11 (tptp.s (tptp.fun _let_7 _let_10) tptp.sum))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (let ((_let_13 (tptp.s (tptp.fun tptp.num _let_12) tptp.p_))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_6)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_5)) _let_1)))))) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_5)))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (M0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1)))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num _let_2))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.o_o_))) (let ((_let_10 (tptp.fun _let_2 tptp.real))) (let ((_let_11 (tptp.s (tptp.fun _let_7 _let_10) tptp.sum))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.l_a_) _let_1)) _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) _let_5)))) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.m_) _let_5)) _let_1)))))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1)))))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (let ((_let_10 (tptp.s (tptp.fun _let_6 _let_9) tptp.sum))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_a_) _let_5)) _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_2 _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.p_) _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_3)))) _let_2)))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num tptp.u_0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 tptp.numeral))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) _let_7)))) (let ((_let_11 (tptp.fun _let_2 tptp.real))) (let ((_let_12 (tptp.s (tptp.fun _let_8 _let_11) tptp.sum))) (let ((_let_13 (tptp.fun tptp.real tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_) (tptp.s tptp.num (tptp.i _let_6 _let_4)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_a_) _let_7)) _let_1)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_10 _let_1)))) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.real _let_13) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.m_) _let_1)) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_4)))))))))) _let_3)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.t_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) _let_4)))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) U_0) _let_8)) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_8 _let_6)))) (tptp.s tptp.real (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.p_) _let_6)) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_))) (let ((_let_8 (tptp.fun _let_1 tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_5 _let_8) tptp.sum))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_12 (tptp.s _let_10 tptp.numeral))) (let ((_let_13 (tptp.fun tptp.num _let_10))) (let ((_let_14 (tptp.s _let_10 (tptp.i (tptp.s _let_13 tptp.t_) (tptp.s tptp.num (tptp.i _let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit0) _let_11)))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_14 _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_13 tptp.p_) (tptp.s tptp.num (tptp.i _let_14 _let_3)))) (tptp.s tptp.num (tptp.i _let_12 _let_11)))))))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))) (let ((_let_7 (tptp.fun _let_3 tptp.real))) (let ((_let_8 (tptp.fun _let_1 tptp.num))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.nsum) _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.sum) _let_6)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 G0))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_1) _let_4)) _let_2)) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s _let_2 F0))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_0) _let_7)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_7 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s _let_4 G0))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.s (tptp.fun _let_4 _let_7) U_0))) (let ((_let_9 (tptp.s tptp.num N0))) (let ((_let_10 (tptp.s tptp.num M0))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_4 tptp.real))) (let ((_let_14 (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) _let_10)) _let_9)))))) (let ((_let_15 (tptp.fun tptp.real tptp.real))) (let ((_let_16 (tptp.fun tptp.real _let_15))) (let ((_let_17 (tptp.s _let_16 tptp.realu_mul))) (let ((_let_18 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_9)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_19 (tptp.s _let_16 tptp.realu_sub))) (= (tptp.s tptp.real (tptp.i _let_14 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun tptp.bool _let_16) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.l_a_) _let_10)) _let_9)))) (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i _let_19 (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i _let_19 (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i _let_17 (tptp.s tptp.real (tptp.i _let_5 _let_18)))) (tptp.s tptp.real (tptp.i _let_6 _let_18)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i _let_17 (tptp.s tptp.real (tptp.i _let_5 _let_10)))) (tptp.s tptp.real (tptp.i _let_6 _let_10)))))))) (tptp.s tptp.real (tptp.i _let_14 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_7 U_1) _let_6)))) _let_5)))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((G0 $$unsorted) (F0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s _let_2 G0))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_1) _let_7)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_7 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s _let_3 F0))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_0) _let_7)) _let_4)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_7 _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s _let_4 G0))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.s tptp.num N0))) (let ((_let_10 (tptp.s tptp.num M0))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_4 tptp.real))) (let ((_let_14 (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) _let_10)) _let_9)))))) (let ((_let_15 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (let ((_let_16 (tptp.fun tptp.num _let_2))) (let ((_let_17 (tptp.fun tptp.real tptp.real))) (let ((_let_18 (tptp.fun tptp.real _let_17))) (let ((_let_19 (tptp.s _let_18 tptp.realu_mul))) (let ((_let_20 (tptp.s _let_18 tptp.realu_sub))) (= (tptp.s tptp.real (tptp.i _let_14 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_0) _let_5)) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun tptp.bool _let_18) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.l_a_) _let_10)) _let_9)))) (tptp.s tptp.real (tptp.i (tptp.s _let_17 (tptp.i _let_20 (tptp.s tptp.real (tptp.i (tptp.s _let_17 (tptp.i _let_20 (tptp.s tptp.real (tptp.i (tptp.s _let_17 (tptp.i _let_19 (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_16 tptp.p_) _let_9)) _let_15)))))) (tptp.s tptp.real (tptp.i _let_6 _let_9)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_17 (tptp.i _let_19 (tptp.s tptp.real (tptp.i _let_5 _let_10)))) (tptp.s tptp.real (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_16 tptp.m_) _let_10)) _let_15)))))))))) (tptp.s tptp.real (tptp.i _let_14 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_1) _let_6)) _let_5)))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.f))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 U_0) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.s _let_4 tptp.f))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.real _let_8))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (let ((_let_12 (tptp.fun _let_4 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.sum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.o_o_) _let_7)) _let_5)))) (tptp.s _let_4 U_0))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.l_a_) _let_7)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_6 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_5)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.f))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 U_0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.s _let_4 tptp.f))) (let ((_let_7 (tptp.s tptp.num N0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.real _let_8))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (let ((_let_12 (tptp.fun _let_4 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.sum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.o_o_) _let_5)) _let_7)))) (tptp.s _let_4 U_0))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.l_a_) _let_5)) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_7)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))) (tptp.s tptp.real (tptp.i _let_6 _let_5)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s tptp.num P0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_))) (let ((_let_8 (tptp.s _let_6 (tptp.i _let_7 _let_4)))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (let ((_let_10 (tptp.s (tptp.fun _let_5 _let_9) tptp.sum))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (let ((_let_12 (tptp.s tptp.num N0))) (let ((_let_13 (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.p_) _let_12)) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_14 (tptp.fun tptp.real tptp.real))) (let ((_let_15 (tptp.s _let_6 tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_15 _let_4)) _let_13))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_15 _let_12)) _let_3)))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.real _let_14) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_5 (tptp.i _let_8 _let_12)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_13)) _let_3)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_5 (tptp.i _let_8 _let_3)))) _let_2)))))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s tptp.num P0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_))) (let ((_let_8 (tptp.s _let_6 (tptp.i _let_7 _let_4)))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (let ((_let_10 (tptp.s (tptp.fun _let_5 _let_9) tptp.sum))) (let ((_let_11 (tptp.s tptp.num N0))) (let ((_let_12 (tptp.s tptp.num tptp.u_0))) (let ((_let_13 (tptp.fun tptp.num tptp.num))) (let ((_let_14 (tptp.s _let_13 tptp.numeral))) (let ((_let_15 (tptp.s tptp.num (tptp.i _let_14 (tptp.s tptp.num (tptp.i (tptp.s _let_13 tptp.bit1) _let_12)))))) (let ((_let_16 (tptp.fun tptp.num _let_13))) (let ((_let_17 (tptp.fun tptp.real tptp.real))) (let ((_let_18 (tptp.s _let_6 tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_) (tptp.s tptp.num (tptp.i _let_14 _let_12)))) _let_11))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_18 _let_4)) _let_11))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_18 _let_11)) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_16 tptp.p_) _let_3)) _let_15)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun tptp.real _let_17) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_5 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_16 tptp.m_) _let_11)) _let_15)))))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_11)) _let_3)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_5 (tptp.i _let_8 _let_3)))) _let_2))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_2) tptp.m_))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow))) (let ((_let_8 (tptp.s tptp.real X))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.num _let_6))) (let ((_let_11 (tptp.fun tptp.real _let_10))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) U_0) _let_8)) _let_5)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s tptp.num tptp.u_0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.s _let_8 tptp.numeral))) (let ((_let_10 (tptp.s tptp.num (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) _let_7)))))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_4 tptp.real))) (let ((_let_14 (tptp.fun tptp.real tptp.real))) (let ((_let_15 (tptp.fun tptp.real _let_14))) (let ((_let_16 (tptp.s _let_15 tptp.realu_sub))) (let ((_let_17 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.l_a_) _let_10)) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i _let_16 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_17 _let_3)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_17 _let_2)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i _let_16 _let_3)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_9 _let_7)))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.m_) _let_1)) _let_10)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) U_0) _let_3)) _let_2)) _let_1)))))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s tptp.num tptp.u_0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 tptp.numeral))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_4)))))) (let ((_let_8 (tptp.s tptp.num N0))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun _let_2 tptp.real))) (let ((_let_12 (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_7)))) (let ((_let_13 (tptp.fun tptp.real tptp.real))) (let ((_let_14 (tptp.fun tptp.real _let_13))) (let ((_let_15 (tptp.s _let_14 tptp.realu_sub))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.l_a_) _let_7)) _let_8))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i _let_15 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_pow) _let_1)) _let_8)))) _let_12)) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i _let_15 _let_1)) _let_12)))) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.sum) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_6 _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.m_) _let_8)) _let_7)))))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_0) _let_1)))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s tptp.num tptp.u_0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 tptp.numeral))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) _let_4)))))) (let ((_let_8 (tptp.s tptp.num N0))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun _let_2 tptp.real))) (let ((_let_12 (tptp.fun tptp.real tptp.real))) (let ((_let_13 (tptp.fun tptp.real _let_12))) (let ((_let_14 (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_7)))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.l_a_) _let_7)) _let_8))) (= (tptp.s tptp.real (tptp.i _let_14 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.realu_pow) _let_1)) _let_8)))) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_14 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.sum) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_6 _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.m_) _let_8)) _let_7)))))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_0) _let_1))))))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((A5 $$unsorted) (Y $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num J0))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_1) tptp.m_))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 A5))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.num _let_6))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_2) _let_7)) _let_5)) _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_7 _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i _let_4 _let_3)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((N0 $$unsorted) (A5 $$unsorted) (Y $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.fun tptp.num _let_3))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s tptp.num N0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun _let_3 tptp.real))) (let ((_let_12 (tptp.fun tptp.real _let_3))) (let ((_let_13 (tptp.fun _let_3 _let_12))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.num _let_13) U_1) _let_7)) _let_4)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.sum) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_7)))) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_2) _let_4)) _let_2)) _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 A5))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))))))) (forall ((A5 $$unsorted) (X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.real _let_3))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 U_0))) (let ((_let_9 (tptp.s tptp.num tptp.u_0))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.s _let_10 tptp.numeral))) (let ((_let_12 (tptp.s tptp.num (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) _let_9)))))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.fun tptp.num _let_13))) (let ((_let_15 (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.num _let_14) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_11 _let_9)))))) (let ((_let_16 (tptp.fun _let_3 tptp.real))) (let ((_let_17 (tptp.s (tptp.fun _let_13 _let_16) tptp.sum))) (let ((_let_18 (tptp.fun tptp.real tptp.real))) (let ((_let_19 (tptp.fun tptp.real _let_18))) (let ((_let_20 (tptp.s _let_19 tptp.realu_sub))) (let ((_let_21 (tptp.s _let_6 (tptp.i _let_8 _let_4)))) (let ((_let_22 (tptp.s _let_16 (tptp.i _let_17 (tptp.s _let_13 (tptp.i _let_15 _let_5)))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 tptp.l_a_) _let_12)) _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_18 (tptp.i _let_20 (tptp.s tptp.real (tptp.i _let_22 (tptp.s _let_3 (tptp.i _let_21 _let_1)))))) (tptp.s tptp.real (tptp.i _let_22 (tptp.s _let_3 (tptp.i _let_21 _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_18 (tptp.i _let_20 _let_1)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_16 (tptp.i _let_17 (tptp.s _let_13 (tptp.i _let_15 (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.m_) _let_5)) _let_12)))))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) U_1) _let_5)) _let_4)) _let_2)))) _let_1))))))))))))))))))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((A5 $$unsorted) (J0 $$unsorted) (Y $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.p_))) (let ((_let_7 (tptp.s tptp.num J0))) (let ((_let_8 (tptp.s _let_3 A5))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_2) _let_8)) _let_7)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((N0 $$unsorted) (A5 $$unsorted) (Y $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.num J0))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.fun tptp.real _let_3))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s tptp.num tptp.u_0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.s _let_8 tptp.numeral))) (let ((_let_10 (tptp.s tptp.num N0))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_8) tptp.m_))) (let ((_let_12 (tptp.fun tptp.num tptp.bool))) (let ((_let_13 (tptp.fun tptp.num _let_12))) (let ((_let_14 (tptp.fun _let_3 tptp.real))) (let ((_let_15 (tptp.fun _let_3 _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun tptp.num _let_15) U_1) _let_10)) _let_4)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_12 _let_14) tptp.sum) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.num _let_13) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_9 _let_7)))) (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i _let_11 _let_10)) _let_2)))) (tptp.s tptp.num (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) _let_7)))))))))) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_2) _let_4)) _let_2)) _let_1))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 A5))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))))))) (forall ((A5 $$unsorted) (X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.real _let_3))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 U_0))) (let ((_let_9 (tptp.s tptp.num tptp.u_0))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.s _let_10 tptp.numeral))) (let ((_let_12 (tptp.s tptp.num (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) _let_9)))))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.fun tptp.num _let_13))) (let ((_let_15 (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.num _let_14) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_11 _let_9)))))) (let ((_let_16 (tptp.fun _let_3 tptp.real))) (let ((_let_17 (tptp.s (tptp.fun _let_13 _let_16) tptp.sum))) (let ((_let_18 (tptp.fun tptp.real tptp.real))) (let ((_let_19 (tptp.fun tptp.real _let_18))) (let ((_let_20 (tptp.s _let_19 tptp.realu_sub))) (let ((_let_21 (tptp.s _let_6 (tptp.i _let_8 _let_4)))) (let ((_let_22 (tptp.s _let_16 (tptp.i _let_17 (tptp.s _let_13 (tptp.i _let_15 _let_5)))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 tptp.l_a_) _let_12)) _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_18 (tptp.i _let_20 (tptp.s tptp.real (tptp.i _let_22 (tptp.s _let_3 (tptp.i _let_21 _let_1)))))) (tptp.s tptp.real (tptp.i _let_22 (tptp.s _let_3 (tptp.i _let_21 _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_18 (tptp.i _let_20 _let_1)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_16 (tptp.i _let_17 (tptp.s _let_13 (tptp.i _let_15 (tptp.s tptp.num (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.m_) _let_5)) _let_12)))))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) U_1) _let_5)) _let_4)) _let_2)))) _let_1))))))))))))))))))))))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((C0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 C0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_1) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (C0 $$unsorted) (GENR_PVARR_199 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) U_0) (tptp.s tptp.num N0))) (tptp.s _let_1 C0))) (tptp.s tptp.real GENR_PVARR_199)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun _let_6 tptp.real))) (and (= (tptp.p _let_2) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.sum) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) _let_5)) (tptp.s tptp.num N0))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) U_1) (tptp.s _let_6 C0))) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.setspec) (tptp.s tptp.real GENR_PVARR_199))) _let_2)) _let_1)))))))))))))))))))) (forall ((N0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) U_0) _let_1)) (tptp.s _let_2 C0))))))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (not (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.in) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) _let_1)) (tptp.s tptp.num N0)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 C0) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_1)))))))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_5)))) _let_1)))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((C0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 C0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_1) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (C0 $$unsorted) (GENR_PVARR_202 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) U_0) (tptp.s tptp.num N0))) (tptp.s _let_1 C0))) (tptp.s tptp.real GENR_PVARR_202)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun _let_6 tptp.real))) (and (= (tptp.p _let_2) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.sum) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) _let_5)) (tptp.s tptp.num N0))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) U_1) (tptp.s _let_6 C0))) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.setspec) (tptp.s tptp.real GENR_PVARR_202))) _let_2)) _let_1)))))))))))))))))))) (forall ((N0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) U_0) (tptp.s tptp.num N0))) (tptp.s _let_1 C0)))))))) (exists ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.in) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) _let_1)) (tptp.s tptp.num N0)))))) (not (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 C0) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_1))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 C0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))))))) (forall ((N0 $$unsorted) (C0 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_2 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.sum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) _let_1)) (tptp.s tptp.num N0))))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 C0))) (tptp.s tptp.real X))))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_1)))))))))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.in) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) _let_1)) (tptp.s tptp.num N0)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 C0) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_1))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 C0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))))))) (forall ((N0 $$unsorted) (C0 $$unsorted) (K0 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.sum) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.num N0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 C0))) (tptp.s tptp.real X))))) (tptp.s tptp.real K0)))))))) (and (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) C0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.real K0)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.num I0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.in) _let_5)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (tptp.s tptp.num N0)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 C0) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.univ))) (let ((_let_4 (tptp.fun _let_2 tptp.num))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.dimindex) (tptp.s _let_2 S0))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.card) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (not (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 S0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 S0)))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex))) (= (tptp.s tptp.num (tptp.i _let_2 (tptp.s _let_1 S0))) (tptp.s tptp.num (tptp.i _let_2 (tptp.s _let_1 tptp.univ))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.n))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.univ))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hasu_size) _let_3)) _let_1))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) _let_3)) _let_1))))))) (forall ((A $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num R0))) (let ((_let_2 (tptp.finite_image A))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.in) _let_1)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dimindex) (tptp.s _let_3 tptp.univ)))))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.destu_finiteu_image) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.finiteu_index) _let_1)))) _let_1)))))))))) (forall ((A $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.finite_image A))) (let ((_let_2 (tptp.s _let_1 A5))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.finiteu_index) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.destu_finiteu_image) _let_2)))) _let_2)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.finite_image A))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (= (tptp.s _let_7 tptp.univ) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 tptp.finiteu_index))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.finite_image A) tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.hasu_size) (tptp.s _let_2 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 S0)))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.finite_image A) tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) (tptp.s _let_2 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 S0))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun (tptp.finite_image A) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 tptp.univ)))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.finite_image A) tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 S0))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 T0))))))) (forall ((A $$unsorted) (I0 $$unsorted)) (and (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.finite_image A))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dimindex) (tptp.s _let_3 tptp.univ)))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.finiteu_index) _let_2)) (tptp.s _let_1 I0)))))))))) (forall ((N0 $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.num XI_))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.finite_image A))) (let ((_let_4 (tptp.s _let_3 I0))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_3) tptp.finiteu_index))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (= (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_4) (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) _let_7))) (= (tptp.s _let_3 (tptp.i _let_5 _let_1)) _let_4)) (= _let_2 _let_1)))))))))))))))) (forall ((A $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.finite_image A))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.finiteu_index))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6)))) (= (= (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_3 (tptp.i _let_4 _let_1))) (= _let_2 _let_1)))))))))))))) (forall ((N $$unsorted)) (= (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.finite_image N))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 K0)))))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.finite_image N))) (let ((_let_3 (tptp.fun N tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dimindex) (tptp.s _let_3 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.p0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.finiteu_index) _let_1))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.finite_image B) A))) (let ((_let_2 (tptp.s _let_1 R0))) (let ((_let_3 (tptp.cart A B))) (= (tptp.p (tptp.s tptp.bool tptp.t)) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.destu_cart) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.mku_cart) _let_2)))) _let_2)))))) (forall ((A $$unsorted) (B $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart A B))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun (tptp.finite_image B) A))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.mku_cart) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.destu_cart) _let_2)))) _let_2))))) (forall ((Q77782 $$unsorted) (Q77792 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.finite_image Q77792))) (let ((_let_3 (tptp.cart Q77782 Q77792))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun _let_2 Q77782))) (let ((_let_6 (tptp.fun tptp.num Q77782))) (= (tptp.s Q77782 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.d_) _let_4)) _let_1)) (tptp.s Q77782 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.destu_cart) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.finiteu_index) _let_1)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart A B))) (= (= (tptp.s _let_1 X) (tptp.s _let_1 Y)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart A B))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_3) tptp.d_))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))))) (= (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 X))) _let_1)) (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 Y))) _let_1)))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (U_0 $$unsorted)) (=> (forall ((G0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart A B))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 G0))) (tptp.s _let_1 F0)))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.cart A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))) (= (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.d_) (tptp.s _let_3 F0))) _let_1)) (tptp.s A (tptp.i (tptp.s _let_2 G0) _let_1))))))))))))))))) (forall ((G0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num A))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.cart A B))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.lambda) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.h_) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 tptp.g))) (let ((_let_4 (tptp.cart A B))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))))) (= (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) tptp.d_) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.lambda) _let_3)))) _let_1)) (tptp.s A (tptp.i _let_3 _let_1))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart A B))) (let ((_let_2 (tptp.fun tptp.num A))) (= (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.cart A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))) (= (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.d_) (tptp.s _let_3 F0))) _let_1)) (tptp.s A (tptp.i (tptp.s _let_2 G0) _let_1)))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.lambda) (tptp.s _let_2 G0))) (tptp.s _let_1 F0)))))) (forall ((Q77980 $$unsorted) (Q77984 $$unsorted) (U_0 $$unsorted)) (=> (forall ((G0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart Q77980 Q77984))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun tptp.num Q77980))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s Q77980 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_1)) (tptp.s Q77980 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.d_) _let_3)) _let_1))))))))) (forall ((G0 $$unsorted)) (let ((_let_1 (tptp.cart Q77980 Q77984))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.fun tptp.num Q77980))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))) _let_2))))))) (forall ((A $$unsorted) (N $$unsorted) (I0 $$unsorted)) (exists ((K0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart A N))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.d_) (tptp.s _let_1 X))))) (= (tptp.s A (tptp.i _let_3 (tptp.s tptp.num I0))) (tptp.s A (tptp.i _let_3 (tptp.s tptp.num K0)))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (I0 $$unsorted)) (exists ((K0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart A N))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.d_) (tptp.s _let_1 X))))) (= (tptp.s A (tptp.i _let_3 (tptp.s tptp.num I0))) (tptp.s A (tptp.i _let_3 (tptp.s tptp.num K0)))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart B N))) (let ((_let_2 (tptp.fun tptp.num B))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.d_) (tptp.s _let_1 Y))))) (= (tptp.s B (tptp.i _let_3 (tptp.s tptp.num I0))) (tptp.s B (tptp.i _let_3 (tptp.s tptp.num K0)))))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart A N))) (= (= (tptp.s _let_1 X) (tptp.s _let_1 Y)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart A N))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_3) tptp.d_))) (= (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 X))) _let_1)) (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 Y))) _let_1))))))))))) (forall ((A $$unsorted) (B $$unsorted) (R0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num R0))) (let ((_let_2 (tptp.finite_sum A B))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.in) _let_1)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dimindex) (tptp.s _let_3 tptp.univ)))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.destu_finiteu_sum) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mku_finiteu_sum) _let_1)))) _let_1))))))))))) (forall ((A $$unsorted) (B $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.finite_sum A B))) (let ((_let_2 (tptp.s _let_1 A5))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mku_finiteu_sum) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.destu_finiteu_sum) _let_2)))) _let_2)))) (forall ((M $$unsorted) (A $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun M tptp.bool))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.cart A N))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun tptp.num A))) (let ((_let_8 (tptp.fun _let_5 _let_7))) (let ((_let_9 (tptp.cart A M))) (let ((_let_10 (tptp.s _let_9 F0))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun A A))) (let ((_let_13 (tptp.fun A _let_12))) (= (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_9 _let_8) U_0) _let_10)) _let_6)) _let_3)) (tptp.s A (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.bool _let_13) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.l_a_) _let_3)) _let_2)))) (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_9 _let_7) tptp.d_) _let_10)) _let_3)))) (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.d_) _let_6)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.m_) _let_3)) _let_2))))))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart A N))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.cart A M))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun tptp.num A))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.cart A (tptp.finite_sum M N)))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.pastecart) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_2)))))))))))))))) (forall ((A $$unsorted) (M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart A (tptp.finite_sum M N)))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num A))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s A (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_1)) (tptp.s A (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.d_) _let_3)) _let_1))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart A (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.cart A M))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.fstcart) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))) (forall ((A $$unsorted) (M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun M tptp.bool))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.cart A (tptp.finite_sum M N)))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun tptp.num A))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (= (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_5)) _let_2)) (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.d_) _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart A (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.cart A N))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.sndcart) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.finite_sum A B))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (= (tptp.s _let_8 tptp.univ) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.image) (tptp.s _let_7 tptp.mku_finiteu_sum))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun M tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun (tptp.finite_sum M N) tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.hasu_size) (tptp.s _let_4 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun M tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun (tptp.finite_sum M N) tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))) (forall ((N $$unsorted) (A $$unsorted) (M $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart A M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart A N))) (let ((_let_4 (tptp.cart A (tptp.finite_sum M N)))) (let ((_let_5 (tptp.fun _let_3 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.fstcart) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.pastecart) _let_2)) (tptp.s _let_3 Y))))) _let_2))))))) (forall ((M $$unsorted) (A $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart A N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart A M))) (let ((_let_4 (tptp.cart A (tptp.finite_sum M N)))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.sndcart) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.pastecart) (tptp.s _let_3 X))) _let_2)))) _let_2))))))) (forall ((Q78417 $$unsorted) (Q78414 $$unsorted) (Q78412 $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart Q78417 (tptp.finite_sum Q78414 Q78412)))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.cart Q78417 Q78412))) (let ((_let_4 (tptp.cart Q78417 Q78414))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.pastecart) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.fstcart) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.sndcart) _let_2)))) _let_2))))))) (forall ((Q78455 $$unsorted) (Q78445 $$unsorted) (Q78456 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart Q78455 (tptp.finite_sum Q78445 Q78456)))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart Q78455 Q78456))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.sndcart))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.cart Q78455 Q78445))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.fstcart))) (= (= _let_5 _let_2) (and (= (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s _let_6 (tptp.i _let_7 _let_2))) (= (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((Q78477 $$unsorted) (Q78476 $$unsorted) (Q78478 $$unsorted)) (= (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.cart Q78476 (tptp.finite_sum Q78477 Q78478)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 P0)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart Q78476 Q78478))) (let ((_let_2 (tptp.cart Q78476 Q78477))) (let ((_let_3 (tptp.cart Q78476 (tptp.finite_sum Q78477 Q78478)))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.p0) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.pastecart) (tptp.s _let_2 X))) (tptp.s _let_1 Y))))))))))))) (forall ((Q78499 $$unsorted) (Q78498 $$unsorted) (Q78500 $$unsorted)) (= (exists ((P0 $$unsorted)) (let ((_let_1 (tptp.cart Q78498 (tptp.finite_sum Q78499 Q78500)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 P0)))))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart Q78498 Q78500))) (let ((_let_2 (tptp.cart Q78498 Q78499))) (let ((_let_3 (tptp.cart Q78498 (tptp.finite_sum Q78499 Q78500)))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.p0) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.pastecart) (tptp.s _let_2 X))) (tptp.s _let_1 Y))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted) (W $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.s _let_4 W))) (let ((_let_6 (tptp.s _let_4 X))) (let ((_let_7 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s (tptp.fun _let_4 _let_8) tptp.pastecart))) (= (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_3)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_2))) (and (= _let_6 _let_5) (= _let_3 _let_2))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_67 _let_18) tptp.hasu_size) _let_68)) _let_17))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_65 _let_18) tptp.hasu_size) _let_66)) _let_33))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_63 _let_18) tptp.hasu_size) _let_64)) _let_21))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_67 tptp.num) tptp.dimindex) _let_68)) _let_17) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_65 tptp.num) tptp.dimindex) _let_66)) _let_33) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_63 tptp.num) tptp.dimindex) _let_64)) _let_21) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.suc) (tptp.s tptp.num N0))))))))) (forall ((N $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_210 $$unsorted)) (let ((_let_1 (tptp.cart A N))) (let ((_let_2 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_1) (tptp.s _let_2 P0))) (tptp.s _let_1 GENR_PVARR_210)))) (exists ((V $$unsorted) (V0 $$unsorted)) (let ((_let_1 (tptp.cart A N))) (let ((_let_2 (tptp.s tptp.bool V0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart A N))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun N tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) P0) _let_1)) (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 V))) _let_1)))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_210))) _let_2)) (tptp.s _let_1 V))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (I0 $$unsorted) (GENR_PVARR_209 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 P0))) (tptp.s tptp.num I0))) (tptp.s A GENR_PVARR_209)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.setspec) (tptp.s A GENR_PVARR_209))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) P0) (tptp.s tptp.num I0))) _let_1)))) _let_1))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun (tptp.cart A N) tptp.bool))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_0) (tptp.s _let_3 P0))) _let_1)))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 P0)))))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun (tptp.cart A N) tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.hasu_size) (tptp.s _let_6 tptp.univ))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.hasu_size) (tptp.s _let_4 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.exp0) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))))))))) (forall ((A $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.univ))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun (tptp.cart A N) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.card) (tptp.s _let_5 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.exp0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))))) (forall ((A $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart A N) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 tptp.univ)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 tptp.univ)))))))) (forall ((N $$unsorted) (A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun _let_1 A))) (let ((_let_6 (tptp.fun tptp.num A))) (= (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_2)) _let_4)) (tptp.s A (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.el) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.m_) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)))))))))) (forall ((L $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.cart A N))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vector) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))) (forall ((Q79231 $$unsorted) (Q79230 $$unsorted) (Q79232 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_211 $$unsorted)) (let ((_let_1 (tptp.cart Q79230 (tptp.finite_sum Q79231 Q79232)))) (let ((_let_2 (tptp.fun (tptp.cart Q79230 Q79231) (tptp.fun (tptp.cart Q79230 Q79232) tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 GENR_PVARR_211)))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart Q79230 Q79232))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart Q79230 Q79231))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart Q79230 (tptp.finite_sum Q79231 Q79232)))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.fun tptp.bool _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.setspec) (tptp.s _let_5 GENR_PVARR_211))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) P0) _let_4)) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.pastecart) _let_4)) _let_2)))))))))))))))))))) (forall ((P0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart Q79230 Q79232))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.cart Q79230 Q79231))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_6 P0))) (let ((_let_8 (tptp.cart Q79230 (tptp.finite_sum Q79231 Q79232)))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun _let_1 _let_8))) (let ((_let_11 (tptp.fun _let_9 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.in) (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.pastecart) _let_4)) _let_2)))) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_9 _let_9) tptp.gspec) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_0) _let_7)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_4)) _let_2))))))))))))))))) (forall ((Q79285 $$unsorted) (Q79290 $$unsorted) (Q79289 $$unsorted) (Q79249 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun Q79249 tptp.bool))) (let ((_let_2 (tptp.list (tptp.prod (tptp.fun Q79285 Q79289) (tptp.fun Q79290 (tptp.fun Q79285 Q79249)))))) (let ((_let_3 (tptp.fun Q79289 Q79249))) (let ((_let_4 (tptp.fun Q79290 _let_3))) (=> (forall ((Y $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q79249 tptp.bool) U_0) (tptp.s Q79249 Y))) (tptp.s tptp.bool tptp.t))) (= (tptp.s Q79249 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.casewise) (tptp.s _let_2 tptp.nil))) (tptp.s Q79290 tptp.f))) (tptp.s Q79289 tptp.x))) (tptp.s Q79249 (tptp.i (tptp.s (tptp.fun _let_1 Q79249) tptp.h_) (tptp.s _let_1 U_0)))))))))) (forall ((Q79285 $$unsorted) (Q79249 $$unsorted) (Q79290 $$unsorted) (Q79289 $$unsorted) (U_0 $$unsorted)) (=> (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q79285 Y))) (let ((_let_2 (tptp.fun Q79285 Q79289))) (let ((_let_3 (tptp.prod _let_2 (tptp.fun Q79290 (tptp.fun Q79285 Q79249))))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q79285 tptp.bool) U_0) _let_1))) (= (tptp.s Q79289 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.fst) (tptp.s _let_3 tptp.h0))) _let_1)) (tptp.s Q79289 tptp.x))))))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s Q79289 tptp.x))) (let ((_let_2 (tptp.s Q79290 tptp.f))) (let ((_let_3 (tptp.fun Q79285 Q79249))) (let ((_let_4 (tptp.fun Q79290 _let_3))) (let ((_let_5 (tptp.prod (tptp.fun Q79285 Q79289) _let_4))) (let ((_let_6 (tptp.list _let_5))) (let ((_let_7 (tptp.s _let_6 tptp.t0))) (let ((_let_8 (tptp.fun Q79289 Q79249))) (let ((_let_9 (tptp.fun Q79290 _let_8))) (let ((_let_10 (tptp.s (tptp.fun _let_6 _let_9) tptp.casewise))) (let ((_let_11 (tptp.fun Q79285 tptp.bool))) (let ((_let_12 (tptp.s _let_5 tptp.h0))) (let ((_let_13 (tptp.s tptp.bool V))) (let ((_let_14 (tptp.fun Q79249 Q79249))) (let ((_let_15 (tptp.fun Q79249 _let_14))) (let ((_let_16 (tptp.fun _let_6 _let_6))) (and (= (tptp.p _let_13) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q79285 Q79289))) (let ((_let_2 (tptp.prod _let_1 (tptp.fun Q79290 (tptp.fun Q79285 Q79249))))) (= (tptp.s Q79289 (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.fst) (tptp.s _let_2 tptp.h0))) (tptp.s Q79285 Y))) (tptp.s Q79289 tptp.x)))))) (= (tptp.s Q79249 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_5 _let_16) tptp.cons) _let_12)) _let_7)))) _let_2)) _let_1)) (tptp.s Q79249 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun tptp.bool _let_15) tptp.cond) _let_13)) (tptp.s Q79249 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.snd) _let_12)) _let_2)) (tptp.s Q79285 (tptp.i (tptp.s (tptp.fun _let_11 Q79285) tptp.h_) (tptp.s _let_11 U_0))))))) (tptp.s Q79249 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_7)) _let_2)) _let_1))))))))))))))))))))))))) (forall ((Q79301 $$unsorted) (Q79350 $$unsorted) (Q79349 $$unsorted) (Q79309 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun Q79309 tptp.bool))) (let ((_let_2 (tptp.list (tptp.prod (tptp.fun Q79301 Q79349) (tptp.fun Q79350 (tptp.fun Q79301 Q79309)))))) (let ((_let_3 (tptp.fun Q79349 Q79309))) (let ((_let_4 (tptp.fun Q79350 _let_3))) (=> (forall ((Y $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q79309 tptp.bool) U_0) (tptp.s Q79309 Y))) (tptp.s tptp.bool tptp.t))) (= (tptp.s Q79309 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.casewise) (tptp.s _let_2 tptp.nil))) (tptp.s Q79350 tptp.f))) (tptp.s Q79349 tptp.x))) (tptp.s Q79309 (tptp.i (tptp.s (tptp.fun _let_1 Q79309) tptp.h_) (tptp.s _let_1 U_0)))))))))) (forall ((Q79352 $$unsorted) (Q79310 $$unsorted) (Q79350 $$unsorted) (Q79349 $$unsorted) (U_0 $$unsorted)) (=> (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q79352 Y))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q79352 tptp.bool) U_0) _let_1))) (= (tptp.s Q79349 (tptp.i (tptp.s (tptp.fun Q79352 Q79349) tptp.s0) _let_1)) (tptp.s Q79349 tptp.x))))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s Q79349 tptp.x))) (let ((_let_2 (tptp.s Q79350 tptp.f))) (let ((_let_3 (tptp.fun Q79352 Q79310))) (let ((_let_4 (tptp.fun Q79350 _let_3))) (let ((_let_5 (tptp.fun Q79352 Q79349))) (let ((_let_6 (tptp.prod _let_5 _let_4))) (let ((_let_7 (tptp.list _let_6))) (let ((_let_8 (tptp.s _let_7 tptp.clauses))) (let ((_let_9 (tptp.fun Q79349 Q79310))) (let ((_let_10 (tptp.fun Q79350 _let_9))) (let ((_let_11 (tptp.s (tptp.fun _let_7 _let_10) tptp.casewise))) (let ((_let_12 (tptp.fun Q79352 tptp.bool))) (let ((_let_13 (tptp.s _let_4 tptp.t0))) (let ((_let_14 (tptp.s tptp.bool V))) (let ((_let_15 (tptp.fun Q79310 Q79310))) (let ((_let_16 (tptp.fun Q79310 _let_15))) (let ((_let_17 (tptp.fun _let_4 _let_6))) (let ((_let_18 (tptp.fun _let_7 _let_7))) (and (= (tptp.p _let_14) (exists ((Y $$unsorted)) (= (tptp.s Q79349 (tptp.i (tptp.s (tptp.fun Q79352 Q79349) tptp.s0) (tptp.s Q79352 Y))) (tptp.s Q79349 tptp.x)))) (= (tptp.s Q79310 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_6 _let_18) tptp.cons) (tptp.s _let_6 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_5 _let_17) tptp.c_) (tptp.s _let_5 tptp.s0))) _let_13)))) _let_8)))) _let_2)) _let_1)) (tptp.s Q79310 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun tptp.bool _let_16) tptp.cond) _let_14)) (tptp.s Q79310 (tptp.i (tptp.s _let_3 (tptp.i _let_13 _let_2)) (tptp.s Q79352 (tptp.i (tptp.s (tptp.fun _let_12 Q79352) tptp.h_) (tptp.s _let_12 U_0))))))) (tptp.s Q79310 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_8)) _let_2)) _let_1))))))))))))))))))))))))))) (forall ((Q79444 $$unsorted) (Q79442 $$unsorted) (Q79441 $$unsorted) (Q79451 $$unsorted) (U_0 $$unsorted)) (=> (forall ((Y $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q79451 tptp.bool) U_0) (tptp.s Q79451 Y))) (tptp.s tptp.bool tptp.t))) (forall ((CLAUSES $$unsorted) (C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q79451 tptp.bool))) (let ((_let_2 (tptp.list (tptp.prod (tptp.fun Q79444 Q79441) (tptp.fun Q79442 (tptp.fun Q79444 Q79451)))))) (let ((_let_3 (tptp.fun Q79441 Q79451))) (let ((_let_4 (tptp.fun Q79442 _let_3))) (or (exists ((S0 $$unsorted) (T0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q79444 A5))) (let ((_let_2 (tptp.s Q79442 C0))) (let ((_let_3 (tptp.fun Q79444 Q79451))) (let ((_let_4 (tptp.fun Q79442 _let_3))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.s Q79441 X))) (let ((_let_7 (tptp.fun Q79444 Q79441))) (let ((_let_8 (tptp.prod _let_7 _let_4))) (let ((_let_9 (tptp.list _let_8))) (let ((_let_10 (tptp.s _let_9 CLAUSES))) (let ((_let_11 (tptp.fun Q79441 Q79451))) (let ((_let_12 (tptp.fun Q79442 _let_11))) (let ((_let_13 (tptp.s _let_7 S0))) (let ((_let_14 (tptp.fun _let_4 _let_8))) (let ((_let_15 (tptp.fun _let_9 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_8 _let_15) tptp.mem) (tptp.s _let_8 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_7 _let_14) tptp.c_) _let_13)) _let_5)))) _let_10))) (= (tptp.s Q79441 (tptp.i _let_13 _let_1)) _let_6) (= (tptp.s Q79451 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.casewise) _let_10)) _let_2)) _let_6)) (tptp.s Q79451 (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))))) (and (not (exists ((S0 $$unsorted) (T0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun Q79444 Q79441))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q79442 (tptp.fun Q79444 Q79451)))) (let ((_let_4 (tptp.prod _let_1 _let_3))) (let ((_let_5 (tptp.list _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_4))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.mem) (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.c_) _let_2)) (tptp.s _let_3 T0))))) (tptp.s _let_5 CLAUSES)))) (= (tptp.s Q79441 (tptp.i _let_2 (tptp.s Q79444 A5))) (tptp.s Q79441 X)))))))))))) (= (tptp.s Q79451 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.casewise) (tptp.s _let_2 CLAUSES))) (tptp.s Q79442 C0))) (tptp.s Q79441 X))) (tptp.s Q79451 (tptp.i (tptp.s (tptp.fun _let_1 Q79451) tptp.h_) (tptp.s _let_1 U_0))))))))))))) (forall ((A $$unsorted) (C $$unsorted) (P $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((CLAUSES $$unsorted) (C0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun P A) (tptp.fun C (tptp.fun P B))))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.list _let_1))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun C _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 CLAUSES))) (tptp.s C C0))) (tptp.s _let_2 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun C (tptp.fun P B)))) (let ((_let_3 (tptp.fun P A))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.s C C0))) (let ((_let_3 (tptp.fun P B))) (let ((_let_4 (tptp.fun C _let_3))) (let ((_let_5 (tptp.fun P A))) (let ((_let_6 (tptp.list (tptp.prod _let_5 _let_4)))) (let ((_let_7 (tptp.fun A B))) (let ((_let_8 (tptp.fun C _let_7))) (= (tptp.s B (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.casewise) (tptp.s _let_6 CLAUSES))) _let_2)) (tptp.s A (tptp.i (tptp.s _let_5 S0) _let_1)))) (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 T0) _let_2)) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))))))) _let_1))))))))))))))))))) (forall ((CLAUSES $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun P A) (tptp.fun C (tptp.fun P B))))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.s _let_2 CLAUSES))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun C _let_5))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (SI_ $$unsorted) (TI_ $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s P Y))) (let ((_let_2 (tptp.s C C0))) (let ((_let_3 (tptp.fun P B))) (let ((_let_4 (tptp.fun C _let_3))) (let ((_let_5 (tptp.s _let_4 TI_))) (let ((_let_6 (tptp.s P X))) (let ((_let_7 (tptp.s _let_4 T0))) (let ((_let_8 (tptp.fun P A))) (let ((_let_9 (tptp.s _let_8 SI_))) (let ((_let_10 (tptp.s _let_8 S0))) (let ((_let_11 (tptp.prod _let_8 _let_4))) (let ((_let_12 (tptp.list _let_11))) (let ((_let_13 (tptp.s _let_12 CLAUSES))) (let ((_let_14 (tptp.fun _let_4 _let_11))) (let ((_let_15 (tptp.s (tptp.fun _let_8 _let_14) tptp.c_))) (let ((_let_16 (tptp.fun _let_12 tptp.bool))) (let ((_let_17 (tptp.s (tptp.fun _let_11 _let_16) tptp.mem))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_16 (tptp.i _let_17 (tptp.s _let_11 (tptp.i (tptp.s _let_14 (tptp.i _let_15 _let_10)) _let_7)))) _let_13))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_16 (tptp.i _let_17 (tptp.s _let_11 (tptp.i (tptp.s _let_14 (tptp.i _let_15 _let_9)) _let_5)))) _let_13))) (= (tptp.s A (tptp.i _let_10 _let_6)) (tptp.s A (tptp.i _let_9 _let_1)))) (= (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_2)) _let_6)) (tptp.s B (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.all0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_3)) (tptp.s C C0))))))) _let_3)))))))))))))) (forall ((Q79580 $$unsorted) (Q79588 $$unsorted) (Q79587 $$unsorted) (Q79583 $$unsorted) (Q79593 $$unsorted) (P0 $$unsorted) (L_L_ $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q79587 Q79583))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun Q79593 Q79588)))) (let ((_let_3 (tptp.fun Q79593 Q79580))) (let ((_let_4 (tptp.fun _let_1 (tptp.fun Q79593 tptp.bool)))) (let ((_let_5 (tptp.fun Q79587 (tptp.fun Q79580 tptp.bool)))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.admissible) (tptp.s _let_5 L_L_))) (tptp.s _let_4 P0))) (tptp.s _let_3 S0))) (tptp.s _let_2 T0)))) (forall ((F0 $$unsorted) (G0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q79593 A5))) (let ((_let_2 (tptp.fun Q79587 Q79583))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun Q79593 Q79588))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) T0))) (let ((_let_6 (tptp.s _let_2 F0))) (let ((_let_7 (tptp.fun Q79593 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_2 _let_7) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_1))) (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s Q79587 Z0))) (let ((_let_2 (tptp.fun Q79587 Q79583))) (let ((_let_3 (tptp.fun Q79580 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q79587 _let_3) L_L_) _let_1)) (tptp.s Q79580 (tptp.i (tptp.s (tptp.fun Q79593 Q79580) S0) (tptp.s Q79593 A5)))))) (= (tptp.s Q79583 (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s Q79583 (tptp.i (tptp.s _let_2 G0) _let_1))))))))) (= (tptp.s Q79588 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_1)) (tptp.s Q79588 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (P $$unsorted) (L_L_ $$unsorted) (S0 $$unsorted) (P0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P B)))) (let ((_let_3 (tptp.fun P A))) (let ((_let_4 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_5 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.tailadmissible) (tptp.s _let_5 L_L_))) (tptp.s _let_4 P0))) (tptp.s _let_3 S0))) (tptp.s _let_2 T0)))) (exists ((P1 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (and (forall ((F0 $$unsorted) (A5 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) L_L_) (tptp.s A Y))))) (let ((_let_5 (tptp.fun A B))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun P tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) P1) _let_6)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) G0) _let_6)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s A (tptp.i (tptp.s _let_2 S0) _let_1)))))))))))))) (forall ((F0 $$unsorted) (G1 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G1))) (let ((_let_4 (tptp.fun P B))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) H0))) (let ((_let_6 (tptp.s _let_2 F0))) (let ((_let_7 (tptp.fun P A))) (let ((_let_8 (tptp.s (tptp.fun _let_2 _let_7) G0))) (let ((_let_9 (tptp.fun P tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_2 _let_9) P1))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) L_L_) _let_1)) (tptp.s A (tptp.i (tptp.s (tptp.fun P A) S0) (tptp.s P A5)))))) (= (tptp.s B (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G1) _let_1)))))))) (and (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_6)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) _let_1))) (= (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_1)) (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_1))) (= (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)))))))))))))))) (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P B))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun P A))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun B B))) (let ((_let_10 (tptp.fun B _let_9))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 P0) _let_3)) _let_1))) (= (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 T0) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 P1) _let_3)) _let_1)))) (tptp.s B (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) G0) _let_3)) _let_1)))))) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 H0) _let_3)) _let_1))))))))))))))))))))))))))))) (forall ((Q79737 $$unsorted) (Q79745 $$unsorted) (Q79739 $$unsorted) (U_1 $$unsorted)) (=> (forall ((A5 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q79745 tptp.bool) U_1) (tptp.s Q79745 A5))) (tptp.s tptp.bool tptp.t))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q79745 tptp.bool))) (let ((_let_2 (tptp.fun Q79737 Q79739))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 U_1))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q79737 Q79739))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun Q79745 Q79739)))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun Q79745 Q79737))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun Q79745 tptp.bool)))) (let ((_let_7 (tptp.s _let_6 P0))) (let ((_let_8 (tptp.fun Q79737 (tptp.fun Q79737 tptp.bool)))) (let ((_let_9 (tptp.s _let_8 L_L_))) (let ((_let_10 (tptp.fun _let_2 tptp.bool))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (let ((_let_12 (tptp.fun _let_6 _let_11))) (let ((_let_13 (tptp.fun _let_8 _let_12))) (let ((_let_14 (tptp.fun _let_6 tptp.bool))) (let ((_let_15 (tptp.fun _let_4 _let_14))) (let ((_let_16 (tptp.fun _let_6 _let_15))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.superadmissible) _let_9)) _let_7)) _let_5)) _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_8 _let_16) tptp.admissible) _let_9)) (tptp.s _let_6 U_0))) _let_5)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.tailadmissible) _let_9)) _let_7)) _let_5)) _let_3)))))))))))))))))))))))))) (forall ((Q79780 $$unsorted) (Q79773 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun Q79780 (tptp.fun Q79773 tptp.bool)))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun _let_1 Q79773))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q79780 _let_3) tptp.u_match) (tptp.s Q79780 tptp.x))))) (let ((_let_5 (tptp.s _let_1 tptp.r0))) (let ((_let_6 (tptp.s tptp.bool V))) (let ((_let_7 (tptp.fun Q79773 Q79773))) (let ((_let_8 (tptp.fun Q79773 _let_7))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (and (= (tptp.p _let_6) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q79773 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q79780 _let_1) tptp.r0) (tptp.s Q79780 tptp.x))) (tptp.s Q79773 Y))))))) (= (tptp.s Q79773 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.u_seqpattern) _let_5)) _let_2)))) (tptp.s Q79773 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) _let_6)) (tptp.s Q79773 (tptp.i _let_4 _let_5)))) (tptp.s Q79773 (tptp.i _let_4 _let_2))))))))))))))))) (forall ((Q79800 $$unsorted) (Q79801 $$unsorted) (Q79802 $$unsorted) (Q79803 $$unsorted) (Q79804 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q79803 Q79804))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.fun Q79801 Q79802))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2)) (tptp.s _let_3 F0))) _let_2)))))) (forall ((P0 $$unsorted) (S0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.fun Q79803 Q79804))) (let ((_let_2 (tptp.fun Q79801 Q79802))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun Q79803 Q79800))) (let ((_let_5 (tptp.fun _let_2 (tptp.fun Q79803 tptp.bool)))) (let ((_let_6 (tptp.fun Q79801 (tptp.fun Q79800 tptp.bool)))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.fun _let_5 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.admissible) (tptp.s _let_6 tptp.l_l_))) (tptp.s _let_5 P0))) (tptp.s _let_4 S0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 C0)))))))))))))))))) (forall ((B $$unsorted) (P $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun P B))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (= (tptp.s B (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_1) _let_5)) _let_3)) _let_1)) (tptp.s B (tptp.i _let_5 (tptp.s A (tptp.i _let_3 _let_1))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun P A))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun P B))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) U_0) _let_2)) _let_4)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_1) _let_4)) _let_2))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun P A))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P B)))) (let ((_let_4 (tptp.fun _let_2 (tptp.fun P tptp.bool)))) (let ((_let_5 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (=> (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.fun P tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) P0) (tptp.s _let_4 F0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) L_L_) (tptp.s A (tptp.i (tptp.s _let_2 T0) _let_1)))) (tptp.s A (tptp.i (tptp.s _let_2 S0) _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.admissible) (tptp.s _let_5 L_L_))) (tptp.s _let_4 P0))) (tptp.s _let_1 S0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 T0)))))))))))))))))))) (forall ((D $$unsorted) (A $$unsorted) (B $$unsorted) (P $$unsorted) (C $$unsorted) (U_1 $$unsorted)) (=> (forall ((G0 $$unsorted) (Y $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P C))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 Y))) (let ((_let_7 (tptp.fun C D))) (let ((_let_8 (tptp.fun P _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 G0))) (let ((_let_11 (tptp.fun P D))) (let ((_let_12 (tptp.fun _let_2 _let_11))) (let ((_let_13 (tptp.fun _let_5 _let_12))) (= (tptp.s D (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_9 _let_13) U_1) _let_10)) _let_6)) _let_3)) _let_1)) (tptp.s D (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_1)) (tptp.s C (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((G0 $$unsorted) (Y $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P C)))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun C D))))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun P D))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_0) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_1) _let_6)) _let_4)) _let_2)))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (G0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P C)))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.fun _let_1 (tptp.fun P (tptp.fun C D))))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P D)))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun P A))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_11 (tptp.s _let_10 P0))) (let ((_let_12 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_13 (tptp.s _let_12 L_L_))) (let ((_let_14 (tptp.fun _let_6 tptp.bool))) (let ((_let_15 (tptp.fun _let_8 _let_14))) (let ((_let_16 (tptp.fun _let_10 _let_15))) (let ((_let_17 (tptp.fun _let_2 tptp.bool))) (let ((_let_18 (tptp.fun _let_8 _let_17))) (let ((_let_19 (tptp.fun _let_10 _let_18))) (let ((_let_20 (tptp.fun _let_4 tptp.bool))) (let ((_let_21 (tptp.fun _let_8 _let_20))) (let ((_let_22 (tptp.fun _let_10 _let_21))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_12 _let_22) tptp.admissible) _let_13)) _let_11)) _let_9)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_12 _let_19) tptp.admissible) _let_13)) _let_11)) _let_9)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) tptp.admissible) _let_13)) _let_11)) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)) _let_3))))))))))))))))))))))))))))))))) (forall ((D $$unsorted) (A $$unsorted) (B $$unsorted) (P $$unsorted) (C $$unsorted) (U_1 $$unsorted)) (=> (forall ((G0 $$unsorted) (Y $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P C))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 Y))) (let ((_let_7 (tptp.fun C D))) (let ((_let_8 (tptp.fun P _let_7))) (let ((_let_9 (tptp.s _let_8 G0))) (let ((_let_10 (tptp.fun P D))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (= (tptp.s D (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_8 _let_12) U_1) _let_9)) _let_6)) _let_3)) _let_1)) (tptp.s D (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_1)) (tptp.s C (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((G0 $$unsorted) (Y $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P C)))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.fun P (tptp.fun C D)))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun P D))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_0) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_1) _let_6)) _let_4)) _let_2)))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (G0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P C)))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.fun P (tptp.fun C D)))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P D)))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun P A))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_10 (tptp.s _let_9 P0))) (let ((_let_11 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_12 (tptp.s _let_11 L_L_))) (let ((_let_13 (tptp.fun _let_5 tptp.bool))) (let ((_let_14 (tptp.fun _let_7 _let_13))) (let ((_let_15 (tptp.fun _let_9 _let_14))) (let ((_let_16 (tptp.fun _let_2 tptp.bool))) (let ((_let_17 (tptp.fun _let_7 _let_16))) (let ((_let_18 (tptp.fun _let_9 _let_17))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_11 _let_18) tptp.admissible) _let_12)) _let_10)) _let_8)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_11 _let_15) tptp.admissible) _let_12)) _let_10)) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 G0))) _let_3))))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (P $$unsorted) (U_7 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted) (X $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.s C U))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun P tptp.bool))) (let ((_let_6 (tptp.fun C _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun C tptp.bool))) (let ((_let_10 (tptp.fun P _let_9))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) U_7) _let_8)) _let_4)) _let_1)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_4)) _let_2)) _let_1))))))))))))))) (forall ((U_6 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_2 (tptp.fun C (tptp.fun P tptp.bool))))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun C tptp.bool))) (let ((_let_7 (tptp.fun P _let_6))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 U_6) _let_5)) _let_3)) _let_1)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 U_7) _let_5)) _let_3)) _let_1))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun C (tptp.fun P tptp.bool))))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun P (tptp.fun C tptp.bool)))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_5) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_6) _let_4)) _let_2))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod C P) tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun C (tptp.fun P tptp.bool))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_4) (tptp.s _let_3 T0))) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.s C U))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun C _let_4))) (let ((_let_6 (tptp.prod C P))) (let ((_let_7 (tptp.fun P _let_6))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) F1) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun C _let_7) tptp.c_) _let_2)) _let_1)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) T0) (tptp.s _let_3 F0))) _let_2)) _let_1))))))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun C (tptp.fun P tptp.bool))))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun (tptp.prod C P) tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_3) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_4) _let_4)) _let_2)))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod C P) A))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_2) (tptp.s _let_2 S0))) (tptp.s _let_1 F0)))) (forall ((U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.prod C P))) (let ((_let_3 (tptp.fun P _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.geq) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) F0) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun C _let_3) tptp.c_) (tptp.s C U))) _let_1)))))) (tptp.s A (tptp.i (tptp.s (tptp.fun P A) S0) _let_1))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod C P) tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P tptp.bool)))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun P tptp.bool))) (let ((_let_4 (tptp.prod C P))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun C _let_5) tptp.c_) (tptp.s C U))) _let_1)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) P0) (tptp.s _let_2 F0))) _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun (tptp.prod C P) tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_1) _let_4)) _let_2)))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun P tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun C _let_1)))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_2 (tptp.fun P (tptp.fun C tptp.bool))))) (let ((_let_6 (tptp.fun P A))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_2 _let_1))) (let ((_let_9 (tptp.s _let_8 P0))) (let ((_let_10 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_11 (tptp.s _let_10 L_L_))) (let ((_let_12 (tptp.fun _let_5 tptp.bool))) (let ((_let_13 (tptp.fun _let_6 _let_12))) (let ((_let_14 (tptp.fun _let_8 _let_13))) (let ((_let_15 (tptp.prod C P))) (let ((_let_16 (tptp.fun _let_2 (tptp.fun _let_15 tptp.bool)))) (let ((_let_17 (tptp.fun _let_15 A))) (let ((_let_18 (tptp.fun _let_17 tptp.bool))) (let ((_let_19 (tptp.fun _let_16 tptp.bool))) (let ((_let_20 (tptp.fun _let_17 _let_19))) (let ((_let_21 (tptp.fun _let_16 _let_20))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun _let_10 _let_21) tptp.admissible) _let_11)) (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_8 _let_16) U_0) _let_9)))) (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_18 _let_17) tptp.gabs) (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_6 _let_18) U_2) _let_7)))))) (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_3 _let_16) U_3) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_10 _let_14) tptp.admissible) _let_11)) _let_9)) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_5) _let_4)))))))))))))))))))))))))))))))))))))))))))) (forall ((B $$unsorted) (P $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P A))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 T0))) (let ((_let_7 (tptp.fun P B))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s B (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_6)) _let_3)) _let_1)) (tptp.s B (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P A)))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun P B))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_1) _let_4)) _let_2))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun P A))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_2 (tptp.fun P B)))) (let ((_let_6 (tptp.s _let_1 S0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P tptp.bool)))) (let ((_let_8 (tptp.s _let_7 P0))) (let ((_let_9 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_10 (tptp.s _let_9 L_L_))) (let ((_let_11 (tptp.fun _let_5 tptp.bool))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_7 _let_12))) (let ((_let_14 (tptp.fun _let_3 tptp.bool))) (let ((_let_15 (tptp.fun _let_1 _let_14))) (let ((_let_16 (tptp.fun _let_7 _let_15))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_9 _let_16) tptp.admissible) _let_10)) _let_8)) _let_6)) _let_4))) (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun P tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) P0) _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) L_L_) (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) T0) _let_4)) _let_1)))) (tptp.s A (tptp.i (tptp.s _let_2 S0) _let_1)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_9 _let_13) tptp.admissible) _let_10)) _let_8)) _let_6)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4))))))))))))))))))))))))))) (forall ((Q80137 $$unsorted) (Q80138 $$unsorted) (Q80169 $$unsorted) (P $$unsorted) (Q80194 $$unsorted) (U_5 $$unsorted)) (=> (forall ((P0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80138 Q80169))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80194))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 K0))) (let ((_let_7 (tptp.s _let_5 H0))) (let ((_let_8 (tptp.fun P tptp.bool))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 P0))) (let ((_let_11 (tptp.fun Q80194 Q80194))) (let ((_let_12 (tptp.fun Q80194 _let_11))) (let ((_let_13 (tptp.fun _let_5 _let_5))) (let ((_let_14 (tptp.fun _let_5 _let_13))) (= (tptp.s Q80194 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_9 _let_14) U_5) _let_10)) _let_7)) _let_6)) _let_3)) _let_1)) (tptp.s Q80194 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.bool _let_12) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_1)))) (tptp.s Q80194 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) (tptp.s Q80194 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((P0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80138 Q80169))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P Q80194))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 K0))) (let ((_let_6 (tptp.s _let_4 H0))) (let ((_let_7 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_8 (tptp.s _let_7 P0))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_4) _let_8)) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_5) _let_8)) _let_6)) _let_5)) _let_2))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80138 Q80169))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) U_3) _let_6)) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80138 Q80169))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 U_2) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 U_3) _let_5)) _let_2)))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (P1 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80138 Q80169))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P1))) (let ((_let_7 (tptp.s _let_5 P0))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_7)) _let_6)) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (P1 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80138 Q80169))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 P1))) (let ((_let_6 (tptp.s _let_4 P0))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_0) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_1) _let_6)) _let_5)) _let_2)))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (P1 $$unsorted) (S0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun Q80138 Q80169))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P Q80194)))) (let ((_let_3 (tptp.s _let_2 K0))) (let ((_let_4 (tptp.s _let_2 H0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_6 (tptp.s _let_5 P1))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun P Q80137))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.s _let_5 P0))) (let ((_let_12 (tptp.fun Q80138 (tptp.fun Q80137 tptp.bool)))) (let ((_let_13 (tptp.s _let_12 L_L_))) (let ((_let_14 (tptp.fun _let_2 tptp.bool))) (let ((_let_15 (tptp.fun _let_9 _let_14))) (let ((_let_16 (tptp.fun _let_5 _let_15))) (let ((_let_17 (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) tptp.admissible) _let_13)))) (let ((_let_18 (tptp.fun _let_5 _let_5))) (let ((_let_19 (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_5 _let_18) U_0) _let_11)))) (let ((_let_20 (tptp.fun _let_5 tptp.bool))) (let ((_let_21 (tptp.fun _let_9 _let_20))) (let ((_let_22 (tptp.fun _let_5 _let_21))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_12 _let_22) tptp.admissible) _let_13)) _let_11)) _let_10)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_17 (tptp.s _let_5 (tptp.i _let_19 _let_6)))) _let_10)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_17 (tptp.s _let_5 (tptp.i _let_19 (tptp.s _let_5 (tptp.i (tptp.s _let_18 U_2) _let_6)))))) _let_10)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_17 _let_11)) _let_10)) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_4) _let_6)) _let_4)) _let_3))))))))))))))))))))))))))))))))))))))))) (forall ((Q80235 $$unsorted) (Q80236 $$unsorted) (Q80237 $$unsorted) (P $$unsorted) (Q80272 $$unsorted) (Q80269 $$unsorted) (U_3 $$unsorted)) (=> (forall ((E0 $$unsorted) (C0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80236 Q80237))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q80272 (tptp.fun Q80269 tptp.bool)))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 C0))) (let ((_let_8 (tptp.fun P Q80272))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 E0))) (let ((_let_11 (tptp.fun _let_4 Q80269))) (let ((_let_12 (tptp.fun P Q80269))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (= (tptp.s Q80269 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_9 _let_14) U_3) _let_10)) _let_7)) _let_3)) _let_1)) (tptp.s Q80269 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q80272 _let_11) tptp.u_match) (tptp.s Q80272 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((E0 $$unsorted) (C0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80236 Q80237))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q80272 (tptp.fun Q80269 tptp.bool)))))) (let ((_let_4 (tptp.s _let_3 C0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P Q80272)))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.fun P Q80269))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_2) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_3) _let_6)) _let_4)) _let_2)))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((C0 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80236 Q80237))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80272))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.fun Q80269 tptp.bool))) (let ((_let_8 (tptp.fun Q80272 _let_7))) (let ((_let_9 (tptp.fun P _let_8))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.s _let_10 C0))) (let ((_let_12 (tptp.fun P _let_7))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_5 _let_13))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_10 _let_14) U_1) _let_11)) _let_6)) _let_3)) _let_1)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_3)) _let_1)) (tptp.s Q80272 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80236 Q80237))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80272)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun Q80269 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q80272 _let_5))))) (let ((_let_7 (tptp.s _let_6 C0))) (let ((_let_8 (tptp.fun P _let_5))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_0) _let_7)) _let_4)) _let_2)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_1) _let_7)) _let_4)) _let_2))))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (E0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.fun Q80269 tptp.bool))) (let ((_let_2 (tptp.fun Q80236 Q80237))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P (tptp.fun Q80272 _let_1))))) (let ((_let_4 (tptp.s _let_3 C0))) (let ((_let_5 (tptp.fun _let_2 (tptp.fun P Q80272)))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P Q80269)))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun P Q80235))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun _let_2 (tptp.fun P tptp.bool)))) (let ((_let_12 (tptp.s _let_11 P0))) (let ((_let_13 (tptp.fun Q80236 (tptp.fun Q80235 tptp.bool)))) (let ((_let_14 (tptp.s _let_13 L_L_))) (let ((_let_15 (tptp.fun _let_7 tptp.bool))) (let ((_let_16 (tptp.fun _let_9 _let_15))) (let ((_let_17 (tptp.fun _let_11 _let_16))) (let ((_let_18 (tptp.fun _let_2 (tptp.fun P _let_1)))) (let ((_let_19 (tptp.fun _let_5 _let_18))) (let ((_let_20 (tptp.fun _let_18 tptp.bool))) (let ((_let_21 (tptp.fun _let_9 _let_20))) (let ((_let_22 (tptp.fun _let_11 _let_21))) (let ((_let_23 (tptp.fun _let_5 tptp.bool))) (let ((_let_24 (tptp.fun _let_9 _let_23))) (let ((_let_25 (tptp.fun _let_11 _let_24))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_23 (tptp.i (tptp.s _let_24 (tptp.i (tptp.s _let_25 (tptp.i (tptp.s (tptp.fun _let_13 _let_25) tptp.admissible) _let_14)) _let_12)) _let_10)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_13 _let_22) tptp.admissible) _let_14)) _let_12)) _let_10)) (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_3 _let_19) U_0) _let_4)) _let_6)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_13 _let_17) tptp.admissible) _let_14)) _let_12)) _let_10)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_2) _let_6)) _let_4)))))))))))))))))))))))))))))))))))))))) (forall ((Q80312 $$unsorted) (Q80391 $$unsorted) (Q80313 $$unsorted) (Q80375 $$unsorted) (P $$unsorted) (Q80401 $$unsorted) (U_9 $$unsorted)) (=> (forall ((C1 $$unsorted) (C2 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80313 Q80375))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q80401 (tptp.fun Q80391 tptp.bool)))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 C2))) (let ((_let_8 (tptp.s _let_6 C1))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.fun _let_6 _let_6))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_9) _let_8)) _let_7)) _let_3)) _let_1)) (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.u_seqpattern) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_8 _let_3)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))))))))))))))) (forall ((U_8 $$unsorted)) (=> (forall ((C1 $$unsorted) (C2 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80313 Q80375))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P (tptp.fun Q80401 (tptp.fun Q80391 tptp.bool))))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 C2))) (let ((_let_6 (tptp.s _let_4 C1))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_8) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_9) _let_6)) _let_5)) _let_2)))))))))))) (forall ((U_7 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80313 Q80375))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P Q80401)))) (let ((_let_8 (tptp.fun _let_2 (tptp.fun P (tptp.fun Q80401 (tptp.fun Q80391 tptp.bool)))))) (let ((_let_9 (tptp.fun _let_7 _let_5))) (let ((_let_10 (tptp.fun _let_8 _let_9))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_7) _let_6)) (tptp.s _let_8 C1))) (tptp.s _let_7 E0))) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))) (not (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80313 Q80375))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80401))) (let ((_let_5 (tptp.fun Q80391 tptp.bool))) (let ((_let_6 (tptp.fun Q80401 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q80401 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q80391 Y)))))))))))))))))))))))))) (forall ((U_6 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80313 Q80375))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80401)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q80401 (tptp.fun Q80391 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_8 P0))) (let ((_let_10 (tptp.fun _let_3 _let_8))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_6) _let_9)) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_7) _let_9)) _let_6)) _let_4)) _let_2)))))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80313 Q80375))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80401))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.fun Q80391 tptp.bool))) (let ((_let_8 (tptp.fun Q80401 _let_7))) (let ((_let_9 (tptp.fun P _let_8))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.s _let_10 C1))) (let ((_let_12 (tptp.fun P _let_7))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_5 _let_13))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_10 _let_14) U_5) _let_11)) _let_6)) _let_3)) _let_1)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_3)) _let_1)) (tptp.s Q80401 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80313 Q80375))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80401)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun Q80391 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q80401 _let_5))))) (let ((_let_7 (tptp.s _let_6 C1))) (let ((_let_8 (tptp.fun P _let_5))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_4) _let_7)) _let_4)) _let_2)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_5) _let_7)) _let_4)) _let_2))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80313 Q80375))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P Q80401)))) (let ((_let_8 (tptp.fun _let_2 (tptp.fun P (tptp.fun Q80401 (tptp.fun Q80391 tptp.bool)))))) (let ((_let_9 (tptp.fun _let_7 _let_5))) (let ((_let_10 (tptp.fun _let_8 _let_9))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_3) _let_6)) (tptp.s _let_8 C1))) (tptp.s _let_7 E0))) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80313 Q80375))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80401))) (let ((_let_5 (tptp.fun Q80391 tptp.bool))) (let ((_let_6 (tptp.fun Q80401 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q80401 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q80391 Y))))))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80313 Q80375))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80401)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q80401 (tptp.fun Q80391 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_8 P0))) (let ((_let_10 (tptp.fun _let_3 _let_8))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_2) _let_9)) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_3) _let_9)) _let_6)) _let_4)) _let_2)))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q80313 Q80375))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P Q80401)))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q80401 (tptp.fun Q80391 tptp.bool)))))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_1) (tptp.s _let_3 C1))) (tptp.s _let_2 E0))) (tptp.s _let_1 F0))) (tptp.s P X)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80313 Q80375))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80401))) (let ((_let_5 (tptp.fun Q80391 tptp.bool))) (let ((_let_6 (tptp.fun Q80401 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q80401 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q80391 Y)))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80313 Q80375))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80401)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q80401 (tptp.fun Q80391 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_0) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_1) _let_6)) _let_4)) _let_2)))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (C1 $$unsorted) (C2 $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.fun Q80313 Q80375))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P Q80401)))) (let ((_let_3 (tptp.s _let_2 E0))) (let ((_let_4 (tptp.fun Q80391 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q80401 _let_4))))) (let ((_let_6 (tptp.s _let_5 C2))) (let ((_let_7 (tptp.s _let_5 C1))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (let ((_let_9 (tptp.fun _let_1 (tptp.fun P _let_4)))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.s (tptp.fun _let_5 _let_10) U_4))) (let ((_let_12 (tptp.fun P Q80312))) (let ((_let_13 (tptp.s _let_12 S0))) (let ((_let_14 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_15 (tptp.s _let_14 P0))) (let ((_let_16 (tptp.fun Q80313 (tptp.fun Q80312 tptp.bool)))) (let ((_let_17 (tptp.s _let_16 L_L_))) (let ((_let_18 (tptp.fun _let_9 tptp.bool))) (let ((_let_19 (tptp.fun _let_12 _let_18))) (let ((_let_20 (tptp.fun _let_14 _let_19))) (let ((_let_21 (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_16 _let_20) tptp.admissible) _let_17)))) (let ((_let_22 (tptp.fun _let_2 _let_14))) (let ((_let_23 (tptp.fun _let_5 _let_22))) (let ((_let_24 (tptp.fun _let_14 _let_23))) (let ((_let_25 (tptp.fun _let_14 tptp.bool))) (let ((_let_26 (tptp.fun _let_12 _let_25))) (let ((_let_27 (tptp.fun _let_14 _let_26))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_25 (tptp.i (tptp.s _let_26 (tptp.i (tptp.s _let_27 (tptp.i (tptp.s (tptp.fun _let_16 _let_27) tptp.admissible) _let_17)) _let_15)) _let_13)) (tptp.s _let_14 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s _let_23 U_0) _let_7)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i _let_21 (tptp.s _let_14 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s _let_23 (tptp.i (tptp.s _let_24 U_2) _let_15)) _let_7)) _let_3)))) _let_13)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_7)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i _let_21 (tptp.s _let_14 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s _let_23 (tptp.i (tptp.s _let_24 U_6) _let_15)) _let_7)) _let_3)))) _let_13)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_6)) _let_3)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i _let_21 _let_15)) _let_13)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_8) _let_7)) _let_6)))) _let_3)))))))))))))))))))))))))))))))))))))))))))))))))))))) (forall ((Q80486 $$unsorted) (Q80567 $$unsorted) (Q80487 $$unsorted) (Q80534 $$unsorted) (P $$unsorted) (Q80574 $$unsorted) (U_3 $$unsorted)) (=> (forall ((PAT $$unsorted) (E0 $$unsorted) (T0 $$unsorted) (Y $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80487 Q80534))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80574))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 Y))) (let ((_let_7 (tptp.s _let_5 T0))) (let ((_let_8 (tptp.fun Q80574 tptp.bool))) (let ((_let_9 (tptp.fun P Q80567))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.s _let_10 E0))) (let ((_let_12 (tptp.s _let_10 PAT))) (let ((_let_13 (tptp.fun Q80567 tptp.bool))) (let ((_let_14 (tptp.fun tptp.bool tptp.bool))) (let ((_let_15 (tptp.fun P tptp.bool))) (let ((_let_16 (tptp.fun _let_2 _let_15))) (let ((_let_17 (tptp.fun _let_5 _let_16))) (let ((_let_18 (tptp.fun _let_5 _let_17))) (let ((_let_19 (tptp.fun _let_10 _let_18))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_10 _let_19) U_3) _let_12)) _let_11)) _let_7)) _let_6)) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.bool _let_14) tptp.u_unguardedu_pattern) (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun Q80567 _let_13) tptp.geq) (tptp.s Q80567 (tptp.i (tptp.s _let_9 (tptp.i _let_12 _let_3)) _let_1)))) (tptp.s Q80567 (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_3)) _let_1)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q80574 _let_8) tptp.geq) (tptp.s Q80574 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) (tptp.s Q80574 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))))))))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((PAT $$unsorted) (E0 $$unsorted) (T0 $$unsorted) (Y $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80487 Q80534))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80574)))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.s _let_3 T0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P Q80567)))) (let ((_let_7 (tptp.s _let_6 E0))) (let ((_let_8 (tptp.s _let_6 PAT))) (let ((_let_9 (tptp.fun P tptp.bool))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun _let_6 _let_12))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 U_2) _let_8)) _let_7)) _let_5)) _let_4)) _let_2)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 U_3) _let_8)) _let_7)) _let_5)) _let_4)) _let_2)))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (PAT $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80487 Q80534))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80567))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.s _let_5 PAT))) (let ((_let_8 (tptp.fun P tptp.bool))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 P0))) (let ((_let_11 (tptp.fun _let_5 _let_9))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) U_1) _let_10)) _let_7)) _let_6)) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_1))) (= (tptp.s Q80567 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)) (tptp.s Q80567 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (PAT $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80487 Q80534))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80567)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.s _let_3 PAT))) (let ((_let_6 (tptp.fun P tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s _let_7 P0))) (let ((_let_9 (tptp.fun _let_3 _let_7))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_0) _let_8)) _let_5)) _let_4)) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_1) _let_8)) _let_5)) _let_4)) _let_2))))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (PAT $$unsorted) (E0 $$unsorted) (T0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun Q80487 Q80534))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P Q80574)))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.s _let_2 T0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P Q80567)))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.s _let_5 PAT))) (let ((_let_8 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun P Q80486))) (let ((_let_13 (tptp.s _let_12 S0))) (let ((_let_14 (tptp.s _let_8 P0))) (let ((_let_15 (tptp.fun Q80487 (tptp.fun Q80486 tptp.bool)))) (let ((_let_16 (tptp.s _let_15 L_L_))) (let ((_let_17 (tptp.fun _let_8 tptp.bool))) (let ((_let_18 (tptp.fun _let_12 _let_17))) (let ((_let_19 (tptp.fun _let_8 _let_18))) (let ((_let_20 (tptp.fun _let_5 _let_8))) (let ((_let_21 (tptp.fun _let_5 _let_20))) (let ((_let_22 (tptp.fun _let_2 tptp.bool))) (let ((_let_23 (tptp.fun _let_12 _let_22))) (let ((_let_24 (tptp.fun _let_8 _let_23))) (let ((_let_25 (tptp.s _let_22 (tptp.i (tptp.s _let_23 (tptp.i (tptp.s _let_24 (tptp.i (tptp.s (tptp.fun _let_15 _let_24) tptp.admissible) _let_16)) (tptp.s _let_8 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun _let_8 _let_21) U_0) _let_14)) _let_7)) _let_6)))) _let_13)))) (let ((_let_26 (tptp.fun _let_5 tptp.bool))) (let ((_let_27 (tptp.fun _let_12 _let_26))) (let ((_let_28 (tptp.fun _let_8 _let_27))) (let ((_let_29 (tptp.s _let_26 (tptp.i (tptp.s _let_27 (tptp.i (tptp.s _let_28 (tptp.i (tptp.s (tptp.fun _let_15 _let_28) tptp.admissible) _let_16)) _let_14)) _let_13)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_29 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_29 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_25 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_25 _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_15 _let_19) tptp.admissible) _let_16)) _let_14)) _let_13)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_5 _let_11) U_2) _let_7)) _let_6)) _let_4)) _let_3)))))))))))))))))))))))))))))))))))))))))))) (forall ((Q80660 $$unsorted) (Q80776 $$unsorted) (Q80661 $$unsorted) (Q80738 $$unsorted) (P $$unsorted) (Q80785 $$unsorted) (U_5 $$unsorted)) (=> (forall ((PAT $$unsorted) (E0 $$unsorted) (Q0 $$unsorted) (T0 $$unsorted) (Y $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80661 Q80738))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80785))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 Y))) (let ((_let_7 (tptp.s _let_5 T0))) (let ((_let_8 (tptp.fun Q80785 tptp.bool))) (let ((_let_9 (tptp.fun P tptp.bool))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.s _let_10 Q0))) (let ((_let_12 (tptp.fun P Q80776))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.s _let_13 E0))) (let ((_let_15 (tptp.s _let_13 PAT))) (let ((_let_16 (tptp.fun Q80776 tptp.bool))) (let ((_let_17 (tptp.fun tptp.bool tptp.bool))) (let ((_let_18 (tptp.fun tptp.bool _let_17))) (let ((_let_19 (tptp.fun _let_5 _let_10))) (let ((_let_20 (tptp.fun _let_5 _let_19))) (let ((_let_21 (tptp.fun _let_10 _let_20))) (let ((_let_22 (tptp.fun _let_13 _let_21))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_13 _let_22) U_5) _let_15)) _let_14)) _let_11)) _let_7)) _let_6)) _let_3)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun tptp.bool _let_18) tptp.u_guardedu_pattern) (tptp.s tptp.bool (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun Q80776 _let_16) tptp.geq) (tptp.s Q80776 (tptp.i (tptp.s _let_12 (tptp.i _let_15 _let_3)) _let_1)))) (tptp.s Q80776 (tptp.i (tptp.s _let_12 (tptp.i _let_14 _let_3)) _let_1)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_3)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q80785 _let_8) tptp.geq) (tptp.s Q80785 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) (tptp.s Q80785 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((PAT $$unsorted) (E0 $$unsorted) (Q0 $$unsorted) (T0 $$unsorted) (Y $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80661 Q80738))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80785)))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.s _let_3 T0))) (let ((_let_6 (tptp.fun P tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s _let_7 Q0))) (let ((_let_9 (tptp.fun _let_1 (tptp.fun P Q80776)))) (let ((_let_10 (tptp.s _let_9 E0))) (let ((_let_11 (tptp.s _let_9 PAT))) (let ((_let_12 (tptp.fun _let_3 _let_7))) (let ((_let_13 (tptp.fun _let_3 _let_12))) (let ((_let_14 (tptp.fun _let_7 _let_13))) (let ((_let_15 (tptp.fun _let_9 _let_14))) (let ((_let_16 (tptp.fun _let_9 _let_15))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 U_4) _let_11)) _let_10)) _let_8)) _let_5)) _let_4)) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 U_5) _let_11)) _let_10)) _let_8)) _let_5)) _let_4)) _let_2)))))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((P0 $$unsorted) (PAT $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80661 Q80738))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q80776))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.s _let_5 PAT))) (let ((_let_8 (tptp.fun P tptp.bool))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 P0))) (let ((_let_11 (tptp.fun _let_5 _let_9))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) U_3) _let_10)) _let_7)) _let_6)) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_1))) (= (tptp.s Q80776 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)) (tptp.s Q80776 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (PAT $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80661 Q80738))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q80776)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.s _let_3 PAT))) (let ((_let_6 (tptp.fun P tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s _let_7 P0))) (let ((_let_9 (tptp.fun _let_3 _let_7))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_2) _let_8)) _let_5)) _let_4)) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_3) _let_8)) _let_5)) _let_4)) _let_2))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (PAT $$unsorted) (E0 $$unsorted) (Q0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q80661 Q80738))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 Q0))) (let ((_let_7 (tptp.fun P Q80776))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.s _let_8 E0))) (let ((_let_10 (tptp.s _let_8 PAT))) (let ((_let_11 (tptp.s _let_5 P0))) (let ((_let_12 (tptp.fun _let_5 _let_5))) (let ((_let_13 (tptp.fun _let_8 _let_12))) (let ((_let_14 (tptp.fun _let_8 _let_13))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_5 _let_14) U_1) _let_11)) _let_10)) _let_9)) _let_6)) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_11 _let_3)) _let_1))) (= (tptp.s Q80776 (tptp.i (tptp.s _let_7 (tptp.i _let_10 _let_3)) _let_1)) (tptp.s Q80776 (tptp.i (tptp.s _let_7 (tptp.i _let_9 _let_3)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (PAT $$unsorted) (E0 $$unsorted) (Q0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q80661 Q80738))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 Q0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P Q80776)))) (let ((_let_7 (tptp.s _let_6 E0))) (let ((_let_8 (tptp.s _let_6 PAT))) (let ((_let_9 (tptp.s _let_4 P0))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (let ((_let_12 (tptp.fun _let_6 _let_11))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 U_0) _let_9)) _let_8)) _let_7)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 U_1) _let_9)) _let_8)) _let_7)) _let_5)) _let_2))))))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (PAT $$unsorted) (Q0 $$unsorted) (E0 $$unsorted) (T0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun Q80661 Q80738))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P Q80785)))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.s _let_2 T0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_6 (tptp.s _let_5 Q0))) (let ((_let_7 (tptp.fun _let_1 (tptp.fun P Q80776)))) (let ((_let_8 (tptp.s _let_7 E0))) (let ((_let_9 (tptp.s _let_7 PAT))) (let ((_let_10 (tptp.fun _let_2 _let_5))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (let ((_let_13 (tptp.fun _let_7 _let_12))) (let ((_let_14 (tptp.fun P Q80660))) (let ((_let_15 (tptp.s _let_14 S0))) (let ((_let_16 (tptp.s _let_5 P0))) (let ((_let_17 (tptp.fun Q80661 (tptp.fun Q80660 tptp.bool)))) (let ((_let_18 (tptp.s _let_17 L_L_))) (let ((_let_19 (tptp.fun _let_5 tptp.bool))) (let ((_let_20 (tptp.fun _let_14 _let_19))) (let ((_let_21 (tptp.fun _let_5 _let_20))) (let ((_let_22 (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun _let_17 _let_21) tptp.admissible) _let_18)))) (let ((_let_23 (tptp.fun _let_5 _let_5))) (let ((_let_24 (tptp.fun _let_7 _let_23))) (let ((_let_25 (tptp.fun _let_7 _let_24))) (let ((_let_26 (tptp.fun _let_2 tptp.bool))) (let ((_let_27 (tptp.fun _let_14 _let_26))) (let ((_let_28 (tptp.fun _let_5 _let_27))) (let ((_let_29 (tptp.s _let_26 (tptp.i (tptp.s _let_27 (tptp.i (tptp.s _let_28 (tptp.i (tptp.s (tptp.fun _let_17 _let_28) tptp.admissible) _let_18)) (tptp.s _let_5 (tptp.i (tptp.s _let_23 (tptp.i (tptp.s _let_24 (tptp.i (tptp.s _let_25 (tptp.i (tptp.s (tptp.fun _let_5 _let_25) U_0) _let_16)) _let_9)) _let_8)) _let_6)))) _let_15)))) (let ((_let_30 (tptp.fun _let_7 _let_5))) (let ((_let_31 (tptp.fun _let_7 _let_30))) (let ((_let_32 (tptp.fun _let_7 tptp.bool))) (let ((_let_33 (tptp.fun _let_14 _let_32))) (let ((_let_34 (tptp.fun _let_5 _let_33))) (let ((_let_35 (tptp.s _let_32 (tptp.i (tptp.s _let_33 (tptp.i (tptp.s _let_34 (tptp.i (tptp.s (tptp.fun _let_17 _let_34) tptp.admissible) _let_18)) _let_16)) _let_15)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_35 _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i _let_35 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i _let_29 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i _let_22 (tptp.s _let_5 (tptp.i (tptp.s _let_30 (tptp.i (tptp.s _let_31 (tptp.i (tptp.s (tptp.fun _let_5 _let_31) U_2) _let_16)) _let_9)) _let_8)))) _let_15)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_29 _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i _let_22 _let_16)) _let_15)) (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_7 _let_13) U_4) _let_9)) _let_8)) _let_6)) _let_4)) _let_3)))))))))))))))))))))))))))))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (P $$unsorted) (U_6 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (H0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun B C))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 H0))) (let ((_let_8 (tptp.fun P tptp.num))) (let ((_let_9 (tptp.s _let_8 B0))) (let ((_let_10 (tptp.s _let_8 A5))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_4 tptp.num))) (let ((_let_14 (tptp.fun _let_2 _let_8))) (let ((_let_15 (tptp.fun _let_6 _let_14))) (let ((_let_16 (tptp.fun _let_8 _let_15))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_8 _let_16) U_6) _let_10)) _let_9)) _let_7)) _let_3)) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.nsum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_10 _let_1)))) (tptp.s tptp.num (tptp.i _let_9 _let_1)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))))))))))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (H0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun tptp.num tptp.num))))) (let ((_let_4 (tptp.s _let_3 H0))) (let ((_let_5 (tptp.fun P tptp.num))) (let ((_let_6 (tptp.s _let_5 B0))) (let ((_let_7 (tptp.s _let_5 A5))) (let ((_let_8 (tptp.fun _let_1 _let_5))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_5) _let_7)) _let_6)) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_6) _let_7)) _let_6)) _let_4)) _let_2))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.num P) tptp.num))) (let ((_let_2 (tptp.fun B C))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P (tptp.fun tptp.num tptp.num))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_4) (tptp.s _let_3 H0))) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.s P X))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.prod tptp.num P))) (let ((_let_7 (tptp.fun P _let_6))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.geq) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) F1) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.c_) _let_1)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) H0) (tptp.s _let_3 F0))) _let_2)) _let_1))))))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun tptp.num tptp.num))))) (let ((_let_4 (tptp.s _let_3 H0))) (let ((_let_5 (tptp.fun (tptp.prod tptp.num P) tptp.num))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_3) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_4) _let_4)) _let_2)))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.num P) A))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_2) (tptp.s _let_2 S0))) (tptp.s _let_1 F0)))) (forall ((K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.prod tptp.num P))) (let ((_let_3 (tptp.fun P _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.geq) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) F0) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.c_) (tptp.s tptp.num K0))) _let_1)))))) (tptp.s A (tptp.i (tptp.s (tptp.fun P A) S0) _let_1))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.num P) tptp.bool))) (let ((_let_2 (tptp.fun B C))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P tptp.bool)))) (let ((_let_4 (tptp.fun P tptp.num))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) (tptp.s _let_4 A5))) (tptp.s _let_4 B0))) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((K0 $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s P X))) (let ((_let_3 (tptp.s tptp.num K0))) (let ((_let_4 (tptp.prod tptp.num P))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun B C))) (let ((_let_8 (tptp.fun P tptp.bool))) (let ((_let_9 (tptp.fun P tptp.num))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.l_a_))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_9 A5) _let_2)))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 B0) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) P0) (tptp.s _let_7 F0))) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.c_) _let_3)) _let_2)))))) _let_1))))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun P tptp.num))) (let ((_let_6 (tptp.s _let_5 B0))) (let ((_let_7 (tptp.s _let_5 A5))) (let ((_let_8 (tptp.fun (tptp.prod tptp.num P) tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (let ((_let_13 (tptp.fun _let_1 _let_8))) (let ((_let_14 (tptp.fun _let_3 _let_13))) (let ((_let_15 (tptp.fun _let_5 _let_14))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_5 _let_15) U_0) _let_7)) _let_6)) _let_4)) _let_2)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_9 _let_8) tptp.gabs) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) U_1) _let_7)) _let_6)) _let_4)) _let_2))))))))))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (H0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P (tptp.fun tptp.num tptp.num))))) (let ((_let_3 (tptp.s _let_2 H0))) (let ((_let_4 (tptp.fun P tptp.num))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.s _let_4 A5))) (let ((_let_7 (tptp.fun _let_1 _let_4))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun P A))) (let ((_let_11 (tptp.s _let_10 S0))) (let ((_let_12 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_13 (tptp.s _let_12 P0))) (let ((_let_14 (tptp.fun B (tptp.fun A tptp.bool)))) (let ((_let_15 (tptp.s _let_14 L_L_))) (let ((_let_16 (tptp.fun _let_7 tptp.bool))) (let ((_let_17 (tptp.fun _let_10 _let_16))) (let ((_let_18 (tptp.fun _let_12 _let_17))) (let ((_let_19 (tptp.prod tptp.num P))) (let ((_let_20 (tptp.fun _let_1 (tptp.fun _let_19 tptp.num)))) (let ((_let_21 (tptp.fun _let_19 A))) (let ((_let_22 (tptp.fun _let_21 tptp.bool))) (let ((_let_23 (tptp.fun _let_1 (tptp.fun _let_19 tptp.bool)))) (let ((_let_24 (tptp.fun _let_12 _let_23))) (let ((_let_25 (tptp.fun _let_4 _let_24))) (let ((_let_26 (tptp.fun _let_20 tptp.bool))) (let ((_let_27 (tptp.fun _let_21 _let_26))) (let ((_let_28 (tptp.fun _let_23 _let_27))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_26 (tptp.i (tptp.s _let_27 (tptp.i (tptp.s _let_28 (tptp.i (tptp.s (tptp.fun _let_14 _let_28) tptp.admissible) _let_15)) (tptp.s _let_23 (tptp.i (tptp.s _let_24 (tptp.i (tptp.s _let_25 (tptp.i (tptp.s (tptp.fun _let_4 _let_25) U_0) _let_6)) _let_5)) _let_13)))) (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun _let_22 _let_21) tptp.gabs) (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_10 _let_22) U_2) _let_11)))))) (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_2 _let_20) U_3) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_14 _let_18) tptp.admissible) _let_15)) _let_13)) _let_11)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) U_5) _let_6)) _let_5)) _let_3))))))))))))))))))))))))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (P $$unsorted) (U_6 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (H0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun B C))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 H0))) (let ((_let_8 (tptp.fun P tptp.num))) (let ((_let_9 (tptp.s _let_8 B0))) (let ((_let_10 (tptp.s _let_8 A5))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_4 tptp.real))) (let ((_let_14 (tptp.fun P tptp.real))) (let ((_let_15 (tptp.fun _let_2 _let_14))) (let ((_let_16 (tptp.fun _let_6 _let_15))) (let ((_let_17 (tptp.fun _let_8 _let_16))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_8 _let_17) U_6) _let_10)) _let_9)) _let_7)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_10 _let_1)))) (tptp.s tptp.num (tptp.i _let_9 _let_1)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1))))))))))))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (H0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun tptp.num tptp.real))))) (let ((_let_4 (tptp.s _let_3 H0))) (let ((_let_5 (tptp.fun P tptp.num))) (let ((_let_6 (tptp.s _let_5 B0))) (let ((_let_7 (tptp.s _let_5 A5))) (let ((_let_8 (tptp.fun P tptp.real))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_5) _let_7)) _let_6)) _let_4)) _let_2)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_6) _let_7)) _let_6)) _let_4)) _let_2)))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.num P) tptp.real))) (let ((_let_2 (tptp.fun B C))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P (tptp.fun tptp.num tptp.real))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_4) (tptp.s _let_3 H0))) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.s P X))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.prod tptp.num P))) (let ((_let_7 (tptp.fun P _let_6))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.geq) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_6 tptp.real) F1) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.c_) _let_1)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) H0) (tptp.s _let_3 F0))) _let_2)) _let_1))))))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun tptp.num tptp.real))))) (let ((_let_4 (tptp.s _let_3 H0))) (let ((_let_5 (tptp.fun (tptp.prod tptp.num P) tptp.real))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_3) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_4) _let_4)) _let_2)))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.num P) A))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_2) (tptp.s _let_2 S0))) (tptp.s _let_1 F0)))) (forall ((K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.prod tptp.num P))) (let ((_let_3 (tptp.fun P _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.geq) (tptp.s A (tptp.i (tptp.s (tptp.fun _let_2 A) F0) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.c_) (tptp.s tptp.num K0))) _let_1)))))) (tptp.s A (tptp.i (tptp.s (tptp.fun P A) S0) _let_1))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod tptp.num P) tptp.bool))) (let ((_let_2 (tptp.fun B C))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P tptp.bool)))) (let ((_let_4 (tptp.fun P tptp.num))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) (tptp.s _let_4 A5))) (tptp.s _let_4 B0))) (tptp.s _let_3 P0))) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((K0 $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s P X))) (let ((_let_3 (tptp.s tptp.num K0))) (let ((_let_4 (tptp.prod tptp.num P))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun B C))) (let ((_let_8 (tptp.fun P tptp.bool))) (let ((_let_9 (tptp.fun P tptp.num))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.l_a_))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_9 A5) _let_2)))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_9 B0) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) P0) (tptp.s _let_7 F0))) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.c_) _let_3)) _let_2)))))) _let_1))))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun P tptp.num))) (let ((_let_6 (tptp.s _let_5 B0))) (let ((_let_7 (tptp.s _let_5 A5))) (let ((_let_8 (tptp.fun (tptp.prod tptp.num P) tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (let ((_let_13 (tptp.fun _let_1 _let_8))) (let ((_let_14 (tptp.fun _let_3 _let_13))) (let ((_let_15 (tptp.fun _let_5 _let_14))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_5 _let_15) U_0) _let_7)) _let_6)) _let_4)) _let_2)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_9 _let_8) tptp.gabs) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) U_1) _let_7)) _let_6)) _let_4)) _let_2))))))))))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (H0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun B C))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P (tptp.fun tptp.num tptp.real))))) (let ((_let_3 (tptp.s _let_2 H0))) (let ((_let_4 (tptp.fun P tptp.num))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.s _let_4 A5))) (let ((_let_7 (tptp.fun _let_1 (tptp.fun P tptp.real)))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun P A))) (let ((_let_11 (tptp.s _let_10 S0))) (let ((_let_12 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_13 (tptp.s _let_12 P0))) (let ((_let_14 (tptp.fun B (tptp.fun A tptp.bool)))) (let ((_let_15 (tptp.s _let_14 L_L_))) (let ((_let_16 (tptp.fun _let_7 tptp.bool))) (let ((_let_17 (tptp.fun _let_10 _let_16))) (let ((_let_18 (tptp.fun _let_12 _let_17))) (let ((_let_19 (tptp.prod tptp.num P))) (let ((_let_20 (tptp.fun _let_1 (tptp.fun _let_19 tptp.real)))) (let ((_let_21 (tptp.fun _let_19 A))) (let ((_let_22 (tptp.fun _let_21 tptp.bool))) (let ((_let_23 (tptp.fun _let_1 (tptp.fun _let_19 tptp.bool)))) (let ((_let_24 (tptp.fun _let_12 _let_23))) (let ((_let_25 (tptp.fun _let_4 _let_24))) (let ((_let_26 (tptp.fun _let_20 tptp.bool))) (let ((_let_27 (tptp.fun _let_21 _let_26))) (let ((_let_28 (tptp.fun _let_23 _let_27))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_26 (tptp.i (tptp.s _let_27 (tptp.i (tptp.s _let_28 (tptp.i (tptp.s (tptp.fun _let_14 _let_28) tptp.admissible) _let_15)) (tptp.s _let_23 (tptp.i (tptp.s _let_24 (tptp.i (tptp.s _let_25 (tptp.i (tptp.s (tptp.fun _let_4 _let_25) U_0) _let_6)) _let_5)) _let_13)))) (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun _let_22 _let_21) tptp.gabs) (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_10 _let_22) U_2) _let_11)))))) (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_2 _let_20) U_3) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_14 _let_18) tptp.admissible) _let_15)) _let_13)) _let_11)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) U_5) _let_6)) _let_5)) _let_3))))))))))))))))))))))))))))))))))))))))))))))))) (forall ((Q81078 $$unsorted) (Q81087 $$unsorted) (A $$unsorted) (B $$unsorted) (P $$unsorted) (Q81093 $$unsorted) (U_6 $$unsorted)) (=> (forall ((H0 $$unsorted) (L $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.list Q81093))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.fun Q81093 Q81087))) (let ((_let_9 (tptp.fun P _let_8))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.s _let_10 H0))) (let ((_let_12 (tptp.list Q81087))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (let ((_let_14 (tptp.fun P _let_12))) (let ((_let_15 (tptp.fun _let_2 _let_14))) (let ((_let_16 (tptp.fun _let_6 _let_15))) (= (tptp.s _let_12 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_10 _let_16) U_6) _let_11)) _let_7)) _let_3)) _let_1)) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_8 _let_13) tptp.map0) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_3)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))))))))))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((H0 $$unsorted) (L $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.list Q81093))))) (let ((_let_4 (tptp.s _let_3 L))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81093 Q81087))))) (let ((_let_6 (tptp.s _let_5 H0))) (let ((_let_7 (tptp.fun P (tptp.list Q81087)))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_5) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_6) _let_6)) _let_4)) _let_2)))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q81093 P) Q81087))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P (tptp.fun Q81093 Q81087))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_4) (tptp.s _let_3 H0))) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q81093 Y))) (let ((_let_2 (tptp.s P X))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun Q81093 Q81087))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.prod Q81093 P))) (let ((_let_7 (tptp.fun P _let_6))) (let ((_let_8 (tptp.fun Q81087 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q81087 _let_8) tptp.geq) (tptp.s Q81087 (tptp.i (tptp.s (tptp.fun _let_6 Q81087) F1) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q81093 _let_7) tptp.c_) _let_1)) _let_2)))))) (tptp.s Q81087 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) H0) (tptp.s _let_3 F0))) _let_2)) _let_1))))))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81093 Q81087))))) (let ((_let_4 (tptp.s _let_3 H0))) (let ((_let_5 (tptp.fun (tptp.prod Q81093 P) Q81087))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_3) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_4) _let_4)) _let_2)))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q81093 P) Q81078))) (let ((_let_2 (tptp.fun P Q81078))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_2) (tptp.s _let_2 S0))) (tptp.s _let_1 F0)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.prod Q81093 P))) (let ((_let_3 (tptp.fun P _let_2))) (let ((_let_4 (tptp.fun Q81078 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q81078 _let_4) tptp.geq) (tptp.s Q81078 (tptp.i (tptp.s (tptp.fun _let_2 Q81078) F0) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q81093 _let_3) tptp.c_) (tptp.s Q81093 Y))) _let_1)))))) (tptp.s Q81078 (tptp.i (tptp.s (tptp.fun P Q81078) S0) _let_1))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (L $$unsorted) (F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q81093 P) tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_2 (tptp.fun P (tptp.list Q81093))))) (let ((_let_4 (tptp.fun _let_2 (tptp.fun P tptp.bool)))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_1) (tptp.s _let_4 P0))) (tptp.s _let_3 L))) (tptp.s _let_2 F0))) (tptp.s _let_1 F1)))) (forall ((Y $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s P X))) (let ((_let_3 (tptp.s Q81093 Y))) (let ((_let_4 (tptp.prod Q81093 P))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun A B))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.list Q81093))) (let ((_let_10 (tptp.fun P _let_9))) (let ((_let_11 (tptp.fun _let_9 tptp.bool))) (let ((_let_12 (tptp.fun P tptp.bool))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_7 _let_12) P0) _let_8)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q81093 _let_11) tptp.mem) _let_3)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) L) _let_8)) _let_2))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q81093 _let_5) tptp.c_) _let_3)) _let_2)))))) _let_1))))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (L $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.list Q81093))))) (let ((_let_4 (tptp.s _let_3 L))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun (tptp.prod Q81093 P) tptp.bool))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun _let_1 _let_7))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) U_0) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_8 _let_7) tptp.gabs) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_1) _let_6)) _let_4)) _let_2)))))))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (H0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P (tptp.list Q81093))))) (let ((_let_3 (tptp.s _let_2 L))) (let ((_let_4 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81093 Q81087))))) (let ((_let_5 (tptp.s _let_4 H0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P (tptp.list Q81087))))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun P Q81078))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_11 (tptp.s _let_10 P0))) (let ((_let_12 (tptp.fun A (tptp.fun Q81078 tptp.bool)))) (let ((_let_13 (tptp.s _let_12 L_L_))) (let ((_let_14 (tptp.fun _let_6 tptp.bool))) (let ((_let_15 (tptp.fun _let_8 _let_14))) (let ((_let_16 (tptp.fun _let_10 _let_15))) (let ((_let_17 (tptp.prod Q81093 P))) (let ((_let_18 (tptp.fun _let_1 (tptp.fun _let_17 Q81087)))) (let ((_let_19 (tptp.fun _let_17 Q81078))) (let ((_let_20 (tptp.fun _let_19 tptp.bool))) (let ((_let_21 (tptp.fun _let_1 (tptp.fun _let_17 tptp.bool)))) (let ((_let_22 (tptp.fun _let_2 _let_21))) (let ((_let_23 (tptp.fun _let_18 tptp.bool))) (let ((_let_24 (tptp.fun _let_19 _let_23))) (let ((_let_25 (tptp.fun _let_21 _let_24))) (let ((_let_26 (tptp.fun _let_2 tptp.bool))) (let ((_let_27 (tptp.fun _let_8 _let_26))) (let ((_let_28 (tptp.fun _let_10 _let_27))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_26 (tptp.i (tptp.s _let_27 (tptp.i (tptp.s _let_28 (tptp.i (tptp.s (tptp.fun _let_12 _let_28) tptp.admissible) _let_13)) _let_11)) _let_9)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_23 (tptp.i (tptp.s _let_24 (tptp.i (tptp.s _let_25 (tptp.i (tptp.s (tptp.fun _let_12 _let_25) tptp.admissible) _let_13)) (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_10 _let_22) U_0) _let_11)) _let_3)))) (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_20 _let_19) tptp.gabs) (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_8 _let_20) U_2) _let_9)))))) (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_4 _let_18) U_3) _let_5)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) tptp.admissible) _let_13)) _let_11)) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_5) _let_5)) _let_3))))))))))))))))))))))))))))))))))))))))))))))))) (forall ((Q81150 $$unsorted) (Q81151 $$unsorted) (Q81216 $$unsorted) (P $$unsorted) (Q81271 $$unsorted) (Q81240 $$unsorted) (U_9 $$unsorted)) (=> (forall ((C1 $$unsorted) (C2 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81151 Q81216))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 C2))) (let ((_let_8 (tptp.s _let_6 C1))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.fun _let_6 _let_6))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_9) _let_8)) _let_7)) _let_3)) _let_1)) (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.u_seqpattern) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_8 _let_3)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))))))))))))))) (forall ((U_8 $$unsorted)) (=> (forall ((C1 $$unsorted) (C2 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81151 Q81216))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool))))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 C2))) (let ((_let_6 (tptp.s _let_4 C1))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_8) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_9) _let_6)) _let_5)) _let_2)))))))))))) (forall ((U_7 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81151 Q81216))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P Q81271)))) (let ((_let_8 (tptp.fun _let_2 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))))) (let ((_let_9 (tptp.fun _let_7 _let_5))) (let ((_let_10 (tptp.fun _let_8 _let_9))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_7) _let_6)) (tptp.s _let_8 C1))) (tptp.s _let_7 E0))) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))) (not (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81151 Q81216))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q81271))) (let ((_let_5 (tptp.fun Q81240 tptp.bool))) (let ((_let_6 (tptp.fun Q81271 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q81271 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q81240 Y)))))))))))))))))))))))))) (forall ((U_6 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81151 Q81216))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q81271)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_8 P0))) (let ((_let_10 (tptp.fun _let_3 _let_8))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_6) _let_9)) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_7) _let_9)) _let_6)) _let_4)) _let_2)))))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((E0 $$unsorted) (C1 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81151 Q81216))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 C1))) (let ((_let_8 (tptp.fun P Q81271))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 E0))) (let ((_let_11 (tptp.fun _let_4 Q81240))) (let ((_let_12 (tptp.fun P Q81240))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (= (tptp.s Q81240 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_9 _let_14) U_5) _let_10)) _let_7)) _let_3)) _let_1)) (tptp.s Q81240 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q81271 _let_11) tptp.u_match) (tptp.s Q81271 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))))))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((E0 $$unsorted) (C1 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81151 Q81216))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))))) (let ((_let_4 (tptp.s _let_3 C1))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P Q81271)))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.fun P Q81240))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_4) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_5) _let_6)) _let_4)) _let_2)))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81151 Q81216))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P Q81271)))) (let ((_let_8 (tptp.fun _let_2 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))))) (let ((_let_9 (tptp.fun _let_7 _let_5))) (let ((_let_10 (tptp.fun _let_8 _let_9))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_3) _let_6)) (tptp.s _let_8 C1))) (tptp.s _let_7 E0))) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81151 Q81216))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q81271))) (let ((_let_5 (tptp.fun Q81240 tptp.bool))) (let ((_let_6 (tptp.fun Q81271 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q81271 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q81240 Y))))))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81151 Q81216))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q81271)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_8 P0))) (let ((_let_10 (tptp.fun _let_3 _let_8))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_2) _let_9)) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_3) _let_9)) _let_6)) _let_4)) _let_2)))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q81151 Q81216))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P Q81271)))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_1) (tptp.s _let_3 C1))) (tptp.s _let_2 E0))) (tptp.s _let_1 F0))) (tptp.s P X)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81151 Q81216))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q81271))) (let ((_let_5 (tptp.fun Q81240 tptp.bool))) (let ((_let_6 (tptp.fun Q81271 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q81271 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q81240 Y)))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81151 Q81216))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q81271)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_0) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_1) _let_6)) _let_4)) _let_2)))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (C1 $$unsorted) (C2 $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.fun Q81151 Q81216))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81271 (tptp.fun Q81240 tptp.bool)))))) (let ((_let_3 (tptp.s _let_2 C2))) (let ((_let_4 (tptp.s _let_2 C1))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P Q81271)))) (let ((_let_7 (tptp.s _let_6 E0))) (let ((_let_8 (tptp.fun _let_1 (tptp.fun P Q81240)))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_4) _let_7)))) (let ((_let_11 (tptp.fun P Q81150))) (let ((_let_12 (tptp.s _let_11 S0))) (let ((_let_13 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_14 (tptp.s _let_13 P0))) (let ((_let_15 (tptp.fun Q81151 (tptp.fun Q81150 tptp.bool)))) (let ((_let_16 (tptp.s _let_15 L_L_))) (let ((_let_17 (tptp.fun _let_8 tptp.bool))) (let ((_let_18 (tptp.fun _let_11 _let_17))) (let ((_let_19 (tptp.fun _let_13 _let_18))) (let ((_let_20 (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_15 _let_19) tptp.admissible) _let_16)))) (let ((_let_21 (tptp.fun _let_6 _let_13))) (let ((_let_22 (tptp.fun _let_2 _let_21))) (let ((_let_23 (tptp.fun _let_13 _let_22))) (let ((_let_24 (tptp.fun _let_13 tptp.bool))) (let ((_let_25 (tptp.fun _let_11 _let_24))) (let ((_let_26 (tptp.fun _let_13 _let_25))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_24 (tptp.i (tptp.s _let_25 (tptp.i (tptp.s _let_26 (tptp.i (tptp.s (tptp.fun _let_15 _let_26) tptp.admissible) _let_16)) _let_14)) _let_12)) (tptp.s _let_13 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 U_0) _let_4)) _let_7))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i _let_20 (tptp.s _let_13 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s _let_23 U_2) _let_14)) _let_4)) _let_7)))) _let_12)) (tptp.s _let_8 (tptp.i _let_10 _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i _let_20 (tptp.s _let_13 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s _let_23 U_6) _let_14)) _let_4)) _let_7)))) _let_12)) (tptp.s _let_8 (tptp.i _let_10 _let_3)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i _let_20 _let_14)) _let_12)) (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_8) _let_4)) _let_3))))))))))))))))))))))))))))))))))))))))))))))))))))))) (forall ((A $$unsorted) (P $$unsorted) (B $$unsorted) (L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P B)))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun P A))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_7 (tptp.s _let_6 P0))) (let ((_let_8 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_9 (tptp.s _let_8 L_L_))) (let ((_let_10 (tptp.fun _let_2 tptp.bool))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (let ((_let_12 (tptp.fun _let_6 _let_11))) (let ((_let_13 (tptp.fun _let_8 _let_12))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.admissible) _let_9)) _let_7)) _let_5)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.superadmissible) _let_9)) _let_7)) _let_5)) _let_3)))))))))))))))))) (forall ((Q81350 $$unsorted) (Q81351 $$unsorted) (Q81352 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81351 Q81352))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.fun Q81350 Q81352))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2)) (tptp.s _let_3 F0))) _let_2)))))) (forall ((P0 $$unsorted) (S0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.fun Q81351 Q81352))) (let ((_let_2 (tptp.fun Q81350 Q81352))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun Q81351 Q81350))) (let ((_let_5 (tptp.fun _let_2 (tptp.fun Q81351 tptp.bool)))) (let ((_let_6 (tptp.fun Q81350 (tptp.fun Q81350 tptp.bool)))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.fun _let_5 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.superadmissible) (tptp.s _let_6 tptp.l_l_))) (tptp.s _let_5 P0))) (tptp.s _let_4 S0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 C0)))))))))))))))))) (forall ((B $$unsorted) (P $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P A))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 T0))) (let ((_let_7 (tptp.fun P B))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s B (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_6)) _let_3)) _let_1)) (tptp.s B (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P A)))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun P B))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_1) _let_4)) _let_2))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun P A))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_2 (tptp.fun P B)))) (let ((_let_6 (tptp.s _let_1 S0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P tptp.bool)))) (let ((_let_8 (tptp.s _let_7 P0))) (let ((_let_9 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_10 (tptp.s _let_9 L_L_))) (let ((_let_11 (tptp.fun _let_5 tptp.bool))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_7 _let_12))) (let ((_let_14 (tptp.fun _let_3 tptp.bool))) (let ((_let_15 (tptp.fun _let_1 _let_14))) (let ((_let_16 (tptp.fun _let_7 _let_15))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_9 _let_16) tptp.admissible) _let_10)) _let_8)) _let_6)) _let_4))) (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun P tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) P0) (tptp.s _let_1 F0))) (tptp.s P A5)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) L_L_) (tptp.s A Y))))) (let ((_let_5 (tptp.fun A B))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) T0) (tptp.s _let_5 F0))) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s A (tptp.i (tptp.s _let_2 S0) _let_1))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_9 _let_13) tptp.superadmissible) _let_10)) _let_8)) _let_6)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4))))))))))))))))))))))))))) (forall ((A $$unsorted) (P $$unsorted) (B $$unsorted) (U_5 $$unsorted)) (=> (forall ((P0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P B))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 K0))) (let ((_let_7 (tptp.s _let_5 H0))) (let ((_let_8 (tptp.fun P tptp.bool))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 P0))) (let ((_let_11 (tptp.fun B B))) (let ((_let_12 (tptp.fun B _let_11))) (let ((_let_13 (tptp.fun _let_5 _let_5))) (let ((_let_14 (tptp.fun _let_5 _let_13))) (= (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_9 _let_14) U_5) _let_10)) _let_7)) _let_6)) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.bool _let_12) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_1)))) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1)))) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((P0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P B))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 K0))) (let ((_let_6 (tptp.s _let_4 H0))) (let ((_let_7 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_8 (tptp.s _let_7 P0))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_4) _let_8)) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_5) _let_8)) _let_6)) _let_5)) _let_2))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) U_3) _let_6)) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 U_2) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 U_3) _let_5)) _let_2)))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (P1 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P1))) (let ((_let_7 (tptp.s _let_5 P0))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_7)) _let_6)) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (P1 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 P1))) (let ((_let_6 (tptp.s _let_4 P0))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_0) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_1) _let_6)) _let_5)) _let_2)))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (P1 $$unsorted) (S0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P B)))) (let ((_let_3 (tptp.s _let_2 K0))) (let ((_let_4 (tptp.s _let_2 H0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_6 (tptp.s _let_5 P1))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun P A))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.s _let_5 P0))) (let ((_let_12 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_13 (tptp.s _let_12 L_L_))) (let ((_let_14 (tptp.fun _let_2 tptp.bool))) (let ((_let_15 (tptp.fun _let_9 _let_14))) (let ((_let_16 (tptp.fun _let_5 _let_15))) (let ((_let_17 (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) tptp.superadmissible) _let_13)))) (let ((_let_18 (tptp.fun _let_5 _let_5))) (let ((_let_19 (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_5 _let_18) U_0) _let_11)))) (let ((_let_20 (tptp.fun _let_5 tptp.bool))) (let ((_let_21 (tptp.fun _let_9 _let_20))) (let ((_let_22 (tptp.fun _let_5 _let_21))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_12 _let_22) tptp.admissible) _let_13)) _let_11)) _let_10)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_17 (tptp.s _let_5 (tptp.i _let_19 _let_6)))) _let_10)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_17 (tptp.s _let_5 (tptp.i _let_19 (tptp.s _let_5 (tptp.i (tptp.s _let_18 U_2) _let_6)))))) _let_10)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_17 _let_11)) _let_10)) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_4) _let_6)) _let_4)) _let_3))))))))))))))))))))))))))))))))))))))))) (forall ((Q81671 $$unsorted) (P $$unsorted) (Q81786 $$unsorted) (Q81787 $$unsorted) (U_9 $$unsorted)) (=> (forall ((C1 $$unsorted) (C2 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81671 Q81787))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 C2))) (let ((_let_8 (tptp.s _let_6 C1))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.fun _let_6 _let_6))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_9) _let_8)) _let_7)) _let_3)) _let_1)) (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.u_seqpattern) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_8 _let_3)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))))))))))))))) (forall ((U_8 $$unsorted)) (=> (forall ((C1 $$unsorted) (C2 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81671 Q81787))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun P (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool))))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 C2))) (let ((_let_6 (tptp.s _let_4 C1))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_8) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_9) _let_6)) _let_5)) _let_2)))))))))))) (forall ((U_7 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81671 Q81787))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P Q81786)))) (let ((_let_8 (tptp.fun _let_2 (tptp.fun P (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))))) (let ((_let_9 (tptp.fun _let_7 _let_5))) (let ((_let_10 (tptp.fun _let_8 _let_9))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_7) _let_6)) (tptp.s _let_8 C1))) (tptp.s _let_7 E0))) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))) (not (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81671 Q81787))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q81786))) (let ((_let_5 (tptp.fun Q81787 tptp.bool))) (let ((_let_6 (tptp.fun Q81786 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q81786 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q81787 Y)))))))))))))))))))))))))) (forall ((U_6 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81671 Q81787))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q81786)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_8 P0))) (let ((_let_10 (tptp.fun _let_3 _let_8))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_6) _let_9)) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_7) _let_9)) _let_6)) _let_4)) _let_2)))))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((E0 $$unsorted) (C1 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81671 Q81787))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 C1))) (let ((_let_8 (tptp.fun P Q81786))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.s _let_9 E0))) (let ((_let_11 (tptp.fun _let_4 Q81787))) (let ((_let_12 (tptp.fun P Q81787))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (= (tptp.s Q81787 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_9 _let_14) U_5) _let_10)) _let_7)) _let_3)) _let_1)) (tptp.s Q81787 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q81786 _let_11) tptp.u_match) (tptp.s Q81786 (tptp.i (tptp.s _let_8 (tptp.i _let_10 _let_3)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_1)))))))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((E0 $$unsorted) (C1 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81671 Q81787))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))))) (let ((_let_4 (tptp.s _let_3 C1))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P Q81786)))) (let ((_let_6 (tptp.s _let_5 E0))) (let ((_let_7 (tptp.fun P Q81787))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_4) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_5) _let_6)) _let_4)) _let_2)))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81671 Q81787))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_2 (tptp.fun P Q81786)))) (let ((_let_8 (tptp.fun _let_2 (tptp.fun P (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))))) (let ((_let_9 (tptp.fun _let_7 _let_5))) (let ((_let_10 (tptp.fun _let_8 _let_9))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_3) _let_6)) (tptp.s _let_8 C1))) (tptp.s _let_7 E0))) _let_3)) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81671 Q81787))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q81786))) (let ((_let_5 (tptp.fun Q81787 tptp.bool))) (let ((_let_6 (tptp.fun Q81786 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q81786 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q81787 Y))))))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81671 Q81787))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q81786)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_8 P0))) (let ((_let_10 (tptp.fun _let_3 _let_8))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_2) _let_9)) _let_6)) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 U_3) _let_9)) _let_6)) _let_4)) _let_2)))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q81671 Q81787))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P Q81786)))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))))) (let ((_let_4 (tptp.fun P tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_1) (tptp.s _let_3 C1))) (tptp.s _let_2 E0))) (tptp.s _let_1 F0))) (tptp.s P X)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun Q81671 Q81787))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P Q81786))) (let ((_let_5 (tptp.fun Q81787 tptp.bool))) (let ((_let_6 (tptp.fun Q81786 _let_5))) (let ((_let_7 (tptp.fun P _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) C1) _let_3)) _let_1)) (tptp.s Q81786 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) E0) _let_3)) _let_1)))) (tptp.s Q81787 Y)))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C1 $$unsorted) (E0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q81671 Q81787))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 (tptp.fun P Q81786)))) (let ((_let_4 (tptp.s _let_3 E0))) (let ((_let_5 (tptp.fun _let_1 (tptp.fun P (tptp.fun Q81786 (tptp.fun Q81787 tptp.bool)))))) (let ((_let_6 (tptp.s _let_5 C1))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_0) _let_6)) _let_4)) 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((_let_16 (tptp.s _let_15 L_L_))) (let ((_let_17 (tptp.fun _let_8 tptp.bool))) (let ((_let_18 (tptp.fun _let_11 _let_17))) (let ((_let_19 (tptp.fun _let_13 _let_18))) (let ((_let_20 (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_15 _let_19) tptp.superadmissible) _let_16)))) (let ((_let_21 (tptp.fun _let_6 _let_13))) (let ((_let_22 (tptp.fun _let_2 _let_21))) (let ((_let_23 (tptp.fun _let_13 _let_22))) (let ((_let_24 (tptp.fun _let_13 tptp.bool))) (let ((_let_25 (tptp.fun _let_11 _let_24))) (let ((_let_26 (tptp.fun _let_13 _let_25))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_24 (tptp.i (tptp.s _let_25 (tptp.i (tptp.s _let_26 (tptp.i (tptp.s (tptp.fun _let_15 _let_26) tptp.admissible) _let_16)) _let_14)) _let_12)) (tptp.s _let_13 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 U_0) _let_4)) _let_7))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i _let_20 (tptp.s _let_13 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s _let_23 U_2) _let_14)) _let_4)) _let_7)))) _let_12)) (tptp.s _let_8 (tptp.i _let_10 _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i _let_20 (tptp.s _let_13 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s _let_23 U_6) _let_14)) _let_4)) _let_7)))) _let_12)) (tptp.s _let_8 (tptp.i _let_10 _let_3)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i _let_20 _let_14)) _let_12)) (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_8) _let_4)) _let_3))))))))))))))))))))))))))))))))))))))))))))))))))))))) (forall ((B $$unsorted) (D $$unsorted) (P $$unsorted) (Q $$unsorted) (A $$unsorted) (U_3 $$unsorted)) (=> (forall ((PAT $$unsorted) (U $$unsorted) (F0 $$unsorted) (ARG $$unsorted) (X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun P (tptp.fun Q A)))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun Q D))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun P _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun D _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_3) (tptp.s _let_3 PAT))) (tptp.s D U))) (tptp.s _let_2 F0))) (tptp.s _let_1 ARG))) (tptp.s P X))) (tptp.s B V)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.s Q T0))) (let ((_let_2 (tptp.fun Q A))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun D tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.bool _let_5) tptp.u_unguardedu_pattern) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun D _let_4) tptp.geq) (tptp.s D (tptp.i (tptp.s (tptp.fun Q D) PAT) _let_1)))) (tptp.s D U))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.geq) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun P _let_2) ARG) (tptp.s P X))) _let_1)))))) (tptp.s B V)))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((PAT $$unsorted) (F0 $$unsorted) (ARG $$unsorted) (X $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun P (tptp.fun Q A)))) (let ((_let_3 (tptp.s _let_2 ARG))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s D U))) (let ((_let_7 (tptp.fun Q D))) (let ((_let_8 (tptp.s _let_7 PAT))) (let ((_let_9 (tptp.fun B tptp.bool))) (let ((_let_10 (tptp.fun P _let_9))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun _let_4 _let_11))) (let ((_let_13 (tptp.fun D _let_12))) (let ((_let_14 (tptp.fun D _let_9))) (let ((_let_15 (tptp.fun P _let_14))) (let ((_let_16 (tptp.fun _let_2 _let_15))) (let ((_let_17 (tptp.fun _let_4 _let_16))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_7 _let_17) U_2) _let_8)) _let_5)) _let_3)) _let_1)) _let_6)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_7 _let_13) U_3) _let_8)) _let_6)) _let_5)) _let_3)) _let_1))))))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((E0 $$unsorted) (PAT $$unsorted) (F0 $$unsorted) (ARG $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun P (tptp.fun Q A)))) (let ((_let_3 (tptp.s _let_2 ARG))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q D))) (let ((_let_7 (tptp.s _let_6 PAT))) (let ((_let_8 (tptp.fun D (tptp.fun B tptp.bool)))) (let ((_let_9 (tptp.fun P _let_8))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (let ((_let_12 (tptp.fun P D))) (let ((_let_13 (tptp.s _let_12 E0))) (let ((_let_14 (tptp.fun _let_8 B))) (let ((_let_15 (tptp.fun P B))) (let ((_let_16 (tptp.fun _let_2 _let_15))) (let ((_let_17 (tptp.fun _let_4 _let_16))) (let ((_let_18 (tptp.fun _let_6 _let_17))) (= (tptp.s B (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_12 _let_18) U_1) _let_13)) _let_7)) _let_5)) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun D _let_14) tptp.u_match) (tptp.s D (tptp.i _let_13 _let_1)))) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_6 _let_11) U_2) _let_7)) _let_5)) _let_3)) _let_1)))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((E0 $$unsorted) (PAT $$unsorted) (ARG $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun P (tptp.fun Q A)))) (let ((_let_2 (tptp.s _let_1 ARG))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q D))) (let ((_let_6 (tptp.s _let_5 PAT))) (let ((_let_7 (tptp.fun P D))) (let ((_let_8 (tptp.s _let_7 E0))) (let ((_let_9 (tptp.fun P B))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (let ((_let_13 (tptp.fun _let_3 _let_9))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (let ((_let_15 (tptp.fun _let_5 _let_14))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_7 _let_15) U_0) _let_8)) _let_6)) _let_2)) _let_4)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_7 _let_12) U_1) _let_8)) _let_6)) _let_4)) _let_2))))))))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (E0 $$unsorted) (PAT $$unsorted) (ARG $$unsorted)) (let ((_let_1 (tptp.fun P (tptp.fun Q A)))) (let ((_let_2 (tptp.fun Q D))) (let ((_let_3 (tptp.fun P D))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.fun _let_4 (tptp.fun P B)))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun P A))) (let ((_let_9 (tptp.fun _let_4 (tptp.fun P tptp.bool)))) (let ((_let_10 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_11 (tptp.fun _let_5 tptp.bool))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (let ((_let_13 (tptp.fun _let_9 _let_12))) (=> (and (forall ((F0 $$unsorted) (A5 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.s Q U))) (let ((_let_2 (tptp.s P A5))) (let ((_let_3 (tptp.fun Q A))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun P _let_3) ARG) _let_2)))) (let ((_let_5 (tptp.s Q T0))) (let ((_let_6 (tptp.s D (tptp.i (tptp.s (tptp.fun P D) E0) _let_2)))) (let ((_let_7 (tptp.s (tptp.fun Q D) PAT))) (let ((_let_8 (tptp.fun A B))) (let ((_let_9 (tptp.fun P tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_8 _let_9) P0) (tptp.s _let_8 F0))) _let_2))) (= (tptp.s D (tptp.i _let_7 _let_5)) _let_6) (= (tptp.s D (tptp.i _let_7 _let_1)) _let_6)) (= (tptp.s A (tptp.i _let_4 _let_5)) (tptp.s A (tptp.i _let_4 _let_1)))))))))))))) (forall ((F0 $$unsorted) (A5 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun P tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) P0) (tptp.s _let_2 F0))) _let_1))) (= (tptp.s D (tptp.i (tptp.s (tptp.fun Q D) PAT) (tptp.s Q T0))) (tptp.s D (tptp.i (tptp.s (tptp.fun P D) E0) _let_1)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) L_L_) (tptp.s A Y))))) (let ((_let_4 (tptp.fun Q A))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun P _let_4) ARG) _let_1)) (tptp.s Q T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s (tptp.fun P A) S0) _let_1))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_10 _let_13) tptp.superadmissible) (tptp.s _let_10 L_L_))) (tptp.s _let_9 P0))) (tptp.s _let_8 S0))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) (tptp.s _let_3 E0))) (tptp.s _let_2 PAT))) (tptp.s _let_1 ARG))))))))))))))))))))))))))))) (forall ((B $$unsorted) (D $$unsorted) (P $$unsorted) (Q $$unsorted) (A $$unsorted) (U_3 $$unsorted)) (=> (forall ((PAT $$unsorted) (U $$unsorted) (Q0 $$unsorted) (F0 $$unsorted) (ARG $$unsorted) (X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun P (tptp.fun Q A)))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun P (tptp.fun Q tptp.bool)))) (let ((_let_4 (tptp.fun Q D))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun P _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun D _let_9))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) U_3) (tptp.s _let_4 PAT))) (tptp.s D U))) (tptp.s _let_3 Q0))) (tptp.s _let_2 F0))) (tptp.s _let_1 ARG))) (tptp.s P X))) (tptp.s B V)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.s Q T0))) (let ((_let_2 (tptp.s P X))) (let ((_let_3 (tptp.fun Q A))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun Q tptp.bool))) (let ((_let_6 (tptp.fun D tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.u_guardedu_pattern) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun D _let_6) tptp.geq) (tptp.s D (tptp.i (tptp.s (tptp.fun Q D) PAT) _let_1)))) (tptp.s D U))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun P _let_5) Q0) _let_2)) _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.geq) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun P _let_3) ARG) _let_2)) _let_1)))))) (tptp.s B V))))))))))))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((PAT $$unsorted) (Q0 $$unsorted) (F0 $$unsorted) (ARG $$unsorted) (X $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun P (tptp.fun Q A)))) (let ((_let_3 (tptp.s _let_2 ARG))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun P (tptp.fun Q tptp.bool)))) (let ((_let_7 (tptp.s _let_6 Q0))) (let ((_let_8 (tptp.s D U))) (let ((_let_9 (tptp.fun Q D))) (let ((_let_10 (tptp.s _let_9 PAT))) (let ((_let_11 (tptp.fun B tptp.bool))) (let ((_let_12 (tptp.fun P _let_11))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_4 _let_13))) (let ((_let_15 (tptp.fun _let_6 _let_14))) (let ((_let_16 (tptp.fun D _let_15))) (let ((_let_17 (tptp.fun D _let_11))) (let ((_let_18 (tptp.fun P _let_17))) (let ((_let_19 (tptp.fun _let_2 _let_18))) (let ((_let_20 (tptp.fun _let_4 _let_19))) (let ((_let_21 (tptp.fun _let_6 _let_20))) (= (tptp.s _let_11 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun _let_9 _let_21) U_2) _let_10)) _let_7)) _let_5)) _let_3)) _let_1)) _let_8)) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_9 _let_16) U_3) _let_10)) _let_8)) _let_7)) _let_5)) _let_3)) _let_1))))))))))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((E0 $$unsorted) (PAT $$unsorted) (Q0 $$unsorted) (F0 $$unsorted) (ARG $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun P (tptp.fun Q A)))) (let ((_let_3 (tptp.s _let_2 ARG))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun P (tptp.fun Q tptp.bool)))) (let ((_let_7 (tptp.s _let_6 Q0))) (let ((_let_8 (tptp.fun Q D))) (let ((_let_9 (tptp.s _let_8 PAT))) (let ((_let_10 (tptp.fun D (tptp.fun B tptp.bool)))) (let ((_let_11 (tptp.fun P _let_10))) (let ((_let_12 (tptp.fun _let_2 _let_11))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (let ((_let_15 (tptp.fun P D))) (let ((_let_16 (tptp.s _let_15 E0))) (let ((_let_17 (tptp.fun _let_10 B))) (let ((_let_18 (tptp.fun P B))) (let ((_let_19 (tptp.fun _let_2 _let_18))) (let ((_let_20 (tptp.fun _let_4 _let_19))) (let ((_let_21 (tptp.fun _let_6 _let_20))) (let ((_let_22 (tptp.fun _let_8 _let_21))) (= (tptp.s B (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_15 _let_22) U_1) _let_16)) _let_9)) _let_7)) _let_5)) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun D _let_17) tptp.u_match) (tptp.s D (tptp.i _let_16 _let_1)))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_8 _let_14) U_2) _let_9)) _let_7)) _let_5)) _let_3)) _let_1)))))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((E0 $$unsorted) (PAT $$unsorted) (Q0 $$unsorted) (ARG $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun P (tptp.fun Q A)))) (let ((_let_2 (tptp.s _let_1 ARG))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun P (tptp.fun Q tptp.bool)))) (let ((_let_6 (tptp.s _let_5 Q0))) (let ((_let_7 (tptp.fun Q D))) (let ((_let_8 (tptp.s _let_7 PAT))) (let ((_let_9 (tptp.fun P D))) (let ((_let_10 (tptp.s _let_9 E0))) (let ((_let_11 (tptp.fun P B))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_3 _let_12))) (let ((_let_14 (tptp.fun _let_5 _let_13))) (let ((_let_15 (tptp.fun _let_7 _let_14))) (let ((_let_16 (tptp.fun _let_3 _let_11))) (let ((_let_17 (tptp.fun _let_1 _let_16))) (let ((_let_18 (tptp.fun _let_5 _let_17))) (let ((_let_19 (tptp.fun _let_7 _let_18))) (= (tptp.s _let_11 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_9 _let_19) U_0) _let_10)) _let_8)) _let_6)) _let_2)) _let_4)) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_9 _let_15) U_1) _let_10)) _let_8)) _let_6)) _let_4)) _let_2))))))))))))))))))))))) (forall ((L_L_ $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (E0 $$unsorted) (PAT $$unsorted) (Q0 $$unsorted) (ARG $$unsorted)) (let ((_let_1 (tptp.fun P (tptp.fun Q A)))) (let ((_let_2 (tptp.fun P (tptp.fun Q tptp.bool)))) (let ((_let_3 (tptp.fun Q D))) (let ((_let_4 (tptp.fun P D))) (let ((_let_5 (tptp.fun A B))) (let ((_let_6 (tptp.fun _let_5 (tptp.fun P B)))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun P A))) (let ((_let_11 (tptp.fun _let_5 (tptp.fun P tptp.bool)))) (let ((_let_12 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_13 (tptp.fun _let_6 tptp.bool))) (let ((_let_14 (tptp.fun _let_10 _let_13))) (let ((_let_15 (tptp.fun _let_11 _let_14))) (=> (and (forall ((F0 $$unsorted) (A5 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.s Q U))) (let ((_let_2 (tptp.s P A5))) (let ((_let_3 (tptp.fun Q A))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun P _let_3) ARG) _let_2)))) (let ((_let_5 (tptp.s Q T0))) (let ((_let_6 (tptp.fun Q tptp.bool))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun P _let_6) Q0) _let_2)))) (let ((_let_8 (tptp.s D (tptp.i (tptp.s (tptp.fun P D) E0) _let_2)))) (let ((_let_9 (tptp.s (tptp.fun Q D) PAT))) (let ((_let_10 (tptp.fun A B))) (let ((_let_11 (tptp.fun P tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_10 _let_11) P0) (tptp.s _let_10 F0))) _let_2))) (= (tptp.s D (tptp.i _let_9 _let_5)) _let_8) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_5))) (= (tptp.s D (tptp.i _let_9 _let_1)) _let_8) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_1)))) (= (tptp.s A (tptp.i _let_4 _let_5)) (tptp.s A (tptp.i _let_4 _let_1)))))))))))))))) (forall ((F0 $$unsorted) (A5 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.s Q T0))) (let ((_let_3 (tptp.fun Q tptp.bool))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.fun P tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) P0) (tptp.s _let_4 F0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun P _let_3) Q0) _let_1)) _let_2))) (= (tptp.s D (tptp.i (tptp.s (tptp.fun Q D) PAT) _let_2)) (tptp.s D (tptp.i (tptp.s (tptp.fun P D) E0) _let_1)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) L_L_) (tptp.s A Y))))) (let ((_let_4 (tptp.fun Q A))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun P _let_4) ARG) _let_1)) (tptp.s Q T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s (tptp.fun P A) S0) _let_1))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_12 _let_15) tptp.superadmissible) (tptp.s _let_12 L_L_))) (tptp.s _let_11 P0))) (tptp.s _let_10 S0))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) U_0) (tptp.s _let_4 E0))) (tptp.s _let_3 PAT))) (tptp.s _let_2 Q0))) (tptp.s _let_1 ARG))))))))))))))))))))))))))))))) (forall ((Q82421 $$unsorted) (Q82424 $$unsorted) (P0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted) (HI_ $$unsorted)) (let ((_let_1 (tptp.fun Q82424 (tptp.fun Q82424 tptp.bool)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.wf) (tptp.s _let_1 tptp.l_l_)))) (forall ((F0 $$unsorted) (G1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q82424 X))) (let ((_let_2 (tptp.fun Q82424 Q82421))) (let ((_let_3 (tptp.s _let_2 G1))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_2) HI_))) (let ((_let_5 (tptp.s _let_2 F0))) (let ((_let_6 (tptp.fun Q82424 Q82424))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_6) G0))) (let ((_let_8 (tptp.fun Q82424 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_2 _let_8) P0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s Q82424 Z0))) (let ((_let_2 (tptp.fun Q82424 Q82421))) (let ((_let_3 (tptp.fun Q82424 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q82424 _let_3) tptp.l_l_) _let_1)) (tptp.s Q82424 X)))) (= (tptp.s Q82421 (tptp.i (tptp.s _let_2 F0) _let_1)) (tptp.s Q82421 (tptp.i (tptp.s _let_2 G1) _let_1)))))))) (and (= (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_1))) (= (tptp.s Q82424 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_1)) (tptp.s Q82424 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_1))) (= (tptp.s Q82421 (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_5)) _let_1)) (tptp.s Q82421 (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_3)) _let_1))))))))))))))) (forall ((F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q82424 X))) (let ((_let_2 (tptp.fun Q82424 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q82424 _let_2) tptp.l_l_) (tptp.s Q82424 Y))))) (let ((_let_4 (tptp.fun Q82424 Q82421))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q82424 Q82424))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) P0) _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s Q82424 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) G0) _let_5)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))))) (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q82424 X))) (let ((_let_2 (tptp.fun Q82424 Q82421))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun Q82424 Q82424))) (let ((_let_6 (tptp.fun Q82424 tptp.bool))) (let ((_let_7 (tptp.fun Q82421 Q82421))) (let ((_let_8 (tptp.fun Q82421 _let_7))) (= (tptp.s Q82421 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 H0) _let_3)) _let_1)) (tptp.s Q82421 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) P0) _let_3)) _let_1)))) (tptp.s Q82421 (tptp.i _let_3 (tptp.s Q82424 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) G0) _let_3)) _let_1)))))) (tptp.s Q82421 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_4 HI_) _let_3)) _let_1))))))))))))))) (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q82424 X))) (let ((_let_2 (tptp.fun Q82424 Q82421))) (let ((_let_3 (tptp.s _let_2 F0))) (= (tptp.s Q82421 (tptp.i _let_3 _let_1)) (tptp.s Q82421 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) H0) _let_3)) _let_1))))))))))) (forall ((P $$unsorted) (B $$unsorted) (A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L_L_ $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod (tptp.fun P A) (tptp.fun (tptp.fun A B) (tptp.fun P B))) tptp.bool))) (let ((_let_2 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 L_L_))) (tptp.s _let_1 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun (tptp.fun A B) (tptp.fun P B)))) (let ((_let_3 (tptp.fun P A))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (exists ((P0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (and (forall ((F1 $$unsorted) (A5 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun P A))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) L_L_) (tptp.s A Y))))) (let ((_let_5 (tptp.fun A B))) (let ((_let_6 (tptp.s _let_5 F1))) (let ((_let_7 (tptp.fun P tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) P0) _let_6)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s A (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) G0) _let_6)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s A (tptp.i (tptp.s _let_2 S0) _let_1)))))))))))))) (forall ((F1 $$unsorted) (G1 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 G1))) (let ((_let_4 (tptp.fun P B))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) H0))) (let ((_let_6 (tptp.s _let_2 F1))) (let ((_let_7 (tptp.fun P A))) (let ((_let_8 (tptp.s (tptp.fun _let_2 _let_7) G0))) (let ((_let_9 (tptp.fun P tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_2 _let_9) P0))) (=> (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) L_L_) _let_1)) (tptp.s A (tptp.i (tptp.s (tptp.fun P A) S0) (tptp.s P A5)))))) (= (tptp.s B (tptp.i (tptp.s _let_2 F1) _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 G1) _let_1)))))))) (and (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_6)) _let_1)) (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) _let_1))) (= (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_1)) (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_1))) (= (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)))))))))))))))) (forall ((F1 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s P A5))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F1))) (let ((_let_4 (tptp.fun P B))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun P A))) (let ((_let_7 (tptp.fun P tptp.bool))) (let ((_let_8 (tptp.fun B B))) (let ((_let_9 (tptp.fun B _let_8))) (= (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 T0) _let_3)) _let_1)) (tptp.s B (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) P0) _let_3)) _let_1)))) (tptp.s B (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) G0) _let_3)) _let_1)))))) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 H0) _let_3)) _let_1)))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))))))) _let_1))))))))))))))))) (forall ((L_L_ $$unsorted) (CLAUSES $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun P A) (tptp.fun (tptp.fun A B) (tptp.fun P B))))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_4 (tptp.s _let_3 L_L_))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.wf) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.all0) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))))) (tptp.s _let_2 CLAUSES))))) (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.list (tptp.prod (tptp.fun P A) (tptp.fun _let_2 (tptp.fun P B)))))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.casewise) (tptp.s _let_4 CLAUSES))) _let_3)) _let_1))))))))))))))))))))) (forall ((Q82753 $$unsorted) (B $$unsorted) (A $$unsorted) (U_2 $$unsorted)) (=> (forall ((A5 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q82753 tptp.bool) U_2) (tptp.s Q82753 A5))) (tptp.s tptp.bool tptp.t))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q82753 tptp.bool))) (let ((_let_2 (tptp.fun A B))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_1) (tptp.s _let_2 F0))) (tptp.s _let_1 U_2))))) (forall ((U_0 $$unsorted)) (=> (forall ((L_L_ $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod (tptp.fun Q82753 A) (tptp.fun (tptp.fun A B) (tptp.fun Q82753 B))) tptp.bool))) (let ((_let_2 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 L_L_))) (tptp.s _let_1 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun Q82753 B)))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun Q82753 A))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun Q82753 tptp.bool)))) (let ((_let_7 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (let ((_let_11 (tptp.prod _let_4 _let_2))) (let ((_let_12 (tptp.fun _let_2 _let_11))) (let ((_let_13 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.bool _let_13) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_11 tptp.bool) F0) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.c_) _let_5)) _let_3)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.tailadmissible) (tptp.s _let_7 L_L_))) (tptp.s _let_6 U_1))) _let_5)) _let_3)))))))))))))))))))))))) (forall ((L_L_ $$unsorted) (CLAUSES $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun Q82753 A) (tptp.fun (tptp.fun A B) (tptp.fun Q82753 B))))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_4 (tptp.s _let_3 L_L_))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.wf) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.all0) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))))) (tptp.s _let_2 CLAUSES))))) (exists ((F0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.list (tptp.prod (tptp.fun Q82753 A) (tptp.fun _let_2 (tptp.fun Q82753 B)))))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (= (tptp.s B (tptp.i _let_3 _let_1)) (tptp.s B (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.casewise) (tptp.s _let_4 CLAUSES))) _let_3)) _let_1))))))))))))))))))))))))) (forall ((A $$unsorted) (P $$unsorted) (B $$unsorted) (U_3 $$unsorted)) (=> (forall ((F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun (tptp.prod (tptp.fun P A) (tptp.fun _let_1 (tptp.fun P B))) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_3) (tptp.s _let_1 F0))) (tptp.s _let_2 F1)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun (tptp.fun A B) (tptp.fun P B)))) (let ((_let_3 (tptp.fun P A))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s P X))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P B))) (= (tptp.s B (tptp.i _let_3 (tptp.s A (tptp.i (tptp.s (tptp.fun P A) S0) _let_1)))) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) T0) _let_3)) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))))))) _let_1))))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((A5 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun P tptp.bool) U_2) (tptp.s P A5))) (tptp.s tptp.bool tptp.t))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun P tptp.bool))) (let ((_let_2 (tptp.fun A B))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_1) (tptp.s _let_2 F0))) (tptp.s _let_1 U_2))))) (forall ((U_0 $$unsorted)) (=> (forall ((L_L_ $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod (tptp.fun P A) (tptp.fun (tptp.fun A B) (tptp.fun P B))) tptp.bool))) (let ((_let_2 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 L_L_))) (tptp.s _let_1 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun P B)))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun P A))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun P tptp.bool)))) (let ((_let_7 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (let ((_let_11 (tptp.prod _let_4 _let_2))) (let ((_let_12 (tptp.fun _let_2 _let_11))) (let ((_let_13 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.bool _let_13) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_11 tptp.bool) F0) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.c_) _let_5)) _let_3)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.tailadmissible) (tptp.s _let_7 L_L_))) (tptp.s _let_6 U_1))) _let_5)) _let_3)))))))))))))))))))))))) (forall ((CLAUSES $$unsorted)) (=> (and (exists ((L_L_ $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun P A) (tptp.fun (tptp.fun A B) (tptp.fun P B))))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.fun A (tptp.fun A tptp.bool)))) (let ((_let_4 (tptp.s _let_3 L_L_))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.wf) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.all0) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))))) (tptp.s _let_2 CLAUSES))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted) (SI_ $$unsorted) (TI_ $$unsorted) (F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s P Y))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun P B))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 TI_))) (let ((_let_7 (tptp.s P X))) (let ((_let_8 (tptp.s _let_5 T0))) (let ((_let_9 (tptp.fun P A))) (let ((_let_10 (tptp.s _let_9 SI_))) (let ((_let_11 (tptp.s _let_9 S0))) (let ((_let_12 (tptp.prod _let_9 _let_5))) (let ((_let_13 (tptp.list _let_12))) (let ((_let_14 (tptp.s _let_13 CLAUSES))) (let ((_let_15 (tptp.fun _let_5 _let_12))) (let ((_let_16 (tptp.s (tptp.fun _let_9 _let_15) tptp.c_))) (let ((_let_17 (tptp.fun _let_13 tptp.bool))) (let ((_let_18 (tptp.s (tptp.fun _let_12 _let_17) tptp.mem))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i _let_18 (tptp.s _let_12 (tptp.i (tptp.s _let_15 (tptp.i _let_16 _let_11)) _let_8)))) _let_14))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i _let_18 (tptp.s _let_12 (tptp.i (tptp.s _let_15 (tptp.i _let_16 _let_10)) _let_6)))) _let_14)))) (=> (= (tptp.s A (tptp.i _let_11 _let_7)) (tptp.s A (tptp.i _let_10 _let_1))) (= (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_8 _let_3)) _let_7)) (tptp.s B (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1))))))))))))))))))))))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.prod (tptp.fun P A) (tptp.fun _let_1 (tptp.fun P B))))) (let ((_let_3 (tptp.list _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.all0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_3) (tptp.s _let_1 F0))))))) (tptp.s _let_3 CLAUSES))))))))))))))))))))) (forall ((Q83010 $$unsorted) (Q83030 $$unsorted) (Q83026 $$unsorted) (U_6 $$unsorted)) (=> (forall ((F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun Q83010 Q83026))) (let ((_let_2 (tptp.fun (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun _let_1 (tptp.fun Q83030 Q83026))) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_6) (tptp.s _let_1 F0))) (tptp.s _let_2 F1)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_3 (tptp.fun Q83030 Q83010))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q83030 X))) (let ((_let_2 (tptp.fun Q83010 Q83026))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q83030 Q83026))) (= (tptp.s Q83026 (tptp.i _let_3 (tptp.s Q83010 (tptp.i (tptp.s (tptp.fun Q83030 Q83010) S0) _let_1)))) (tptp.s Q83026 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) T0) _let_3)) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))))))) _let_1))))))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_2 (tptp.fun Q83030 Q83010))) (let ((_let_3 (tptp.fun (tptp.prod _let_2 _let_1) tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_5) (tptp.s _let_2 S0))) (tptp.s _let_1 T0))) (tptp.s _let_3 F0)))) (forall ((SI_ $$unsorted) (TI_ $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_3 (tptp.fun Q83030 Q83010))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (forall ((F1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q83030 Y))) (let ((_let_2 (tptp.fun Q83010 Q83026))) (let ((_let_3 (tptp.s _let_2 F1))) (let ((_let_4 (tptp.fun Q83030 Q83026))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s Q83030 X))) (let ((_let_7 (tptp.fun Q83030 Q83010))) (=> (= (tptp.s Q83010 (tptp.i (tptp.s _let_7 S0) _let_6)) (tptp.s Q83010 (tptp.i (tptp.s _let_7 SI_) _let_1))) (= (tptp.s Q83026 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 T0) _let_3)) _let_6)) (tptp.s Q83026 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 TI_) _let_3)) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 SI_))) (tptp.s _let_2 TI_))))))) _let_1))))))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun _let_1 tptp.bool)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) U_4) (tptp.s _let_2 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q83030 Q83010))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.prod _let_3 _let_1))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_1 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.geq) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.c_) _let_4)) _let_2)))))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.gabs) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_5) _let_4)) _let_2))))))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_3) (tptp.s _let_1 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_3 (tptp.fun Q83030 Q83010))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (forall ((F1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q83030 Y))) (let ((_let_2 (tptp.fun Q83010 Q83026))) (let ((_let_3 (tptp.fun Q83030 Q83026))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) T0) (tptp.s _let_2 F1))))) (let ((_let_5 (tptp.s Q83030 X))) (let ((_let_6 (tptp.s (tptp.fun Q83030 Q83010) S0))) (=> (= (tptp.s Q83010 (tptp.i _let_6 _let_5)) (tptp.s Q83010 (tptp.i _let_6 _let_1))) (= (tptp.s Q83026 (tptp.i _let_4 _let_5)) (tptp.s Q83026 (tptp.i _let_4 _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))))))) _let_1))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((A5 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q83030 tptp.bool) U_2) (tptp.s Q83030 A5))) (tptp.s tptp.bool tptp.t))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q83030 tptp.bool))) (let ((_let_2 (tptp.fun Q83010 Q83026))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_1) (tptp.s _let_2 F0))) (tptp.s _let_1 U_2))))) (forall ((U_0 $$unsorted)) (=> (forall ((L_L_ $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))) tptp.bool))) (let ((_let_2 (tptp.fun Q83010 (tptp.fun Q83010 tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 L_L_))) (tptp.s _let_1 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q83010 Q83026))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun Q83030 Q83026)))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun Q83030 Q83010))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun Q83030 tptp.bool)))) (let ((_let_7 (tptp.fun Q83010 (tptp.fun Q83010 tptp.bool)))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (let ((_let_11 (tptp.prod _let_4 _let_2))) (let ((_let_12 (tptp.fun _let_2 _let_11))) (let ((_let_13 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.bool _let_13) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_11 tptp.bool) F0) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.c_) _let_5)) _let_3)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.tailadmissible) (tptp.s _let_7 L_L_))) (tptp.s _let_6 U_1))) _let_5)) _let_3)))))))))))))))))))))))) (forall ((CLAUSES $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.s _let_2 CLAUSES))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (=> (and (exists ((L_L_ $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.fun Q83010 (tptp.fun Q83010 tptp.bool)))) (let ((_let_4 (tptp.s _let_3 L_L_))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.wf) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.all0) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))))) (tptp.s _let_2 CLAUSES))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.all0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_8 _let_4) tptp.gabs) (tptp.s _let_8 U_3))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.pairwise0) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 U_4))))) _let_3)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q83010 Q83026))) (let ((_let_2 (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun _let_1 (tptp.fun Q83030 Q83026))))) (let ((_let_3 (tptp.list _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.all0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_6) (tptp.s _let_1 F0))))))) (tptp.s _let_3 CLAUSES))))))))))))))))))))))))))))))))))) (forall ((Q83140 $$unsorted) (Q83146 $$unsorted) (Q83142 $$unsorted) (U_1 $$unsorted)) (=> (forall ((X $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q83146 tptp.bool) U_1) (tptp.s Q83146 X))) (tptp.s tptp.bool tptp.t))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun Q83140 Q83142))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun Q83146 Q83142)))) (let ((_let_3 (tptp.s _let_2 tptp.t0))) (let ((_let_4 (tptp.fun Q83146 Q83140))) (let ((_let_5 (tptp.s _let_4 tptp.s0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun Q83146 tptp.bool)))) (let ((_let_7 (tptp.s _let_6 U_0))) (let ((_let_8 (tptp.fun Q83140 (tptp.fun Q83140 tptp.bool)))) (let ((_let_9 (tptp.s _let_8 tptp.l_l_))) (let ((_let_10 (tptp.fun _let_2 tptp.bool))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (let ((_let_12 (tptp.fun _let_6 _let_11))) (let ((_let_13 (tptp.fun _let_8 _let_12))) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q83146 tptp.bool))) (let ((_let_2 (tptp.fun Q83140 Q83142))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 U_1))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.superadmissible) _let_9)) _let_7)) _let_5)) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 tptp.tailadmissible) _let_9)) _let_7)) _let_5)) _let_3)))))))))))))))))))) (forall ((Q83010 $$unsorted) (Q83030 $$unsorted) (Q83026 $$unsorted) (U_6 $$unsorted)) (=> (forall ((F0 $$unsorted) (F1 $$unsorted)) (let ((_let_1 (tptp.fun Q83010 Q83026))) (let ((_let_2 (tptp.fun (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun _let_1 (tptp.fun Q83030 Q83026))) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_6) (tptp.s _let_1 F0))) (tptp.s _let_2 F1)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_3 (tptp.fun Q83030 Q83010))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q83030 X))) (let ((_let_2 (tptp.fun Q83010 Q83026))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q83030 Q83026))) (= (tptp.s Q83026 (tptp.i _let_3 (tptp.s Q83010 (tptp.i (tptp.s (tptp.fun Q83030 Q83010) S0) _let_1)))) (tptp.s Q83026 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) T0) _let_3)) _let_1))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F1) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))))))) _let_1))))))))))))))))) (forall ((U_5 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_2 (tptp.fun Q83030 Q83010))) (let ((_let_3 (tptp.fun (tptp.prod _let_2 _let_1) tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_5) (tptp.s _let_2 S0))) (tptp.s _let_1 T0))) (tptp.s _let_3 F0)))) (forall ((SI_ $$unsorted) (TI_ $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_3 (tptp.fun Q83030 Q83010))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (forall ((F1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q83030 Y))) (let ((_let_2 (tptp.fun Q83010 Q83026))) (let ((_let_3 (tptp.s _let_2 F1))) (let ((_let_4 (tptp.fun Q83030 Q83026))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s Q83030 X))) (let ((_let_7 (tptp.fun Q83030 Q83010))) (=> (= (tptp.s Q83010 (tptp.i (tptp.s _let_7 S0) _let_6)) (tptp.s Q83010 (tptp.i (tptp.s _let_7 SI_) _let_1))) (= (tptp.s Q83026 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 T0) _let_3)) _let_6)) (tptp.s Q83026 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 TI_) _let_3)) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 SI_))) (tptp.s _let_2 TI_))))))) _let_1))))))))))))))))))) (forall ((U_4 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun _let_1 tptp.bool)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) U_4) (tptp.s _let_2 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q83030 Q83010))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.prod _let_3 _let_1))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_1 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.geq) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.c_) _let_4)) _let_2)))))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.gabs) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_5) _let_4)) _let_2))))))))))))))))))))) (forall ((U_3 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_3) (tptp.s _let_1 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026)))) (let ((_let_3 (tptp.fun Q83030 Q83010))) (let ((_let_4 (tptp.prod _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (and (= (tptp.p _let_1) (forall ((F1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q83030 Y))) (let ((_let_2 (tptp.fun Q83010 Q83026))) (let ((_let_3 (tptp.fun Q83030 Q83026))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) T0) (tptp.s _let_2 F1))))) (let ((_let_5 (tptp.s Q83030 X))) (let ((_let_6 (tptp.s (tptp.fun Q83030 Q83010) S0))) (=> (= (tptp.s Q83010 (tptp.i _let_6 _let_5)) (tptp.s Q83010 (tptp.i _let_6 _let_1))) (= (tptp.s Q83026 (tptp.i _let_4 _let_5)) (tptp.s Q83026 (tptp.i _let_4 _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))))))) _let_1))))))))))))))) (forall ((U_2 $$unsorted)) (=> (forall ((A5 $$unsorted)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q83030 tptp.bool) U_2) (tptp.s Q83030 A5))) (tptp.s tptp.bool tptp.t))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q83030 tptp.bool))) (let ((_let_2 (tptp.fun Q83010 Q83026))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_1) (tptp.s _let_2 F0))) (tptp.s _let_1 U_2))))) (forall ((U_0 $$unsorted)) (=> (forall ((L_L_ $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))) tptp.bool))) (let ((_let_2 (tptp.fun Q83010 (tptp.fun Q83010 tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 L_L_))) (tptp.s _let_1 F0)))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q83010 Q83026))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun Q83030 Q83026)))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun Q83030 Q83010))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun Q83030 tptp.bool)))) (let ((_let_7 (tptp.fun Q83010 (tptp.fun Q83010 tptp.bool)))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (let ((_let_11 (tptp.prod _let_4 _let_2))) (let ((_let_12 (tptp.fun _let_2 _let_11))) (let ((_let_13 (tptp.fun tptp.bool tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.bool _let_13) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_11 tptp.bool) F0) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.c_) _let_5)) _let_3)))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.superadmissible) (tptp.s _let_7 L_L_))) (tptp.s _let_6 U_1))) _let_5)) _let_3)))))))))))))))))))))))) (forall ((CLAUSES $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.s _let_2 CLAUSES))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (=> (and (exists ((L_L_ $$unsorted)) (let ((_let_1 (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun (tptp.fun Q83010 Q83026) (tptp.fun Q83030 Q83026))))) (let ((_let_2 (tptp.list _let_1))) (let ((_let_3 (tptp.fun Q83010 (tptp.fun Q83010 tptp.bool)))) (let ((_let_4 (tptp.s _let_3 L_L_))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.wf) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.all0) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))))) (tptp.s _let_2 CLAUSES))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.all0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_8 _let_4) tptp.gabs) (tptp.s _let_8 U_3))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.pairwise0) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 U_4))))) _let_3)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q83010 Q83026))) (let ((_let_2 (tptp.prod (tptp.fun Q83030 Q83010) (tptp.fun _let_1 (tptp.fun Q83030 Q83026))))) (let ((_let_3 (tptp.list _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.all0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_6) (tptp.s _let_1 F0))))))) (tptp.s _let_3 CLAUSES))))))))))))))))))))))))))))))))))) (forall ((Q83929 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.fun Q83929 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.subset) (tptp.s _let_1 P0))) (tptp.s _let_1 Q0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q83929 X))) (let ((_let_2 (tptp.fun Q83929 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1))))))))))) (forall ((Q83945 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q83945 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 tptp.p0))) (tptp.s Q83945 X)))) (exists ((P0 $$unsorted)) (let ((_let_1 (tptp.fun Q83945 tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_2 (tptp.s Q83945 X)))))))))))) (forall ((A $$unsorted) (L $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1)))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.s _let_6 L))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.less) _let_7)) _let_5))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_5))) (not (= _let_2 _let_1)))))))))))) (forall ((A $$unsorted) (L $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.fl) (tptp.s _let_1 L))) (tptp.s A X)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.bool) L))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 L)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 L))) (let ((_let_6 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.fl) _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.c_))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A X))))) (let ((_let_6 (tptp.s (tptp.fun _let_2 tptp.bool) L))) (let ((_let_7 (tptp.s A Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 _let_7))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_7)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.bool) L))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2)))))) (= _let_2 _let_1))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.chain) (tptp.s _let_2 L))) (tptp.s _let_1 P0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.bool) L))) (let ((_let_7 (tptp.s (tptp.fun A tptp.bool) P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2)))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.toset) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.poset) _let_2))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.fl) _let_7)))) (let ((_let_10 (tptp.fun _let_8 tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun A _let_10) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_1)) _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_2)) _let_9)))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 L))) (let ((_let_6 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.fl) _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.c_))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A X))))) (let ((_let_6 (tptp.s (tptp.fun _let_2 tptp.bool) L))) (let ((_let_7 (tptp.s A Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 _let_7))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_7)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.bool) L))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2)))))) (= _let_2 _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.fl) _let_7)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_2)))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))) (forall ((P0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.fl) (tptp.s _let_2 L))) _let_1)))))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (exists ((Y $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A Y)))) (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) L) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) (tptp.s A Y))) _let_1)))))))))))))))))) (forall ((A $$unsorted) (M0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.inseg) (tptp.s _let_1 L))) (tptp.s _let_1 M0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 L))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun A _let_2))) (let ((_let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.c_) (tptp.s A X))) _let_1)))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_7))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 M0) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.fl) _let_4)) _let_1))))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L $$unsorted) (A5 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 L))) (tptp.s A A5))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A X))) _let_2)))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.s _let_7 L))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.less) _let_9)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) (tptp.s A A5)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 F0) _let_6)))) _let_1)))))))))))))))))))) (forall ((L $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.s _let_2 L))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.fun A _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.linseg) _let_3)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) tptp.gabs) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3)) _let_1)))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 L))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.fun A _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) _let_6)) _let_1)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.less) _let_6)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1)))))))))))))))) (forall ((L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.ordinal) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.woset) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.s _let_2 L))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun A _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.fl) _let_3)) _let_1))) (= _let_1 (tptp.s A (tptp.i (tptp.s (tptp.fun _let_4 A) tptp.h_) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3)) _let_1)))))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 L)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 L))) (let ((_let_6 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.fl) _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) _let_1)))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.c_))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A X))))) (let ((_let_6 (tptp.s (tptp.fun _let_2 tptp.bool) L))) (let ((_let_7 (tptp.s A Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 _let_7))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_7)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 _let_1))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.bool) L))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2)))))) (= _let_2 _let_1)))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 L)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 L))) (let ((_let_6 (tptp.fun A tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.fl) _let_5)) _let_1)) (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) _let_1))))))))))))))) (forall ((A $$unsorted) (L $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 Q0))) (let ((_let_3 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.chain) (tptp.s _let_3 L))))) (let ((_let_6 (tptp.s _let_1 P0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 L))) (let ((_let_6 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.fl) _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) _let_1)))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.c_))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A X))))) (let ((_let_6 (tptp.s (tptp.fun _let_2 tptp.bool) L))) (let ((_let_7 (tptp.s A Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 _let_7))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_7)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 _let_1))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.bool) L))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2)))))) (= _let_2 _let_1)))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.fl) _let_7)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_2)))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((P0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.fl) (tptp.s _let_2 L))) _let_1)))))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (exists ((Y $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A Y)))) (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) L) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) (tptp.s A Y))) _let_1))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.woset) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.poset) _let_2)))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 L))) (let ((_let_6 (tptp.fun A tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.fl) _let_5)) _let_1)) (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) _let_1))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.c_))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A X))))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.less) _let_7)))) (let ((_let_9 (tptp.s A Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_2 (tptp.i _let_5 _let_9))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_9)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_2 (tptp.i _let_5 _let_1))))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.bool) L))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2)))))) (= _let_2 _let_1))))))))) (forall ((P0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.fl) (tptp.s _let_2 L))) _let_1)))))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (exists ((Y $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A Y)))) (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) L) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) (tptp.s A Y))) _let_1)))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) C))) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun B _let_1))) (let ((_let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.c_) (tptp.s A X))) (tptp.s B Y))))) (let ((_let_4 (tptp.fun _let_1 C))) (= (tptp.s C (tptp.i (tptp.s _let_4 L) _let_3)) (tptp.s C (tptp.i (tptp.s _let_4 M0) _let_3)))))))) (= (tptp.s _let_1 L) (tptp.s _let_1 M0))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s (tptp.fun A _let_3) tptp.c_))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s A X))))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.less) _let_7)))) (let ((_let_9 (tptp.s A Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_2 (tptp.i _let_5 _let_9))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_9)) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_2 (tptp.i _let_5 _let_1))))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((P0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.fl) (tptp.s _let_2 L))) _let_1)))))))) (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A X)))))) (exists ((Y $$unsorted)) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) (tptp.s A Y)))) (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.s A Z0))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.less) (tptp.s _let_4 L))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) (tptp.s A Y)))))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.fl) _let_7)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_2)))) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.less) _let_7)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.s _let_6 L))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.less) _let_7)))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.fl) _let_7)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_2)))) (or (= _let_1 _let_2) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1))))))))))))))))))))) (forall ((A $$unsorted) (Q84932 $$unsorted) (P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q84932 Q84932) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun Q84932 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.fl) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 P0))))) (tptp.s Q84932 tptp.x)))) (exists ((L0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q84932 Q84932) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L0))) (let ((_let_3 (tptp.fun Q84932 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.fl) _let_2)) (tptp.s Q84932 tptp.x)))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inseg) _let_2)) (tptp.s _let_1 L))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.inseg) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 P0))))) (tptp.s _let_1 L)))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.inseg) (tptp.s _let_1 M0))) (tptp.s _let_1 L)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod A A))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.c_) (tptp.s A X))) (tptp.s A Y))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 M0) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 L) _let_3))))))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.inseg) (tptp.s _let_1 M0))) (tptp.s _let_1 L)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_3) tptp.fl))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 L))) _let_1))))))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.woset))) (let ((_let_5 (tptp.s _let_1 L))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.inseg) _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))) (forall ((A $$unsorted) (L $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun A _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.woset) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inseg) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.linseg) _let_2)) (tptp.s A A5))))) _let_2))))))))) (forall ((A $$unsorted) (L $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun A _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.linseg) _let_2)) (tptp.s A A5)))))))))))) (forall ((A $$unsorted) (L $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 L))) (let ((_let_7 (tptp.fun A _let_5))) (let ((_let_8 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.woset) _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.fl) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.linseg) _let_6)) _let_1)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.less) _let_6)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s _let_1 L))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inseg) _let_2)) _let_3))) (not (= _let_3 _let_2))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.prod A A))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.c_) (tptp.s A X))) (tptp.s A Y))))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 L) _let_3))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 M0) _let_3)))))))))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s _let_1 L))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inseg) _let_2)) _let_3))) (not (= _let_3 _let_2))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_3) tptp.fl))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 L))) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 M0))) _let_1)))))))))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s _let_1 M0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.woset) _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inseg) _let_3)) _let_2))) (or (= _let_3 _let_2) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.s _let_2 L))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.fl) _let_3)) _let_1))) (= (tptp.s _let_2 M0) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.linseg) _let_3)) _let_1)))))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 L))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A X))) _let_2)))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.s _let_7 L))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) (tptp.s A tptp.a0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 F0) _let_6)))) _let_1))))))))))))))))))) (forall ((L $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 L))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.woset) _let_5))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.fl) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)))))) _let_1)) (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) (tptp.s A tptp.a0))))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L $$unsorted) (A5 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 L))) (tptp.s A A5))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.c_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A X))) _let_2)))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.s _let_7 L))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) (tptp.s A A5)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 F0) _let_6)))) _let_1)))))))))))))))))))) (forall ((L $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s A A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.fun A tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.woset) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.fl) _let_2)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inseg) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.gabs) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_2)) _let_3)))))) _let_2))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L $$unsorted) (A5 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 L))) (tptp.s A A5))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.prod A A))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_3)) _let_2)))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.s A A5))) (let ((_let_10 (tptp.fun A _let_7))) (let ((_let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.linseg) (tptp.s _let_7 L))) _let_9)))) (let ((_let_12 (tptp.fun A tptp.bool))) (and (= (tptp.p _let_1) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_6))) (and (= _let_2 _let_9) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_7 _let_12) tptp.fl) _let_11)) _let_3))) (= _let_3 _let_9))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 F0) _let_6)))) _let_1))))))))))))))))))))))) (forall ((L $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.s A A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.fun A tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.woset) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.fl) _let_2)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inseg) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.gabs) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_2)) _let_3)))))) _let_2))))))))))))) (forall ((A $$unsorted) (K0 $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s _let_1 K0))) (let ((_let_4 (tptp.s _let_1 L))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.inseg) _let_3)))) (let ((_let_7 (tptp.s _let_5 tptp.ordinal))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (or (= _let_3 _let_4) (= _let_3 _let_2) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.s _let_2 M0))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.linseg))) (let ((_let_6 (tptp.s _let_2 K0))) (let ((_let_7 (tptp.s _let_2 L))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_2 _let_8) tptp.fl))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_7)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_1))) (= _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) _let_1))) (= _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))))))))))))))))))))))))) (forall ((A $$unsorted) (L $$unsorted) (M0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 M0))) (let ((_let_3 (tptp.s _let_1 L))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.inseg))) (let ((_let_6 (tptp.s _let_4 tptp.ordinal))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((L $$unsorted) (A5 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 L))) (tptp.s A A5))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.prod A A))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_3)) _let_2)))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.s A A5))) (let ((_let_10 (tptp.s _let_7 L))) (let ((_let_11 (tptp.fun A tptp.bool))) (and (= (tptp.p _let_1) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_6))) (and (= _let_2 _let_9) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) tptp.fl) _let_10)) _let_3))) (= _let_3 _let_9))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 F0) _let_6)))) _let_1)))))))))))))))))))))) (forall ((L $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s A A5))) (let ((_let_2 (tptp.s A tptp.x))) (let ((_let_3 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_4 (tptp.s _let_3 L))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.fl))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun A _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_7 _let_3) tptp.gabs) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_0) _let_4)) _let_1)))))) _let_2))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))) (= _let_2 _let_1)))))))))))))) (forall ((A $$unsorted) (U_1 $$unsorted)) (=> (forall ((L $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.s _let_2 L))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_1) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.fl) _let_3)) _let_1))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((L $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 L))) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.prod A A))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.c_) _let_3)) _let_2)))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.s _let_7 L))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (let ((_let_12 (tptp.s A (tptp.i (tptp.s (tptp.fun _let_10 A) tptp.h_) (tptp.s _let_10 (tptp.i (tptp.s _let_11 U_1) _let_9)))))) (and (= (tptp.p _let_1) (or (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_6))) (and (= _let_2 _let_12) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.fl) _let_9)) _let_3))) (= _let_3 _let_12))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 F0) _let_6)))) _let_1)))))))))))))))))))))) (forall ((L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.ordinal))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.fl) (tptp.s _let_1 L))) (tptp.s A X))))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.gabs) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 L))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.ordinal) _let_2)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.ordinal) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 P0)))))))))) (forall ((A $$unsorted) (L $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.ordinal))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_2 _let_5) tptp.fl))) (let ((_let_7 (tptp.s _let_2 L))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_7))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.unions) _let_4)))) _let_1))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.ordinal) (tptp.s _let_1 L)))) (or (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.fl) (tptp.s _let_1 L))) (tptp.s A X))))))) (exists ((M0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_3) tptp.fl))) (let ((_let_5 (tptp.s _let_2 M0))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.ordinal) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 L))) _let_1))))))))))))))) (forall ((A $$unsorted)) (exists ((L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.ordinal) (tptp.s _let_1 L)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.fl) (tptp.s _let_1 L))) (tptp.s A X))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (L $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i 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((L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.woset) (tptp.s _let_1 L)))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.s A tptp.x))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.s _let_2 L))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.fl))) (let ((_let_6 (tptp.s _let_4 P0))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_7 _let_2) tptp.gabs) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_6)) _let_3)))))) _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))))))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (exists ((L $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.s _let_2 L))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.woset) _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.fl) _let_3)) (tptp.s _let_1 P0)))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 L)))) (exists ((P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.chain) (tptp.s _let_2 L))) (tptp.s _let_1 P0)))) (forall ((Q0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.s _let_1 Q0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.chain) (tptp.s _let_5 L))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) _let_3)))) (= _let_3 _let_2)))))))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 L)))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.chain) (tptp.s _let_2 L))) (tptp.s _let_1 P0)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.fl) (tptp.s _let_1 L))) (tptp.s A Y)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A A))) (let ((_let_3 (tptp.fun A _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) P0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) L) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) (tptp.s A Y))))))))))))))))))))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.fl) (tptp.s _let_1 L))) (tptp.s A Y)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s A Y))) (let ((_let_3 (tptp.prod A A))) (let ((_let_4 (tptp.fun A _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) L) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))) (= _let_2 _let_1)))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod _let_1 _let_1) tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod _let_1 _let_1) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) U_0) (tptp.s _let_2 F0)))) (forall ((C1 $$unsorted) (C2 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 C2))) (let ((_let_4 (tptp.s _let_2 C1))) (let ((_let_5 (tptp.prod _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_9 (tptp.fun _let_2 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_2 _let_9) tptp.subset))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_2 tptp.c0))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_8 _let_9) tptp.chain) (tptp.s _let_8 tptp.l0))) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.c_) _let_4)) _let_3)))))) _let_1)))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.poset) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.gabs) (tptp.s _let_3 U_0))))))))))) (forall ((A $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 L)))) (forall ((C0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.chain) (tptp.s _let_2 L))) (tptp.s _let_1 C0)))) (exists ((P0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun (tptp.prod A A) tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.chain) (tptp.s _let_4 L))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) (tptp.s _let_1 C0))) _let_2))) (forall ((R0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.s _let_1 R0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.chain) (tptp.s _let_5 L))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) _let_3)))) (= _let_3 _let_2)))))))))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.poset) (tptp.s _let_1 P0)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 P0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.fl))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.toset) _let_2))) (= (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_5 (tptp.i _let_6 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)) _let_2)))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (X $$unsorted)) (or (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.sum0 A B))) (= (tptp.s _let_1 X) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) tptp.inl) (tptp.s A A5)))))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.sum0 A B))) (= (tptp.s _let_1 X) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun B _let_1) tptp.inr) (tptp.s B A5)))))))) (forall ((Q87171 $$unsorted) (Q87170 $$unsorted)) (= (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.sum0 Q87171 Q87170))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 Z0)))))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.sum0 Q87171 Q87170))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q87171 _let_1) tptp.inl) (tptp.s Q87171 X)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.sum0 Q87171 Q87170))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q87170 _let_1) tptp.inr) (tptp.s Q87170 X))))))))))) (forall ((Q87197 $$unsorted) (Q87196 $$unsorted)) (= (exists ((Z0 $$unsorted)) (let ((_let_1 (tptp.sum0 Q87197 Q87196))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 Z0)))))) (or (exists ((X $$unsorted)) (let ((_let_1 (tptp.sum0 Q87197 Q87196))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q87197 _let_1) tptp.inl) (tptp.s Q87197 X)))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.sum0 Q87197 Q87196))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q87196 _let_1) tptp.inr) (tptp.s Q87196 X))))))))))) (forall ((Q87220 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q87220 tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod _let_1 _let_1) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) (tptp.s _let_3 P0))) (tptp.s _let_2 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q87220 tptp.bool))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.s _let_2 X))) (let ((_let_5 (tptp.prod _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (let ((_let_9 (tptp.s _let_8 P0))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.subset) _let_4)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.c_) _let_4)) _let_3)))))) _let_1))))))))))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun Q87220 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun (tptp.prod _let_1 _let_1) tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.poset) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.gabs) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 P0))))))))))))))) (forall ((Q87245 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun Q87245 tptp.bool))) (let ((_let_2 (tptp.fun (tptp.prod _let_1 _let_1) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) (tptp.s _let_3 P0))) (tptp.s _let_2 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun Q87245 tptp.bool))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.s _let_2 X))) (let ((_let_5 (tptp.prod _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (let ((_let_9 (tptp.s _let_8 P0))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.subset) _let_4)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.c_) _let_4)) _let_3)))))) _let_1))))))))))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun Q87245 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.fun (tptp.prod _let_1 _let_1) tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) tptp.fl) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3)))))) _let_3))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (=> (forall ((C0 $$unsorted)) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 C0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.s _let_4 C0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_6)))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (exists ((Z0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 Z0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 C0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 Z0))))))))))))))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 A5)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 P0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)) _let_2)))) (= _let_3 _let_2)))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (=> (forall ((C0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 C0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.s _let_4 C0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_6)))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 C0)))))))))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 A5)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 P0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)) _let_2)))) (= _let_3 _let_2)))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (=> (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 X)))))) (forall ((C0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.in) (tptp.s _let_1 X))) (tptp.s _let_2 C0)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 C0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.s _let_4 C0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_6)))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) (tptp.s _let_2 C0))))))))))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 A5)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 P0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)) _let_2)))) (= _let_3 _let_2)))))))))))) (forall ((Q87575 $$unsorted) (Q87572 $$unsorted)) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q87572 X))) (let ((_let_2 (tptp.fun Q87572 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87572 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (= (tptp.s Q87572 (tptp.i (tptp.s (tptp.fun Q87575 Q87572) tptp.g) (tptp.s Q87575 (tptp.i (tptp.s (tptp.fun Q87572 Q87575) tptp.f) _let_1)))) _let_1)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q87572 X))) (let ((_let_2 (tptp.s Q87575 Y))) (let ((_let_3 (tptp.fun Q87572 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q87572 _let_4) tptp.in) _let_1)) (tptp.s _let_3 tptp.s0)))) (= _let_2 (tptp.s Q87575 (tptp.i (tptp.s (tptp.fun Q87572 Q87575) tptp.f) _let_1)))) (= (tptp.s Q87572 (tptp.i (tptp.s (tptp.fun Q87575 Q87572) tptp.g) _let_2)) _let_1))))))))) (forall ((A $$unsorted) (F0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) F0))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.subset))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_3 _let_4)))) (tptp.s _let_1 (tptp.i _let_3 _let_2))))))))))))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) F0) _let_2)) _let_2)))))) (forall ((Q87739 $$unsorted) (Q87740 $$unsorted)) (=> (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun Q87740 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q87740 _let_2) tptp.in) (tptp.s Q87740 X))) (tptp.s _let_1 tptp.s0))))))) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q87740 Y))) (let ((_let_2 (tptp.s Q87740 X))) (let ((_let_3 (tptp.s (tptp.fun Q87740 Q87739) tptp.f))) (let ((_let_4 (tptp.fun Q87740 tptp.bool))) (let ((_let_5 (tptp.s _let_4 tptp.s0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q87740 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q87739 (tptp.i _let_3 _let_2)) (tptp.s Q87739 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (exists ((G0 $$unsorted)) (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q87740 tptp.bool))) (let ((_let_2 (tptp.s Q87739 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q87739 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q87739 _let_5) tptp.in) _let_2)) (tptp.s _let_4 tptp.t0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87740 _let_3) tptp.in) (tptp.s Q87740 (tptp.i (tptp.s (tptp.fun Q87739 Q87740) G0) _let_2)))) (tptp.s _let_1 tptp.s0))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q87740 X))) (let ((_let_2 (tptp.fun Q87740 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87740 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (= (tptp.s Q87740 (tptp.i (tptp.s (tptp.fun Q87739 Q87740) G0) (tptp.s Q87739 (tptp.i (tptp.s (tptp.fun Q87740 Q87739) tptp.f) _let_1)))) _let_1))))))))))) (forall ((Q87847 $$unsorted) (Q87844 $$unsorted)) (= (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q87844 tptp.bool))) (let ((_let_2 (tptp.s Q87847 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q87847 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q87847 _let_5) tptp.in) _let_2)) (tptp.s _let_4 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87844 _let_3) tptp.in) (tptp.s Q87844 (tptp.i (tptp.s (tptp.fun Q87847 Q87844) tptp.f) _let_2)))) (tptp.s _let_1 tptp.t0))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q87844 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q87844 _let_2) tptp.in) (tptp.s Q87844 Y))) (tptp.s _let_1 tptp.t0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q87847 X))) (let ((_let_2 (tptp.fun Q87847 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87847 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (= (tptp.s Q87844 (tptp.i (tptp.s (tptp.fun Q87847 Q87844) tptp.f) _let_1)) (tptp.s Q87844 Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s Q87847 XI_))) (let ((_let_2 (tptp.s Q87847 X))) (let ((_let_3 (tptp.s Q87844 Y))) (let ((_let_4 (tptp.s (tptp.fun Q87847 Q87844) tptp.f))) (let ((_let_5 (tptp.fun Q87847 tptp.bool))) (let ((_let_6 (tptp.s _let_5 tptp.s0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun Q87847 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s Q87844 (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s Q87844 (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q87844 tptp.bool))) (let ((_let_2 (tptp.s Q87847 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q87847 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q87847 _let_5) tptp.in) _let_2)) (tptp.s _let_4 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87844 _let_3) tptp.in) (tptp.s Q87844 (tptp.i (tptp.s (tptp.fun Q87847 Q87844) tptp.f) _let_2)))) (tptp.s _let_1 tptp.t0))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q87847 Y))) (let ((_let_2 (tptp.s Q87847 X))) (let ((_let_3 (tptp.s (tptp.fun Q87847 Q87844) tptp.f))) (let ((_let_4 (tptp.fun Q87847 tptp.bool))) (let ((_let_5 (tptp.s _let_4 tptp.s0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q87847 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q87844 (tptp.i _let_3 _let_2)) (tptp.s Q87844 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q87844 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q87844 _let_2) tptp.in) (tptp.s Q87844 Y))) (tptp.s _let_1 tptp.t0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q87847 X))) (let ((_let_2 (tptp.fun Q87847 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87847 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (= (tptp.s Q87844 (tptp.i (tptp.s (tptp.fun Q87847 Q87844) tptp.f) _let_1)) (tptp.s Q87844 Y)))))))))))))) (forall ((Q87963 $$unsorted) (Q87964 $$unsorted)) (= (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q87963 tptp.bool))) (let ((_let_2 (tptp.s Q87964 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q87964 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q87964 _let_5) tptp.in) _let_2)) (tptp.s _let_4 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87963 _let_3) tptp.in) (tptp.s Q87963 (tptp.i (tptp.s (tptp.fun Q87964 Q87963) tptp.f) _let_2)))) (tptp.s _let_1 tptp.t0))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q87963 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q87963 _let_2) tptp.in) (tptp.s Q87963 Y))) (tptp.s _let_1 tptp.t0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q87964 X))) (let ((_let_2 (tptp.fun Q87964 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87964 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (= (tptp.s Q87963 (tptp.i (tptp.s (tptp.fun Q87964 Q87963) tptp.f) _let_1)) (tptp.s Q87963 Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s Q87964 XI_))) (let ((_let_2 (tptp.s Q87964 X))) (let ((_let_3 (tptp.s Q87963 Y))) (let ((_let_4 (tptp.s (tptp.fun Q87964 Q87963) tptp.f))) (let ((_let_5 (tptp.fun Q87964 tptp.bool))) (let ((_let_6 (tptp.s _let_5 tptp.s0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun Q87964 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s Q87963 (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s Q87963 (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q87963 tptp.bool))) (let ((_let_2 (tptp.s Q87964 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q87964 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q87964 _let_5) tptp.in) _let_2)) (tptp.s _let_4 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87963 _let_3) tptp.in) (tptp.s Q87963 (tptp.i (tptp.s (tptp.fun Q87964 Q87963) tptp.f) _let_2)))) (tptp.s _let_1 tptp.t0))))))))))) (exists ((G0 $$unsorted)) (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun Q87964 tptp.bool))) (let ((_let_2 (tptp.s Q87963 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q87963 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q87963 _let_5) tptp.in) _let_2)) (tptp.s _let_4 tptp.t0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87964 _let_3) tptp.in) (tptp.s Q87964 (tptp.i (tptp.s (tptp.fun Q87963 Q87964) G0) _let_2)))) (tptp.s _let_1 tptp.s0))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s Q87963 Y))) (let ((_let_2 (tptp.fun Q87963 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87963 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.t0)))) (= (tptp.s Q87963 (tptp.i (tptp.s (tptp.fun Q87964 Q87963) tptp.f) (tptp.s Q87964 (tptp.i (tptp.s (tptp.fun Q87963 Q87964) G0) _let_1)))) _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q87964 X))) (let ((_let_2 (tptp.fun Q87964 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q87964 _let_3) tptp.in) _let_1)) (tptp.s _let_2 tptp.s0)))) (= (tptp.s Q87964 (tptp.i (tptp.s (tptp.fun Q87963 Q87964) G0) (tptp.s Q87963 (tptp.i (tptp.s (tptp.fun Q87964 Q87963) tptp.f) _let_1)))) _let_1))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.a_u_c) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))) (exists ((F0 $$unsorted) (G0 $$unsorted)) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_1)) (tptp.s _let_5 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun B _let_4) tptp.in) _let_2)) (tptp.s _let_3 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_2)) _let_1)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) G0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_2)) _let_1))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.a_u_c) (tptp.s _let_2 tptp.s0))) (tptp.s _let_1 tptp.t0)))) (exists ((R0 $$unsorted)) (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s B Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s A X))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.prod A B))) (let ((_let_8 (tptp.fun B _let_7))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) R0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) tptp.c_) _let_5)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.in) _let_5)) (tptp.s _let_4 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) _let_2)) (tptp.s _let_1 tptp.t0))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A X))) (tptp.s _let_1 tptp.s0)))) (and (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.prod A B))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) _let_1)) (tptp.s _let_4 tptp.t0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) R0) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) (tptp.s A X))) _let_1)))))))))))) (forall ((Y $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s B XI_))) (let ((_let_2 (tptp.s B Y))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) (tptp.s A X))))) (let ((_let_6 (tptp.s (tptp.fun _let_3 tptp.bool) R0))) (let ((_let_7 (tptp.fun B tptp.bool))) (let ((_let_8 (tptp.s _let_7 tptp.t0))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun B _let_9) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_2)) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i _let_5 _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_1)) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i _let_5 _let_1)))))) (= _let_2 _let_1)))))))))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 tptp.t0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.prod A B))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) R0) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.c_) _let_1)) (tptp.s B Y))))))))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun B _let_4))) (let ((_let_6 (tptp.s (tptp.fun A _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 tptp.bool) R0))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 tptp.s0))) (let ((_let_10 (tptp.fun _let_8 tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun A _let_10) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_2)) _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_1)) _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) _let_3)))))) (= _let_2 _let_1)))))))))))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.l_a_u_c) _let_2)) _let_2))))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.l_a_u_c) _let_4)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.l_a_u_c) _let_7)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_a_u_c) _let_4)) _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.l_u_c) _let_2)) _let_2)))))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.l_a_u_c) _let_4)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.l_u_c) _let_7)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.l_u_c) _let_4)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.l_a_u_c) _let_7)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.l_u_c) _let_4)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.l_u_c) _let_7)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.a_u_c) _let_2)) _let_2))))))) (forall ((Q88371 $$unsorted) (Q88370 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q88370 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q88371 tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.a_u_c) _let_2)) _let_4)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.a_u_c) _let_4)) _let_2)))))))))) (forall ((Q88389 $$unsorted) (Q88390 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q88390 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q88389 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.a_u_c) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_u_c) _let_4)) _let_2))))))))))) (forall ((Q88408 $$unsorted) (Q88409 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q88409 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q88408 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_u_c) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_u_c) _let_4)) _let_2))))))))))) (forall ((B $$unsorted) (A $$unsorted) (U_0 $$unsorted)) (=> (forall ((R0 $$unsorted) (GENR_PVARR_213 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_0) (tptp.s _let_2 R0))) (tptp.s B GENR_PVARR_213)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (and (= (tptp.p _let_1) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) R0) _let_1)) (tptp.s B Y))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.setspec) (tptp.s B GENR_PVARR_213))) _let_1)) (tptp.s B Y))))))))))))) (forall ((R0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (forall ((X $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.s B YI_))) (let ((_let_2 (tptp.s B Y))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) R0) _let_3)))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_3)) (tptp.s _let_6 tptp.s0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (= _let_2 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.l_a_u_c) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) U_0) (tptp.s _let_3 R0))))))) (tptp.s _let_1 tptp.s0)))))))))))) (forall ((Q88501 $$unsorted) (Q88505 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q88505 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q88501 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.l_a_u_c) _let_2)) (tptp.s _let_3 tptp.empty)))) (= _let_2 (tptp.s _let_1 tptp.empty)))))))) (forall ((Q88517 $$unsorted) (Q88521 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q88521 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q88517 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.a_u_c) _let_2)) (tptp.s _let_3 tptp.empty)))) (= _let_2 (tptp.s _let_1 tptp.empty)))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (= (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_u_c) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.l_a_u_c) _let_2)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.a_u_c) _let_4)) _let_2)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.l_a_u_c) _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_a_u_c) _let_4)) _let_2))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.l_a_u_c) _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.l_u_c) _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_a_u_c) _let_4)) _let_2))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.a_u_c) _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_u_c) _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.l_a_u_c) _let_2)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (= (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.l_u_c) _let_2)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_a_u_c) _let_4)) _let_2))))))))))) (forall ((Q88986 $$unsorted) (Q88987 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q88987 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q88986 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_u_c) _let_4)) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_u_c) _let_4)) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.a_u_c) _let_4)) _let_2))))))))))))) (forall ((Q89012 $$unsorted) (Q89013 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q89013 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q89012 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_a_u_c) _let_4)) _let_2))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_u_c) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.a_u_c) _let_4)) _let_2)))))))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted) (S0 $$unsorted) (SI_ $$unsorted) (T0 $$unsorted) (TI_ $$unsorted)) (let ((_let_1 (tptp.fun D tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 SI_))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun C tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_6 tptp.bool))) (let ((_let_11 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.a_u_c) _let_9)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.a_u_c) _let_7)) _let_2)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.l_a_u_c) _let_9)) _let_7)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_a_u_c) _let_4)) _let_2)))))))))))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted) (S0 $$unsorted) (SI_ $$unsorted) (T0 $$unsorted) (TI_ $$unsorted)) (let ((_let_1 (tptp.fun D tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 SI_))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun C tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_6 tptp.bool))) (let ((_let_11 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.a_u_c) _let_9)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.a_u_c) _let_7)) _let_2)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.l_u_c) _let_9)) _let_7)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2)))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.a_u_c) _let_4)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.a_u_c) _let_7)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.a_u_c) _let_4)) _let_2))))))))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted) (S0 $$unsorted) (SI_ $$unsorted) (T0 $$unsorted) (TI_ $$unsorted)) (let ((_let_1 (tptp.fun D tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 SI_))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun C tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_6 tptp.bool))) (let ((_let_11 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.a_u_c) _let_9)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.a_u_c) _let_7)) _let_2)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.a_u_c) _let_9)) _let_7)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.a_u_c) _let_4)) _let_2)))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.infinite) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.l_a_u_c) (tptp.s _let_3 tptp.univ))) _let_2)))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.l_u_c) _let_3)) (tptp.s _let_1 tptp.univ))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.subset) _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.l_a_u_c) _let_3)) _let_2)))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.l_a_u_c) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.univ))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.l_a_u_c) (tptp.s _let_2 S0))) (tptp.s _let_1 T0)))) (exists ((U $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.a_u_c) (tptp.s _let_3 S0))) _let_2)))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.a_u_c) _let_5)) _let_2))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.infinite) _let_5)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.infinite) _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.a_u_c) _let_5)) _let_2))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2)))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.l_a_u_c) _let_2)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))))))))) (forall ((A $$unsorted) (Q89498 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q89498 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.a_u_c) _let_2)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.infinite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.l_a_u_c) _let_5)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.infinite) _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.infinite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_u_c) _let_4)) _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.l_a_u_c) _let_4)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.a_u_c) _let_4)) _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.l_a_u_c) _let_4)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_2)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.a_u_c) _let_4)) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.l_u_c) _let_4)) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.hasu_size) _let_6)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.a_u_c) _let_6)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hasu_size) _let_3)) _let_1)))))))))))) (forall ((Q89780 $$unsorted) (Q89779 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q89779 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q89779 Q89780))) (let ((_let_4 (tptp.fun Q89780 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.l_a_u_c) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))) _let_2)))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun A B))) (let ((_let_7 (tptp.fun _let_1 _let_3))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.subset) _let_4)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.image) (tptp.s _let_6 F0))) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.l_a_u_c) _let_4)) _let_2))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.a_u_c) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))) _let_2))))))))))) (forall ((Q89903 $$unsorted) (Q89902 $$unsorted) (U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (GENR_PVARR_217 $$unsorted)) (let ((_let_1 (tptp.sum0 Q89903 Q89902))) (let ((_let_2 (tptp.fun Q89902 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_1) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_217)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.s Q89902 Y))) (let ((_let_2 (tptp.sum0 Q89903 Q89902))) (let ((_let_3 (tptp.fun Q89902 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.setspec) (tptp.s _let_2 GENR_PVARR_217))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q89902 _let_4) tptp.in) _let_1)) (tptp.s _let_3 T0))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q89902 _let_2) tptp.inr) _let_1))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_216 $$unsorted)) (let ((_let_1 (tptp.sum0 Q89903 Q89902))) (let ((_let_2 (tptp.fun Q89903 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_216)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s Q89903 X))) (let ((_let_2 (tptp.sum0 Q89903 Q89902))) (let ((_let_3 (tptp.fun Q89903 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.setspec) (tptp.s _let_2 GENR_PVARR_216))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q89903 _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q89903 _let_2) tptp.inl) _let_1))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q89902 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun (tptp.sum0 Q89903 Q89902) tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (let ((_let_6 (tptp.s _let_5 tptp.gspec))) (let ((_let_7 (tptp.fun Q89903 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_7 _let_4) tptp.p_u_c) _let_8)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.union) (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_7 _let_3) U_0) _let_8)))))) (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_1) _let_2)))))))))))))))))))) (forall ((Q89936 $$unsorted) (Q89935 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_218 $$unsorted)) (let ((_let_1 (tptp.prod Q89936 Q89935))) (let ((_let_2 (tptp.fun Q89935 tptp.bool))) (let ((_let_3 (tptp.fun Q89936 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_218)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q89935 Y))) (let ((_let_2 (tptp.s Q89936 X))) (let ((_let_3 (tptp.prod Q89936 Q89935))) (let ((_let_4 (tptp.fun Q89935 _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun Q89935 tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun Q89936 tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q89936 _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun Q89935 _let_9) tptp.in) _let_1)) (tptp.s _let_8 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_218))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q89936 _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q89935 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q89936 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.prod Q89936 Q89935) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.t_u_c) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2))))))))))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted) (S0 $$unsorted) (SI_ $$unsorted) (T0 $$unsorted) (TI_ $$unsorted)) (let ((_let_1 (tptp.fun D tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 SI_))) (let ((_let_5 (tptp.fun (tptp.sum0 B D) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun C tptp.bool))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun (tptp.sum0 A C) tptp.bool))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun _let_5 tptp.bool))) (let ((_let_14 (tptp.fun _let_1 tptp.bool))) (let ((_let_15 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_9 _let_15) tptp.l_a_u_c) _let_10)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_7 _let_14) tptp.l_a_u_c) _let_8)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.l_a_u_c) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.p_u_c) _let_10)) _let_8)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.p_u_c) _let_4)) _let_2)))))))))))))))))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted) (S0 $$unsorted) (SI_ $$unsorted) (T0 $$unsorted) (TI_ $$unsorted)) (let ((_let_1 (tptp.fun D tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 SI_))) (let ((_let_5 (tptp.fun (tptp.prod B D) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun C tptp.bool))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun (tptp.prod A C) tptp.bool))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun _let_5 tptp.bool))) (let ((_let_14 (tptp.fun _let_1 tptp.bool))) (let ((_let_15 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_9 _let_15) tptp.l_a_u_c) _let_10)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_7 _let_14) tptp.l_a_u_c) _let_8)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.l_a_u_c) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.t_u_c) _let_10)) _let_8)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.t_u_c) _let_4)) _let_2)))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (AP $$unsorted) (BP $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun AP BP) tptp.bool))) (let ((_let_2 (tptp.fun (tptp.fun A B) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun BP tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun AP tptp.bool))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_8 _let_9) tptp.l_a_u_c) (tptp.s _let_8 tptp.univ))) (tptp.s _let_7 tptp.univ)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.l_a_u_c) (tptp.s _let_5 tptp.univ))) (tptp.s _let_4 tptp.univ))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.l_a_u_c) (tptp.s _let_2 tptp.univ))) (tptp.s _let_1 tptp.univ))))))))))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted) (S0 $$unsorted) (SI_ $$unsorted) (T0 $$unsorted) (TI_ $$unsorted)) (let ((_let_1 (tptp.fun D tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 SI_))) (let ((_let_5 (tptp.fun (tptp.sum0 B D) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun C tptp.bool))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun (tptp.sum0 A C) tptp.bool))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun _let_5 tptp.bool))) (let ((_let_14 (tptp.fun _let_1 tptp.bool))) (let ((_let_15 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_9 _let_15) tptp.a_u_c) _let_10)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_7 _let_14) tptp.a_u_c) _let_8)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.a_u_c) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.p_u_c) _let_10)) _let_8)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.p_u_c) _let_4)) _let_2)))))))))))))))))))))) (forall ((A $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted) (S0 $$unsorted) (SI_ $$unsorted) (T0 $$unsorted) (TI_ $$unsorted)) (let ((_let_1 (tptp.fun D tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 SI_))) (let ((_let_5 (tptp.fun (tptp.prod B D) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun C tptp.bool))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun (tptp.prod A C) tptp.bool))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun _let_5 tptp.bool))) (let ((_let_14 (tptp.fun _let_1 tptp.bool))) (let ((_let_15 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_9 _let_15) tptp.a_u_c) _let_10)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_7 _let_14) tptp.a_u_c) _let_8)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.a_u_c) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.t_u_c) _let_10)) _let_8)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.t_u_c) _let_4)) _let_2)))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (AP $$unsorted) (BP $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun AP BP) tptp.bool))) (let ((_let_2 (tptp.fun (tptp.fun A B) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun BP tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun AP tptp.bool))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_8 _let_9) tptp.a_u_c) (tptp.s _let_8 tptp.univ))) (tptp.s _let_7 tptp.univ)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.a_u_c) (tptp.s _let_5 tptp.univ))) (tptp.s _let_4 tptp.univ))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.a_u_c) (tptp.s _let_2 tptp.univ))) (tptp.s _let_1 tptp.univ))))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.t_u_c) (tptp.s _let_3 tptp.univ))) (tptp.s _let_2 tptp.univ))) (tptp.s _let_1 tptp.univ))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun (tptp.fun (tptp.prod A B) C) tptp.bool))) (let ((_let_2 (tptp.fun (tptp.fun A (tptp.fun B C)) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.a_u_c) (tptp.s _let_2 tptp.univ))) (tptp.s _let_1 tptp.univ)))))))) (forall ((Q90309 $$unsorted) (Q90290 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q90290 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.s Q90290 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun Q90309 tptp.bool))) (let ((_let_6 (tptp.sum0 Q90290 Q90309))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_5 _let_7))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.in) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q90290 _let_6) tptp.inl) _let_3)))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.p_u_c) _let_2)) (tptp.s _let_5 tptp.t0))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q90290 _let_4) tptp.in) _let_3)) _let_2))))))))))))) (forall ((Q90290 $$unsorted) (Q90309 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun Q90309 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.t0))) (let ((_let_3 (tptp.s Q90309 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun Q90290 tptp.bool))) (let ((_let_6 (tptp.sum0 Q90290 Q90309))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.in) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q90309 _let_6) tptp.inr) _let_3)))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.p_u_c) (tptp.s _let_5 tptp.s0))) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q90309 _let_4) tptp.in) _let_3)) _let_2))))))))))))) (forall ((Q90344 $$unsorted) (Q90347 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun Q90347 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s Q90347 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun Q90344 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.s Q90344 X))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.prod Q90344 Q90347))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun Q90347 _let_9))) (let ((_let_13 (tptp.fun _let_10 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_9 _let_13) tptp.in) (tptp.s _let_9 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun Q90344 _let_12) tptp.c_) _let_7)) _let_3)))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_5 _let_11) tptp.t_u_c) _let_6)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q90344 _let_8) tptp.in) _let_7)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q90347 _let_4) tptp.in) _let_3)) _let_2))))))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.l_a_u_c) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.t_u_c) _let_2)) _let_2))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_58 (tptp.i (tptp.s (tptp.fun _let_61 _let_58) tptp.a_u_c) (tptp.s _let_61 (tptp.i (tptp.s _let_62 (tptp.i (tptp.s (tptp.fun _let_18 _let_62) tptp.t_u_c) _let_50)) _let_50)))) _let_50))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun (tptp.sum0 A A) tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.l_a_u_c) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.union) _let_3)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.p_u_c) _let_3)) _let_2))))))))))))) (forall ((Q90519 $$unsorted) (Q90521 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q90521 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q90519 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun (tptp.sum0 Q90519 Q90521) tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.card) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.p_u_c) _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun (tptp.sum0 B A) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun (tptp.sum0 A B) tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_5 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.a_u_c) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.p_u_c) _let_2)) _let_4)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.p_u_c) _let_4)) _let_2))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.sum0 A B))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun (tptp.sum0 _let_7 C) tptp.bool))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.sum0 B C))) (let ((_let_13 (tptp.fun _let_12 tptp.bool))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (let ((_let_15 (tptp.fun (tptp.sum0 A _let_12) tptp.bool))) (let ((_let_16 (tptp.fun _let_13 _let_15))) (let ((_let_17 (tptp.fun _let_10 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_15 _let_17) tptp.a_u_c) (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_5 _let_16) tptp.p_u_c) _let_6)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_3 _let_14) tptp.p_u_c) _let_4)) _let_2)))))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.p_u_c) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.p_u_c) _let_6)) _let_4)))) _let_2))))))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun (tptp.prod B A) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_5 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.a_u_c) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.t_u_c) _let_2)) _let_4)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.t_u_c) _let_4)) _let_2))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.prod A B))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.fun (tptp.prod _let_7 C) tptp.bool))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.prod B C))) (let ((_let_13 (tptp.fun _let_12 tptp.bool))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (let ((_let_15 (tptp.fun (tptp.prod A _let_12) tptp.bool))) (let ((_let_16 (tptp.fun _let_13 _let_15))) (let ((_let_17 (tptp.fun _let_10 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_15 _let_17) tptp.a_u_c) (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_5 _let_16) tptp.t_u_c) _let_6)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_3 _let_14) tptp.t_u_c) _let_4)) _let_2)))))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.t_u_c) (tptp.s _let_8 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(tptp.fun _let_16 _let_18))) (let ((_let_20 (tptp.fun _let_13 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_18 _let_20) tptp.a_u_c) (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_3 _let_19) tptp.t_u_c) _let_4)) (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_8 _let_17) tptp.p_u_c) _let_9)) _let_2)))))) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_11 _let_14) tptp.p_u_c) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.t_u_c) _let_4)) _let_9)))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.t_u_c) _let_4)) _let_2)))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.prod B C))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.prod A C))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun (tptp.sum0 _let_10 _let_5) tptp.bool))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (let ((_let_15 (tptp.sum0 A B))) (let ((_let_16 (tptp.fun _let_15 tptp.bool))) (let ((_let_17 (tptp.fun _let_3 _let_16))) (let ((_let_18 (tptp.fun (tptp.prod _let_15 C) tptp.bool))) (let ((_let_19 (tptp.fun _let_1 _let_18))) (let ((_let_20 (tptp.fun _let_13 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_18 _let_20) tptp.a_u_c) (tptp.s _let_18 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s (tptp.fun _let_16 _let_19) tptp.t_u_c) (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_8 _let_17) tptp.p_u_c) _let_9)) _let_4)))) _let_2)))) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_11 _let_14) tptp.p_u_c) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_8 _let_12) tptp.t_u_c) _let_9)) _let_2)))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.t_u_c) _let_4)) _let_2)))))))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun (tptp.sum0 A B) tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.l_a_u_c) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.p_u_c) _let_3)) (tptp.s _let_1 T0))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let 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(tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.p_u_c) _let_3)) _let_2))))))))))))))) (forall ((A $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 K0))) (let ((_let_3 (tptp.fun (tptp.prod A A) tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.infinite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.a_u_c) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.t_u_c) _let_2)) _let_2)))) _let_2)))))))))) (forall ((Q92028 $$unsorted) (Q92030 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q92030 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q92028 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.sum0 Q92028 Q92030) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.p_u_c) _let_4)) _let_2))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.sum0 A B) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.p_u_c) _let_4)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) 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_let_1 T0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.infinite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.l_a_u_c) _let_4)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.l_a_u_c) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.t_u_c) _let_4)) _let_2)))) _let_2)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun C tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let 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(tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_9 _let_15) tptp.l_u_c) _let_10)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_7 _let_14) tptp.l_u_c) _let_8)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.l_u_c) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.p_u_c) _let_10)) _let_8)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.p_u_c) _let_4)) _let_2)))))))))))))))))))))) (forall ((Q92448 $$unsorted) (B $$unsorted) (Q92455 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun Q92455 tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun Q92448 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun (tptp.prod Q92448 B) tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.l_a_u_c) _let_6)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.l_u_c) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 tptp.infinite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.l_u_c) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.t_u_c) _let_6)) _let_4)))) _let_2))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (Q92493 $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.fun Q92493 tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun (tptp.prod A B) tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.l_u_c) _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.l_u_c) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 tptp.infinite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.l_u_c) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.t_u_c) _let_6)) _let_4)))) _let_2)))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_225 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_225)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_225))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 S0))))) _let_2)))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.l_u_c) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.l_u_c) (tptp.s _let_1 tptp.univ))) (tptp.s _let_2 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_58 tptp.countable) _let_50))) (forall ((Q92567 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun Q92567 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.countable) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.l_a_u_c) _let_3)) (tptp.s _let_1 tptp.univ))))))))) (forall ((Q92581 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun Q92581 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.countable) _let_3))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.a_u_c) _let_3)) (tptp.s _let_1 tptp.univ)))))))))))) (forall ((A $$unsorted) (Q92609 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q92609 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.countable) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.l_a_u_c) _let_2)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2)))))))))) (forall ((A $$unsorted) (Q92630 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q92630 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.countable) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.a_u_c) _let_2)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2)))))))))) (forall ((Q92647 $$unsorted) (Q92648 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q92648 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun Q92647 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.a_u_c) _let_5)) _let_2))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.countable) _let_5)) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.countable) _let_2)))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.countable))) (let ((_let_5 (tptp.s _let_1 T0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))) (forall ((Q92699 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_226 $$unsorted)) (let ((_let_1 (tptp.fun Q92699 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s Q92699 GENR_PVARR_226)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q92699 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q92699 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q92699 _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q92699 _let_4) tptp.setspec) (tptp.s Q92699 GENR_PVARR_226))) _let_2)) _let_1)))))))))))))) (forall ((S0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.fun Q92699 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)) (tptp.s _let_1 P0)))))))))))))))) (forall ((Q92717 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q92717 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.countable) _let_2)))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.countable) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (A5 $$unsorted) (GENR_PVARR_227 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) (tptp.s _let_1 A5))) (tptp.s A GENR_PVARR_227)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (tptp.s _let_5 A5)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_227))) _let_2)) _let_1))))))))))))))))))) (forall ((F0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.countable) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 S0))) (tptp.s _let_3 F0))) _let_2))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun A _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1)))) (= _let_2 _let_1)))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.countable) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2)))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (A5 $$unsorted) (GENR_PVARR_228 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun A B))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 A5))) (tptp.s A GENR_PVARR_228)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.setspec) (tptp.s A GENR_PVARR_228))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) tptp.in) (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)))) (tptp.s _let_2 A5))))) _let_1))))))))))))))) (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) F0))) (=> (= (tptp.s B (tptp.i _let_3 _let_2)) (tptp.s B (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.countable) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 F0))) _let_2)))))))))))))))) (forall ((Q92923 $$unsorted)) (let ((_let_1 (tptp.fun Q92923 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) (tptp.s _let_1 tptp.empty)))))) (forall ((Q92953 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q92953 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable))) (=> (or (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inter) _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.union) _let_3)) _let_2)))))))))))) (forall ((A $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.union) _let_4)) _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_2))))))))))) (forall ((Q93018 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q93018 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q93018 _let_2) tptp.insert) (tptp.s Q93018 X))) (tptp.s _let_1 tptp.empty))))))))) (forall ((Q93047 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q93047 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q93047 _let_4) tptp.insert) (tptp.s Q93047 X))) _let_2)))) (tptp.s tptp.bool (tptp.i _let_3 _let_2)))))))) (forall ((A $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable))) (let ((_let_4 (tptp.fun A _let_1))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.delete) _let_2)) (tptp.s A X))))) (tptp.s tptp.bool (tptp.i _let_3 _let_2)))))))) (forall ((Q93123 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q93123 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.countable))) (let ((_let_5 (tptp.s _let_1 S0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_5))) (= (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.diff) _let_2)) _let_5)))) (tptp.s tptp.bool (tptp.i _let_4 _let_2))))))))))) (forall ((Q93147 $$unsorted) (Q93149 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q93149 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun Q93147 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun (tptp.prod Q93147 Q93149) tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.countable) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.countable) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.cross0) _let_4)) _let_2))))))))))))) (forall ((Q93175 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q93175 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) (tptp.s _let_1 S0)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun tptp.num Q93175))) (let ((_let_3 (tptp.fun Q93175 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.subset) (tptp.s _let_3 S0))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 tptp.univ))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) (tptp.s _let_1 S0)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.subset) (tptp.s _let_3 S0))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 tptp.univ))))))))))))))) (forall ((A $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun tptp.num A))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_3 S0) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 tptp.univ))))))))))))) (forall ((Q93264 $$unsorted)) (let ((_let_1 (tptp.fun Q93264 tptp.bool))) (= (forall ((D0 $$unsorted)) (let ((_let_1 (tptp.fun Q93264 tptp.bool))) (let ((_let_2 (tptp.s _let_1 D0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.countable) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.p0) _let_2)))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 tptp.empty)))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun tptp.num Q93264))) (let ((_let_3 (tptp.fun Q93264 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.p0) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 tptp.univ))))))))))))))) (forall ((Q93303 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q93303 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.countable) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.infinite) _let_2)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun tptp.num Q93303))) (let ((_let_3 (tptp.fun Q93303 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (and (= (tptp.s _let_3 S0) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.image) (tptp.s _let_2 F0))) (tptp.s _let_1 tptp.univ)))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.s (tptp.fun tptp.num Q93303) F0))) (=> (= (tptp.s Q93303 (tptp.i _let_3 _let_2)) (tptp.s Q93303 (tptp.i _let_3 _let_1))) (= _let_2 _let_1))))))))))))))))) (forall ((A $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 A5))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.countable) _let_3))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 A5)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.countable) _let_2)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.countable) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.unions) _let_3)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_231 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B C)))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun C tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 F0))) (tptp.s C GENR_PVARR_231)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun B C))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun C tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun B tptp.bool))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (and (= (tptp.p _let_4) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun A _let_10) tptp.in) _let_2)) (tptp.s _let_9 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun B _let_8) tptp.in) _let_1)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) T0) _let_2))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun C _let_6) tptp.setspec) (tptp.s C GENR_PVARR_231))) _let_4)) (tptp.s C (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) F0) _let_2)) _let_1))))))))))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.fun B C)))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun C tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.countable) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.countable) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.countable) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_4)) (tptp.s _let_2 T0))) (tptp.s _let_1 F0))))))))))))))))))) (forall ((N $$unsorted) (A $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_238 $$unsorted)) (let ((_let_1 (tptp.cart A N))) (let ((_let_2 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_1) (tptp.s _let_2 P0))) (tptp.s _let_1 GENR_PVARR_238)))) (exists ((V $$unsorted) (V0 $$unsorted)) (let ((_let_1 (tptp.cart A N))) (let ((_let_2 (tptp.s tptp.bool V0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart A N))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun N tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) P0) _let_1)) (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 V))) _let_1)))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_238))) _let_2)) (tptp.s _let_1 V))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (I0 $$unsorted) (GENR_PVARR_237 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 P0))) (tptp.s tptp.num I0))) (tptp.s A GENR_PVARR_237)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.setspec) (tptp.s A GENR_PVARR_237))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) P0) (tptp.s tptp.num I0))) _let_1)))) _let_1))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num (tptp.fun A tptp.bool)))) (let ((_let_2 (tptp.fun (tptp.cart A N) tptp.bool))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun N 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_let_1 tptp.univ))) (let ((_let_3 (tptp.fun (tptp.list A) tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.infinite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.a_u_c) (tptp.s _let_3 tptp.univ))) _let_2))))))))) (forall ((N $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.univ))) (let ((_let_3 (tptp.fun (tptp.cart A N) tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.infinite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.a_u_c) (tptp.s _let_3 tptp.univ))) _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_59 (tptp.i (tptp.s (tptp.fun _let_3 _let_59) tptp.a_u_c) _let_4)) (tptp.s _let_58 tptp.univ)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_57 tptp.countable) _let_4)))) (forall ((Q94935 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q94935 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.a_u_c) _let_2)) (tptp.s _let_3 tptp.univ)))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2)))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_245 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_245)))) (exists ((T0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_245))) _let_3)) _let_2)))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.infinite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.a_u_c) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))) _let_2))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (GENR_PVARR_247 $$unsorted)) (let ((_let_1 (tptp.list B))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_1) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_247)))) (exists ((L $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.list B))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s B X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.list B))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.mem) _let_2)) (tptp.s _let_4 L)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun B _let_3) 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(tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.mem) _let_2)) (tptp.s _let_4 L)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_2)) (tptp.s _let_1 S0)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_246))) _let_2)) (tptp.s _let_1 L))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun (tptp.list B) tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun (tptp.list A) tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.l_a_u_c) _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.l_a_u_c) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_1) _let_2))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (GENR_PVARR_249 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_249)))) (exists ((V $$unsorted) (V0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s tptp.bool V0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.q0) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_249))) _let_3)) _let_2)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_248 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_248)))) (exists ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.p0) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_248))) _let_3)) _let_2)))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.l_a_u_c) _let_5)) _let_2))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun A B))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.q0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 F0))) _let_2))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.l_a_u_c) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_1) _let_2)))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (GENR_PVARR_251 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_251)))) (exists ((V $$unsorted) (V0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s tptp.bool V0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_251))) _let_3)) _let_2)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_250 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_250)))) (exists ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_250))) _let_3)) _let_2)))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.l_a_u_c) _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.l_a_u_c) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_1) _let_2)))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (GENR_PVARR_253 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_253)))) (exists ((V $$unsorted) (V0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s tptp.bool V0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.countable) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_253))) _let_3)) _let_2)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_252 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_252)))) (exists ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.countable) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_252))) _let_3)) _let_2)))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.l_a_u_c) _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.l_a_u_c) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_1) _let_2)))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (U_1 $$unsorted)) (=> (forall ((T0 $$unsorted) (GENR_PVARR_257 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 T0))) (tptp.s _let_1 GENR_PVARR_257)))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_257))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 T0))))) _let_2)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_256 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_256)))) (exists ((U $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 U))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_256))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 S0))))) _let_2)))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.l_a_u_c) _let_5)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.l_a_u_c) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_1) _let_2)))))))))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_259 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_259)))) (exists ((L $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.list A))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.mem) _let_2)) (tptp.s _let_4 L)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_2)) (tptp.s _let_1 S0)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_259))) _let_2)) (tptp.s _let_1 L))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun (tptp.list A) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.countable) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.fun (tptp.list A) tptp.bool))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.countable) (tptp.s _let_2 tptp.univ)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.countable) (tptp.s _let_1 tptp.univ)))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_262 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_262)))) (exists ((T0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_2)) (tptp.s _let_1 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_262))) _let_3)) _let_2)))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.countable) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.countable) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_57 (tptp.i (tptp.s (tptp.fun _let_56 _let_57) tptp.a_u_c) (tptp.s _let_56 tptp.univ))) _let_4))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (forall ((GENR_PVARR_264 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 GENR_PVARR_264)))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_264))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.countable) _let_2)))) _let_2))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.a_u_c) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_2 U_0))))) (tptp.s _let_1 tptp.univ))))))))) (forall ((A $$unsorted)) (= (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.diff) (tptp.s _let_1 tptp.univ))) (tptp.s _let_1 S0))))))))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 S0)))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.g_a_) _let_1)) _let_1)))))) (= (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.p0) _let_1)))))) (forall ((N0 $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.p0) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) (tptp.s tptp.num N0)))))))) (forall ((D0 $$unsorted) (E0 $$unsorted)) (=> (and (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.g_a_) _let_1)) (tptp.s tptp.num tptp.m)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_2 D0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 E0) _let_1))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.m))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.real) E0))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.g_a_) _let_3)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.m))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.g_a_) _let_3)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_2 D0) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 E0) _let_1)))))))))))))) (forall ((E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 _let_2)))))))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.bool (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_div) _let_1)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))))))) (tptp.s tptp.bool (tptp.i _let_7 _let_1)))))))))))) (forall ((E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_div) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) _let_5)) _let_5)) _let_1))))))) (forall ((E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_mul) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_div) _let_1)) _let_3)))) _let_1))))))) (forall ((A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((A5 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1)))) (tptp.s tptp.num A5)))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((A5 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1)))) (tptp.s tptp.real A5)))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((A5 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num A5))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun A tptp.num) F0) _let_1))))))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 S0)))) (exists ((A5 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real A5))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) F0) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (A5 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real tptp.b0))) (let ((_let_2 (tptp.s tptp.real V))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_mul))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s tptp.real A5))) (let ((_let_8 (tptp.s tptp.real U))) (let ((_let_9 (tptp.s _let_3 (tptp.i _let_5 _let_8)))) (let ((_let_10 (tptp.s _let_4 tptp.realu_add))) (let ((_let_11 (tptp.s tptp.real Y))) (let ((_let_12 (tptp.s tptp.real X))) (let ((_let_13 (tptp.fun tptp.real tptp.bool))) (let ((_let_14 (tptp.fun tptp.real _let_13))) (let ((_let_15 (tptp.s _let_14 tptp.realu_lt))) (let ((_let_16 (tptp.s tptp.num tptp.u_0))) (let ((_let_17 (tptp.fun tptp.num tptp.num))) (let ((_let_18 (tptp.s _let_17 tptp.numeral))) (let ((_let_19 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_20 (tptp.s _let_13 (tptp.i (tptp.s _let_14 tptp.realu_le) (tptp.s tptp.real (tptp.i _let_19 (tptp.s tptp.num (tptp.i _let_18 _let_16)))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_15 _let_12)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_15 _let_11)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_20 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i _let_20 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 _let_8)) _let_2)) (tptp.s tptp.real (tptp.i _let_19 (tptp.s tptp.num (tptp.i _let_18 (tptp.s tptp.num (tptp.i (tptp.s _let_17 tptp.bit1) _let_16)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_15 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_12)))) (tptp.s tptp.real (tptp.i _let_6 _let_11)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 _let_1))))))))))))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (A5 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real A5))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.s tptp.real V))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.realu_mul))) (let ((_let_7 (tptp.s tptp.real X))) (let ((_let_8 (tptp.s tptp.real U))) (let ((_let_9 (tptp.s _let_5 tptp.realu_add))) (let ((_let_10 (tptp.fun tptp.real tptp.bool))) (let ((_let_11 (tptp.fun tptp.real _let_10))) (let ((_let_12 (tptp.s _let_11 tptp.realu_lt))) (let ((_let_13 (tptp.s tptp.num tptp.u_0))) (let ((_let_14 (tptp.fun tptp.num tptp.num))) (let ((_let_15 (tptp.s _let_14 tptp.numeral))) (let ((_let_16 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_17 (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.realu_le) (tptp.s tptp.real (tptp.i _let_16 (tptp.s tptp.num (tptp.i _let_15 _let_13)))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_12 _let_7)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_12 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_17 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i _let_17 _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_9 _let_8)) _let_3)) (tptp.s tptp.real (tptp.i _let_16 (tptp.s tptp.num (tptp.i _let_15 (tptp.s tptp.num (tptp.i (tptp.s _let_14 tptp.bit1) _let_13)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_12 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_8)) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))))) _let_1)))))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (A5 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.real A5))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.s tptp.real V))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.realu_mul))) (let ((_let_7 (tptp.s tptp.real X))) (let ((_let_8 (tptp.s tptp.real U))) (let ((_let_9 (tptp.s _let_5 tptp.realu_add))) (let ((_let_10 (tptp.fun tptp.real tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_le))) (let ((_let_12 (tptp.s tptp.num tptp.u_0))) (let ((_let_13 (tptp.fun tptp.num tptp.num))) (let ((_let_14 (tptp.s _let_13 tptp.numeral))) (let ((_let_15 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_16 (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.real (tptp.i _let_15 (tptp.s tptp.num (tptp.i _let_14 _let_12)))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_7)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_2)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_16 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i _let_16 _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_9 _let_8)) _let_3)) (tptp.s tptp.real (tptp.i _let_15 (tptp.s tptp.num (tptp.i _let_14 (tptp.s tptp.num (tptp.i (tptp.s _let_13 tptp.bit1) _let_12)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_8)) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_2)))))) _let_1))))))))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.infinite) (tptp.s _let_1 S0)))) (exists ((R0 $$unsorted)) (and (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.num) R0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_2 _let_3)))) (tptp.s tptp.num (tptp.i _let_2 _let_1)))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.in) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) R0) (tptp.s tptp.num N0))))) (tptp.s _let_1 S0)))))))))))) (forall ((Q96267 $$unsorted) (P0 $$unsorted) (F0 $$unsorted)) (= (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real D0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q96267 X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q96267 tptp.real) F0) _let_1)))) (tptp.s tptp.real D0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q96267 tptp.bool) P0) _let_1)))))))))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real D0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q96267 X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun Q96267 tptp.real) F0) _let_1)))) (tptp.s tptp.real D0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun Q96267 tptp.bool) P0) _let_1)))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real A5))) (tptp.s tptp.real B0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real A5))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_1)) (tptp.s tptp.real B0)))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real A5))) (tptp.s tptp.real B0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real A5))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_3 _let_1)) (tptp.s tptp.real B0)))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real Z0))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (let ((_let_8 (tptp.s tptp.num tptp.u_0))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.s _let_9 tptp.numeral))) (let ((_let_11 (tptp.s tptp.num (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) _let_8)))))))) (let ((_let_12 (tptp.fun tptp.num tptp.real))) (let ((_let_13 (tptp.s (tptp.fun tptp.real _let_12) tptp.realu_pow))) (let ((_let_14 (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_12 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_10 _let_8)))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_5)) _let_11)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_2)) _let_11)))) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_1)) _let_11)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))))))))))) (forall ((A $$unsorted) (N $$unsorted)) (= (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p0) (tptp.s tptp.num I0))) (tptp.s A X))))))))))))) (exists ((X $$unsorted)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart A N))) (let ((_let_3 (tptp.fun tptp.num A))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun N tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.p0) _let_1)) (tptp.s A (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 X))) _let_1)))))))))))))))))) (forall ((Q96506 $$unsorted) (Q96509 $$unsorted) (Q96508 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.prod Q96509 Q96508) Q96506))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q96508 Y))) (let ((_let_2 (tptp.s Q96509 X))) (let ((_let_3 (tptp.fun Q96508 Q96506))) (let ((_let_4 (tptp.prod Q96509 Q96508))) (let ((_let_5 (tptp.fun Q96508 _let_4))) (let ((_let_6 (tptp.fun Q96506 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q96506 _let_6) tptp.geq) (tptp.s Q96506 (tptp.i (tptp.s (tptp.fun _let_4 Q96506) F0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q96509 _let_5) tptp.c_) _let_2)) _let_1)))))) (tptp.s Q96506 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q96509 _let_3) tptp.p0) _let_2)) _let_1))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.prod Q96509 Q96508))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun Q96508 Q96506))) (let ((_let_4 (tptp.fun _let_1 Q96506))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (= (tptp.s Q96506 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.gabs) (tptp.s _let_5 U_0))) _let_2)) (tptp.s Q96506 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q96509 _let_3) tptp.p0) (tptp.s Q96509 (tptp.i (tptp.s (tptp.fun _let_1 Q96509) tptp.fst) _let_2)))) (tptp.s Q96508 (tptp.i (tptp.s (tptp.fun _let_1 Q96508) tptp.snd) _let_2))))))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((Q0 $$unsorted) (GENR_PVARR_269 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) (tptp.s _let_1 Q0))) (tptp.s A GENR_PVARR_269)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.setspec) (tptp.s A GENR_PVARR_269))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1)))) _let_1)))))))))) (forall ((P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_2 U_0) (tptp.s _let_1 Q0)))))))) (forall ((D0 $$unsorted) (E0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.real E0))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) P0))) (let ((_let_5 (tptp.s tptp.real D0))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 Q0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))))) (forall ((X $$unsorted)) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun A tptp.bool) Q0) (tptp.s A X)))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real D0))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) P0) _let_1)) (tptp.s A X)))))))))))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real D0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) P0) (tptp.s tptp.real D0))) _let_1)))))))))))))))) (forall ((Q96736 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (S0 $$unsorted) (GENR_PVARR_270 $$unsorted)) (let ((_let_1 (tptp.fun Q96736 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 S0))) (tptp.s _let_1 GENR_PVARR_270)))) (exists ((T0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun Q96736 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 P0) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 S0))) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_270))) _let_3)) _let_2))))))))))))))) (forall ((P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96736 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.hull) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.inters) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2)))))))))))))))) (forall ((Q96754 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96754 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.hull) _let_4)) _let_2)) _let_2)))))))) (forall ((Q96788 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96788 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q96788 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96788 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 F0)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hull) _let_3)) (tptp.s _let_1 S0)))))))))))) (forall ((Q96826 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96826 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q96826 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96826 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 F0)))))))))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.hull) _let_4)) _let_2)) _let_2) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))))))))))) (forall ((Q96848 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96848 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.hull) (tptp.s _let_2 P0))))) (let ((_let_5 (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 S0))))) (= (tptp.s _let_1 (tptp.i _let_4 _let_5)) _let_5))))))) (forall ((Q96863 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96863 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))) _let_2)))))))))) (forall ((Q96890 $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q96890 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.s _let_1 S0))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_3) tptp.subset))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_7 _let_6)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_5 _let_6)))) (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))))) (forall ((Q96917 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q96917 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.hull))) (let ((_let_7 (tptp.s _let_3 Q0))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.subset) _let_4)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))))) (forall ((Q96944 $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q96944 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.hull) _let_5)) _let_3)))) _let_2)))))))))))) (forall ((Q96968 $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q96968 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.s _let_4 P0))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.hull) _let_6)) _let_3)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((Q97015 $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q97015 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (forall ((TI_ $$unsorted)) (let ((_let_1 (tptp.fun Q97015 tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 S0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 T0))) _let_2)))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.hull) _let_5)) _let_3)) _let_2))))))))) (forall ((Q97046 $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q97046 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.union))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.hull) (tptp.s _let_6 P0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_7 _let_3)))) (tptp.s _let_1 (tptp.i _let_7 _let_2)))))) (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (forall ((Q97080 $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q97080 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.s _let_1 S0))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_4) tptp.union))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_7 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_5 _let_6)))) (tptp.s _let_1 (tptp.i _let_5 _let_2))))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.hull) (tptp.s _let_4 P0))))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_5) tptp.union))) (= (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.union) (tptp.s _let_1 S0))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))))) (forall ((Q97175 $$unsorted) (P0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97175 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s Q97175 A5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q97175 _let_3) tptp.in) _let_7)) _let_6))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q97175 _let_4) tptp.insert) _let_7)) _let_2)))) _let_6)))))))))) (forall ((Q97208 $$unsorted) (P0 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97208 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s Q97208 A5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q97208 _let_3) tptp.in) _let_7)) _let_6))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q97208 _let_4) tptp.insert) _let_7)) _let_2)))) _let_6)))))))))) (forall ((A $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_272 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) (tptp.s _let_1 P0))) (tptp.s A GENR_PVARR_272)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.setspec) (tptp.s A GENR_PVARR_272))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))) _let_1)))))))))) (forall ((P0 $$unsorted) (P1 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P1) _let_1)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_2 U_0) (tptp.s _let_1 P1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))) (tptp.s _let_2 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P1) _let_1))))))))))))))) (forall ((Q97302 $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q97302 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q97302 _let_3) tptp.in) (tptp.s Q97302 X))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))) _let_2)))))))))))) (forall ((Q97352 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97352 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 P0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.hull) _let_4)))) (let ((_let_7 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (let ((_let_8 (tptp.fun Q97352 Q97352))) (let ((_let_9 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_8 _let_5) tptp.image) (tptp.s _let_8 F0))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_7))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97352 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q97352 Q97352))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) P0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 F0))) _let_2))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_9 _let_2)))))) (tptp.s _let_1 (tptp.i _let_9 _let_7)))))))))))))))) (forall ((Q97450 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97450 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.fun Q97450 Q97450))) (let ((_let_7 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.image) (tptp.s _let_6 F0))))) (=> (and (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97450 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hull) _let_3)) (tptp.s _let_1 S0))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97450 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q97450 Q97450))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) P0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 F0))) _let_2)))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97450 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun Q97450 Q97450))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) P0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.image) (tptp.s _let_3 G0))) _let_2)))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q97450 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun Q97450 Q97450))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s (tptp.fun _let_4 _let_5) tptp.image))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.subset))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_4 G0))) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_4 F0))) _let_3)))) _let_2))))))))))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_7 _let_2)))) (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.fun A A))) (let ((_let_7 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.image) (tptp.s _let_6 F0))))) (=> (and (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hull) _let_3)) (tptp.s _let_1 S0))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.bool) P0))) (let ((_let_4 (tptp.fun A A))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.image) (tptp.s _let_4 F0))) _let_2)))) (tptp.s tptp.bool (tptp.i _let_3 _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A A) F0))) (=> (= (tptp.s A (tptp.i _let_3 _let_2)) (tptp.s A (tptp.i _let_3 _let_1))) (= _let_2 _let_1)))))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) F0) (tptp.s A X))) (tptp.s A Y))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_7 _let_2)))) (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))))) (forall ((Q97584 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97584 tptp.bool))) (=> (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q97584 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97584 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 F0)))))))))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 S0)))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun Q97584 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 S0) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.hull) (tptp.s _let_2 P0))) (tptp.s _let_1 T0)))))))))))) (forall ((Q97643 $$unsorted) (P0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun Q97643 tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))))) (let ((_let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s _let_1 S0))) (let ((_let_8 (tptp.s _let_1 (tptp.i _let_5 _let_7)))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_3) tptp.subset))) (=> (and (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q97643 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97643 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 F0)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_9 _let_7)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_9 _let_2)) _let_8)))) (= _let_8 _let_6)))))))))))) (forall ((Q97725 $$unsorted) (U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (Q0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q97725 tptp.bool))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 Q0))) (let ((_let_5 (tptp.s _let_3 P0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_5)) _let_4)) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))))) (forall ((P0 $$unsorted) (Q0 $$unsorted)) (let ((_let_1 (tptp.fun Q97725 tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.s0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 Q0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.hull))) (let ((_let_7 (tptp.s _let_3 P0))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (=> (and (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q97725 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97725 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 F0)))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun Q97725 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97725 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 Q0) _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 Q0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 F0)))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun Q97725 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_3 Q0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 P0))) _let_2))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_0) _let_7)) _let_4)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))))))))))))))))) (forall ((E0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real E0)))) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) (tptp.s tptp.real (tptp.i _let_2 _let_1)))))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (and (not (= _let_1 _let_6)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_2 _let_6)))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s tptp.real E0))))))))))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.num tptp.u_0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s _let_4 tptp.numeral))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 tptp.realu_ofu_num))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.real _let_8))) (let ((_let_10 (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.realu_add) (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) _let_3)))))))))) (let ((_let_11 (tptp.fun tptp.real tptp.bool))) (let ((_let_12 (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_le))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_5 _let_3)))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.real (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_7 _let_1)))) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) (tptp.s tptp.real (tptp.i _let_10 _let_2)))) _let_1))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.real X)))) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real Y))) (tptp.s tptp.real (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_pow) (tptp.s tptp.real X))) (tptp.s tptp.num N0))))))))))))) (forall ((X $$unsorted)) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) (tptp.s tptp.real X))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_pow) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s tptp.num N0))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) (tptp.s tptp.real Y)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real X))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))) (exists ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_pow) (tptp.s tptp.real X))) (tptp.s tptp.num N0))))) (tptp.s tptp.real Y))))))))))))))) (forall ((P0 $$unsorted)) (=> (and (forall ((D0 $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.s tptp.real D0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (=> (not (= _let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) P0) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))))))))))) (forall ((E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))) (forall ((P0 $$unsorted)) (=> (and (forall ((D0 $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (let ((_let_4 (tptp.s tptp.real D0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) P0) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_inv) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.num N0))))) (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))))) (forall ((E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))) (forall ((X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) _let_1)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.real C0)))) (forall ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (tptp.s tptp.real X))))) (tptp.s tptp.real C0))))))))))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.insert))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_max) _let_5)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_1 tptp.empty))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s tptp.real Y))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.insert))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_min) _let_5)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.inf) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_1 tptp.empty))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_0) _let_1)) _let_5))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_4 _let_2)))))) _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_5)) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))) _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.h_) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s tptp.num tptp.u_0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s _let_4 tptp.numeral))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_5 _let_3)))))) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_1)) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) _let_3)))))))) _let_2)) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_2)) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_4 _let_2)))))) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_1)) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))))) _let_1))))))))) (= (tptp.s tptp.real (tptp.i _let_54 _let_55)) _let_55) (= (tptp.s tptp.real (tptp.i _let_54 _let_53)) _let_53) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.sqrt) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_abs) _let_1)))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s tptp.num tptp.u_0))) (let ((_let_7 (tptp.s _let_2 tptp.numeral))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.real _let_8))) (let ((_let_10 (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_6)))))))))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_4 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_10 _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_7 _let_6)))) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)))))) (tptp.s tptp.real (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_pow) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_pow) _let_3)))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.real _let_8))) (let ((_let_10 (tptp.s _let_9 tptp.realu_sub))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_4 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.l_a_) _let_7)) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) _let_7)) _let_1)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_6 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_1)))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 tptp.realu_ofu_num))) (let ((_let_8 (tptp.s tptp.real (tptp.i _let_7 _let_5)))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.s _let_10 tptp.realu_sub))) (let ((_let_12 (tptp.s tptp.num N0))) (let ((_let_13 (tptp.fun tptp.real _let_6))) (let ((_let_14 (tptp.s _let_6 (tptp.i (tptp.s _let_13 tptp.realu_pow) _let_1)))) (let ((_let_15 (tptp.s tptp.num M0))) (let ((_let_16 (tptp.fun tptp.num _let_3))) (let ((_let_17 (tptp.s tptp.bool V))) (let ((_let_18 (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond))) (let ((_let_19 (tptp.fun tptp.num tptp.bool))) (let ((_let_20 (tptp.fun tptp.num _let_19))) (let ((_let_21 (tptp.fun _let_6 tptp.real))) (and (= (tptp.p _let_17) (= _let_1 _let_8)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun _let_19 _let_21) tptp.sum) (tptp.s _let_19 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun tptp.num _let_20) tptp.o_o_) _let_15)) _let_12)))) (tptp.s _let_6 (tptp.i (tptp.s _let_13 U_0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_18 (tptp.s tptp.bool (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_20 tptp.l_) _let_12)) _let_15)))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_4 _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_18 _let_17)) (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_16 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_16 tptp.p_) _let_12)) _let_5)))) _let_15)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.realu_div) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.real (tptp.i _let_14 _let_15)))) (tptp.s tptp.real (tptp.i _let_14 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.suc) _let_12)))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i _let_11 _let_8)) _let_1))))))))))))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_pow) _let_2)) _let_1)))))))) (forall ((X $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.realu_sub) _let_5)))) (let ((_let_9 (tptp.s tptp.num N0))) (let ((_let_10 (tptp.fun tptp.real _let_3))) (let ((_let_11 (tptp.s _let_3 (tptp.i (tptp.s _let_10 tptp.realu_pow) _let_1)))) (let ((_let_12 (tptp.s tptp.num M0))) (let ((_let_13 (tptp.s tptp.bool V))) (let ((_let_14 (tptp.fun tptp.num tptp.bool))) (let ((_let_15 (tptp.fun tptp.num _let_14))) (let ((_let_16 (tptp.fun _let_3 tptp.real))) (and (= (tptp.p _let_13) (= _let_1 _let_5)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_14 _let_16) tptp.sum) (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun tptp.num _let_15) tptp.o_o_) _let_12)) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_12)) _let_9)))))) (tptp.s _let_3 (tptp.i (tptp.s _let_10 U_0) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_13)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.realu_add) (tptp.s tptp.real (tptp.i _let_4 _let_9)))) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_11 _let_12)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.realu_div) (tptp.s tptp.real (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.suc) _let_9)))))))) (tptp.s tptp.real (tptp.i _let_8 _let_1)))))))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (GENR_PVARR_273 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num N0))) (tptp.s tptp.num GENR_PVARR_273)))) (exists ((M0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.setspec) (tptp.s tptp.num GENR_PVARR_273))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_) (tptp.s tptp.num N0))) _let_1)))) _let_1)))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.from) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_0) _let_1))))))))))) (= (tptp.s _let_18 (tptp.i (tptp.s _let_48 tptp.from) _let_51)) _let_50) (forall ((K0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))) (let ((_let_7 (tptp.s tptp.num K0))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.inter) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.from) _let_7)))) _let_6)) (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_) _let_2)) _let_7)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) _let_1)))) _let_6))))))))))))) (forall ((K0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.inter) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.from) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) _let_1)))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_1)))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.in) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.from) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.l_a_) _let_2)) _let_1))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.infinite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.from) (tptp.s tptp.num N0)))))))) (= (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_1)) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1)))))))))) _let_20) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.bool) P0))) (= (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_5 (tptp.s _let_3 tptp.numeral))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_5 _let_4)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_1)) (tptp.s tptp.num (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) _let_4)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1))))))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 tptp.bit1))) (let ((_let_3 (tptp.s tptp.num (tptp.i _let_2 (tptp.s tptp.num tptp.u_0))))) (let ((_let_4 (tptp.s _let_1 tptp.numeral))) (let ((_let_5 (tptp.s (tptp.fun tptp.num tptp.bool) P0))) (= (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.bit1))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num tptp.u_0))))) (let ((_let_6 (tptp.s _let_3 tptp.numeral))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_6 _let_5)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_7 _let_1)) (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_4 _let_5)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 P0) _let_1)))))))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_3))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_2 _let_3))))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_49 (tptp.i (tptp.s (tptp.fun _let_18 _let_49) tptp.sum) (tptp.s _let_18 (tptp.i (tptp.s _let_48 (tptp.i (tptp.s (tptp.fun tptp.num _let_48) tptp.o_o_) _let_17)) _let_17)))) _let_47)) (tptp.s tptp.real (tptp.i _let_47 _let_17))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.s _let_5 T0))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_3 _let_2)))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun _let_5 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.sum) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_) _let_7)) _let_4)))) _let_6)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_6 _let_7)))) (tptp.s tptp.real (tptp.i _let_6 _let_4))))))))))))))))) (= _let_21 (tptp.s tptp.num (tptp.i _let_46 _let_33))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 tptp.bit1))) (let ((_let_3 (tptp.s tptp.num (tptp.i _let_2 (tptp.s tptp.num tptp.u_0))))) (let ((_let_4 (tptp.s _let_1 tptp.numeral))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_2 _let_3)))))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_add))) (let ((_let_10 (tptp.s tptp.num (tptp.i _let_4 _let_3)))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_6 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) _let_10)) _let_5)))) _let_7)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i _let_7 _let_10)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_3)))))))) (tptp.s tptp.real (tptp.i _let_7 _let_5))))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.d_))) (let ((_let_7 (tptp.s _let_2 X))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_7)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_7)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_3)) _let_2)))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.d_))) (let ((_let_7 (tptp.s _let_2 X))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_7)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_7)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_sub) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_3)) _let_2)))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.d_) _let_3)) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s tptp.real C0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) U_0) _let_6)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_6)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.d_) _let_3)) _let_1))))))))))))) (forall ((C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.real C0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) U_0) _let_3)) _let_2)))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((N0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) _let_1)) (tptp.s tptp.num I0))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_1)))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.cart tptp.real N))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.lambda) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) _let_1))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.d_))) (let ((_let_7 (tptp.s _let_2 X))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_7)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_7)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun _let_4 tptp.real))) (let ((_let_11 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.dot) _let_3)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.sum) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_3)) _let_2))))))))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.dot) _let_45)) _let_43)) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i (tptp.s _let_24 (tptp.i _let_44 _let_45)) _let_17)))) (tptp.s tptp.real (tptp.i (tptp.s _let_24 (tptp.i _let_44 _let_43)) _let_17))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_42 (tptp.i (tptp.s (tptp.fun _let_36 _let_42) tptp.dot) _let_40)) _let_37)) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_34 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i _let_41 _let_17)))) (tptp.s tptp.real (tptp.i _let_39 _let_17)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i _let_41 _let_33)))) (tptp.s tptp.real (tptp.i _let_39 _let_33))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_35 (tptp.i (tptp.s (tptp.fun _let_22 _let_35) tptp.dot) _let_27)) _let_23)) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_34 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i _let_28 _let_17)))) (tptp.s tptp.real (tptp.i _let_26 _let_17)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_34 (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i _let_28 _let_33)))) (tptp.s tptp.real (tptp.i _let_26 _let_33)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_29 (tptp.i _let_31 (tptp.s tptp.real (tptp.i _let_28 _let_21)))) (tptp.s tptp.real (tptp.i _let_26 _let_21))))))))) (forall ((N $$unsorted) (K0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.cart tptp.real N))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (tptp.s tptp.num I0))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.realu_ofu_num) _let_1))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.d_))) (let ((_let_6 (tptp.s _let_2 X))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.vectoru_add) _let_6)) _let_3)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.d_))) (let ((_let_6 (tptp.s _let_2 X))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.vectoru_sub) _let_6)) _let_3)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.d_))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.vectoru_neg) _let_3)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))))))))))) (forall ((N $$unsorted) (C0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.d_))) (let ((_let_6 (tptp.s tptp.real C0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) _let_6)) _let_3)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_6)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)))))))))))))) (forall ((Q99503 $$unsorted) (Q99508 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.i0))) (let ((_let_2 (tptp.cart Q99503 Q99508))) (let ((_let_3 (tptp.s _let_2 tptp.y))) (let ((_let_4 (tptp.fun tptp.num Q99503))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_4) tptp.d_))) (let ((_let_6 (tptp.s _let_2 tptp.x))) (let ((_let_7 (tptp.s tptp.bool tptp.b0))) (let ((_let_8 (tptp.fun Q99503 Q99503))) (let ((_let_9 (tptp.fun Q99503 _let_8))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (= (tptp.s Q99503 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.bool _let_11) tptp.cond) _let_7)) _let_6)) _let_3)))) _let_1)) (tptp.s Q99503 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) _let_7)) (tptp.s Q99503 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_1)))) (tptp.s Q99503 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q99561 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99561))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2)) _let_2))))) (forall ((Q99576 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99576))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))))) (forall ((Q99591 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99591))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_sub) _let_2)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((Q99609 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99609))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.vectoru_neg) _let_2)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((Q99628 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99628))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.vectoru_neg) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.vectoru_sub) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.vectoru_add) _let_4)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.vectoru_neg) _let_2))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.vectoru_neg) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q99705 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99705))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_3 _let_2))))))) (forall ((Q99731 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99731))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.real B0))) (let ((_let_4 (tptp.s tptp.real A5))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.r_))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) _let_4)) _let_3)))) _let_2))))))))))) (forall ((Q99745 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99745))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)) _let_2)))))) (forall ((Q99762 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q99762))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (tptp.s _let_2 X))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.s _let_1 tptp.y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vectoru_sub) _let_2)) _let_3)))) _let_3)) _let_2))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.s _let_1 tptp.y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vectoru_add) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vectoru_sub) _let_2)) _let_3)))) _let_2))))))) (forall ((Q99811 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99811))) (let ((_let_2 (tptp.s _let_1 tptp.y))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) (tptp.s tptp.real tptp.c))))) (let ((_let_5 (tptp.s _let_1 tptp.x))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_5)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))))))) (forall ((Q99834 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99834))) (let ((_let_2 (tptp.s _let_1 tptp.y))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) (tptp.s tptp.real tptp.c))))) (let ((_let_5 (tptp.s _let_1 tptp.x))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_sub))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_5)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))))))) (forall ((Q99856 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99856))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.s tptp.real tptp.b0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.r_))) (let ((_let_6 (tptp.s tptp.real tptp.a0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_add) _let_6)) _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))) (forall ((Q99877 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99877))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.s tptp.real tptp.b0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.r_))) (let ((_let_6 (tptp.s tptp.real tptp.a0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_sub) _let_6)) _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.y))) (let ((_let_3 (tptp.s _let_1 tptp.x))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vectoru_sub) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vectoru_add) _let_3)) _let_2)))) _let_3)) _let_2))))))) (forall ((Q99907 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99907))) (let ((_let_2 (tptp.s _let_1 tptp.y))) (let ((_let_3 (tptp.s _let_1 tptp.x))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) _let_3)) _let_2)) _let_3) (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.y))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_1 tptp.x))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.vectoru_sub) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.vectoru_add) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.vectoru_neg) _let_2))))))))))) (forall ((Q99936 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99936))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_sub) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))))) (forall ((Q99948 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99948))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) (tptp.s tptp.real tptp.c))) _let_2)) _let_2))))) (forall ((Q99962 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q99962))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.vectoru_neg) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_2)))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.z))) (let ((_let_3 (tptp.s _let_1 tptp.y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 tptp.x))))) (= (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)))))))))) (forall ((Q100000 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100000))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_sub) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.vectoru_neg) _let_2))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg))) (= (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 (tptp.i _let_3 _let_2)))) _let_2))))) (forall ((Q100029 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100029))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.s tptp.real tptp.c))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.r_))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.vectoru_neg) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))) (forall ((Q100046 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100046))) (let ((_let_2 (tptp.s _let_1 tptp.x))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) (tptp.s tptp.real tptp.c))))) (let ((_let_5 (tptp.s _let_3 tptp.vectoru_neg))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i _let_5 _let_2)))) (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_4 _let_2))))))))))) (forall ((Q100059 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100059))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)) _let_2)))) (forall ((Q100076 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100076))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s _let_1 tptp.x))) (= (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_3)) _let_2) (= _let_3 _let_2)))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.p1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 tptp.m))))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 tptp.n))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.p1))) (let ((_let_3 (tptp.s _let_1 tptp.n))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 tptp.m))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 tptp.m))) (let ((_let_3 (tptp.s _let_1 tptp.n))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q100159 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.s tptp.num M0))) (let ((_let_3 (tptp.cart tptp.real Q100159))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.vec))) (= (= (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_3 (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.infinite) (tptp.s _let_1 tptp.univ)))))) (forall ((Q100205 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100205))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.dot))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q100240 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100240))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.dot))) (let ((_let_6 (tptp.s _let_1 X))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.vectoru_add) _let_6)) _let_3)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))))) (forall ((Q100273 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100273))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) (tptp.s _let_1 X))))) (let ((_let_5 (tptp.s _let_1 Y))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_add) _let_5)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_2))))))))))))) (forall ((Q100306 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100306))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.dot))) (let ((_let_6 (tptp.s _let_1 X))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.vectoru_sub) _let_6)) _let_3)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))))) (forall ((Q100339 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100339))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) (tptp.s _let_1 X))))) (let ((_let_5 (tptp.s _let_1 Y))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_sub) _let_5)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_2))))))))))))) (forall ((Q100362 $$unsorted) (C0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100362))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.dot))) (let ((_let_6 (tptp.s tptp.real C0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) _let_6)) _let_3)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_6)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))))) (forall ((Q100390 $$unsorted) (C0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100390))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) (tptp.s _let_1 X))))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) _let_5)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) _let_5)) (tptp.s tptp.real (tptp.i _let_4 _let_2))))))))))))) (forall ((Q100419 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100419))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.dot))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_3)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))) (forall ((Q100443 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100443))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) (tptp.s _let_1 X))))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i _let_4 _let_2)))))))))) (forall ((Q100457 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q100457))) (let ((_let_3 (tptp.fun _let_2 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.dot) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))) (tptp.s _let_2 X))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))))))) (forall ((Q100472 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q100472))) (let ((_let_3 (tptp.fun _let_2 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.dot) (tptp.s _let_2 X))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))))))) (forall ((Q100487 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100487))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_2)) _let_2)))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.dot) _let_3)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))) (forall ((Q100537 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q100537))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.dot) _let_3)) _let_3))))) (not (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))))) (forall ((Q100563 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100563))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100563))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.dot) (tptp.s _let_1 X))) (tptp.s _let_1 Y))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (= (tptp.s _let_1 Y) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((Q100586 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100586))) (= (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100586))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.dot) (tptp.s _let_1 X))) (tptp.s _let_1 Y))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (= (tptp.s _let_1 X) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((Q100593 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100593))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_2)) _let_2))))))))) (= (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (let ((_let_3 (tptp.fun tptp.n10 tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_2) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dimindex) (tptp.s _let_3 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.p0) _let_1)))))))))) _let_20) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) (tptp.s tptp.num I0))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.d_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) _let_1)) (tptp.s tptp.num I0))) _let_1)))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 X)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.p0) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.lambda) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) U_0) (tptp.s tptp.real X)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.d_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((Q100698 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q100698))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.prod _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_5 tptp.real) tptp.distance) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.c_) _let_3)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub) _let_3)) _let_2)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.d_))) (let ((_let_7 (tptp.s _let_3 X))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.prod _let_3 _let_3))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_9 tptp.real) tptp.distance) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.c_) _let_7)) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)))))))))))))))))) (forall ((N $$unsorted) (F0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (E1 $$unsorted) (E2 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s tptp.real B0))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_1) F0))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (let ((_let_7 (tptp.s tptp.real A5))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_le) _let_7)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_4 _let_7)))) (tptp.s _let_2 E1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_4 _let_3)))) (tptp.s _let_2 E2)))) (forall ((E0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.s _let_2 tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i _let_4 (tptp.s tptp.real A5))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s tptp.real B0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real E0))))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real D0)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) F0))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.prod _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_9 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_sub) _let_4)) _let_1)))))) (tptp.s tptp.real D0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_5 tptp.real) tptp.distance) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.c_) (tptp.s _let_2 (tptp.i _let_3 _let_4)))) (tptp.s _let_2 (tptp.i _let_3 _let_1)))))))) (tptp.s tptp.real E0)))))))))))))))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.in) (tptp.s _let_1 Y))) (tptp.s _let_2 E1)))) (exists ((E0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real E0)))) (forall ((YI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 YI_))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.prod _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_5 tptp.real) tptp.distance) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.c_) _let_3)) (tptp.s _let_1 Y))))))) (tptp.s tptp.real E0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_3)) (tptp.s _let_2 E1))))))))))))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.in) (tptp.s _let_1 Y))) (tptp.s _let_2 E2)))) (exists ((E0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real E0)))) (forall ((YI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 YI_))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.prod _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_5 tptp.real) tptp.distance) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.c_) _let_3)) (tptp.s _let_1 Y))))))) (tptp.s tptp.real E0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_3)) (tptp.s _let_2 E2))))))))))))))))))))) (not (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) F0) _let_3)))))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real A5))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.real B0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 E1)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 E2))))))))))))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) F0) _let_3)))))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real A5))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.real B0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 E1))))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 E2)))))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1)))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_mul) _let_5)) _let_5)))))))))))) (forall ((X $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real E0)))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real D0)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.realu_mul))) (let ((_let_5 (tptp.s tptp.real Y))) (let ((_let_6 (tptp.s _let_3 tptp.realu_sub))) (let ((_let_7 (tptp.s _let_2 tptp.realu_abs))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_lt))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_6 _let_5)) _let_1)))))) (tptp.s tptp.real D0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_5)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_4 _let_1)) _let_1)))))))) (tptp.s tptp.real E0))))))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1)))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_4 _let_2)))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_5)) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))) _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_4 _let_2)))))) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1)))) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.sqrt))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_mul))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_1)))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.sqrt))) (let ((_let_4 (tptp.s _let_2 tptp.realu_inv))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i _let_4 _let_1)))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s _let_2 tptp.sqrt))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_div))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_1)))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_1)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1)))) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))) _let_1) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_4 _let_2)))))) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.realu_lt))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_lt))) (let ((_let_6 (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt))) (let ((_let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_1)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i _let_6 _let_2)))) (tptp.s tptp.real (tptp.i _let_6 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_1)))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) _let_1))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_1)))) (= (= (tptp.s tptp.real (tptp.i _let_3 _let_2)) (tptp.s tptp.real (tptp.i _let_3 _let_1))) (= _let_2 _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_lt) _let_2)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) _let_2)) _let_1))) (= (tptp.s tptp.bool (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1)))) (tptp.s tptp.bool (tptp.i _let_5 _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) _let_1)) _let_2))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_2)) _let_1) (= _let_2 _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.s tptp.num tptp.u_0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.s _let_6 tptp.numeral))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_7 _let_5)))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_pow) _let_1)) (tptp.s tptp.num (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) _let_5)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_2)))) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.realu_lt))) (let ((_let_6 (tptp.s tptp.num tptp.u_0))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.s _let_7 tptp.numeral))) (let ((_let_9 (tptp.fun tptp.num tptp.real))) (let ((_let_10 (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_9 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_8 _let_6)))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_pow) _let_1)) (tptp.s tptp.num (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) _let_6)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_2)))) _let_1))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_pow) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) _let_2)))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.num tptp.bool) tptp.even) _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) (tptp.s tptp.real (tptp.i _let_5 _let_3)))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.div) _let_3)) _let_2)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_2 tptp.sqrt) _let_1)))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_div) _let_1)) _let_3)) _let_3))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_4 _let_2)))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_1)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_pow) _let_5)) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))))))) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.s tptp.real X))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.sqrt) _let_6)))) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))))))))) (forall ((Q102146 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q102146))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))))) (forall ((Q102162 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102162))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) (tptp.s _let_1 X))))))))) (forall ((Q102180 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102180))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))) (tptp.s tptp.real (tptp.i _let_3 _let_2))))))) (forall ((Q102210 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102210))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub))) (let ((_let_6 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)))) (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((Q102231 $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102231))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_4 (tptp.s tptp.real A5))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_abs) _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))) (forall ((Q102254 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_2 (tptp.cart tptp.real Q102254))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.vectoru_norm) _let_3)) _let_1) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.dot) _let_3)) _let_3)) _let_1))))))) (forall ((Q102285 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q102285))) (let ((_let_3 (tptp.s _let_2 X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))) (forall ((Q102307 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q102307))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3))))) (not (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))))) (forall ((Q102322 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102322))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_2)) _let_2))))))))) (forall ((Q102346 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q102346))) (let ((_let_3 (tptp.s _let_2 X))) (=> (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))) (forall ((Q102367 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q102367))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))) (forall ((Q102400 $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q102400))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))) (let ((_let_4 (tptp.s _let_2 X))) (let ((_let_5 (tptp.s tptp.real A5))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_5)) _let_4)) _let_3) (or (= _let_5 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))) (= _let_4 _let_3)))))))))) (forall ((Q102424 $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102424))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s tptp.real A5))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) _let_4)))) (= (= (tptp.s _let_1 (tptp.i _let_6 _let_3)) (tptp.s _let_1 (tptp.i _let_6 _let_2))) (or (= _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_3 _let_2)))))))))) (forall ((Q102468 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102468))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.real B0))) (let ((_let_4 (tptp.s tptp.real A5))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.r_))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))) (or (= _let_4 _let_3) (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((Q102500 $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102500))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s tptp.real A5))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) _let_4)))) (=> (and (not (= _let_4 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s _let_1 (tptp.i _let_6 _let_3)) (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (= _let_3 _let_2))))))))) (forall ((Q102535 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.real B0))) (let ((_let_2 (tptp.s tptp.real A5))) (let ((_let_3 (tptp.cart tptp.real Q102535))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.r_))) (=> (and (not (= _let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_4)) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) _let_4)))) (= _let_2 _let_1))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.vectoru_norm))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_5)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_2))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 tptp.vectoru_norm))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_5)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_2))))))))))))))) (forall ((Q102710 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102710))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) (tptp.s _let_1 X))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_2)) _let_2)))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.fun _let_2 tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.vectoru_norm))) (let ((_let_6 (tptp.s _let_2 X))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_7 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.realu_div) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.dot) _let_6)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_5 _let_6)))) (tptp.s tptp.real (tptp.i _let_5 _let_3)))))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))))))))) (forall ((Q102822 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q102822))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_4)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_5 _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub) _let_3)) _let_2))))))))))))))))) (forall ((Q102893 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real tptp.e0))) (let ((_let_2 (tptp.cart tptp.real Q102893))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.s _let_2 X))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_6 _let_4)))) (tptp.s tptp.real (tptp.i _let_6 _let_3)))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.vectoru_add) _let_4)) _let_3)))))) _let_1)))))))))))))) (forall ((Q102930 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real tptp.e0))) (let ((_let_2 (tptp.cart tptp.real Q102930))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.s _let_2 X))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_6 _let_4)))) (tptp.s tptp.real (tptp.i _let_6 _let_3)))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.vectoru_add) _let_4)) _let_3)))))) _let_1)))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.d_) _let_2)) _let_3)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) (tptp.s _let_1 X))))) (tptp.s tptp.real E0)))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun N tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 X))) _let_1)))))) (tptp.s tptp.real E0)))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) (tptp.s _let_1 X))))) (tptp.s tptp.real E0)))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun N tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 X))) _let_1)))))) (tptp.s tptp.real E0)))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.d_) _let_3)) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_3 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.sum) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))))))))))) (forall ((Q103229 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q103229))) (let ((_let_2 (tptp.s _let_1 tptp.y))) (let ((_let_3 (tptp.s _let_1 tptp.x))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_5 _let_3)))) (tptp.s tptp.real (tptp.i _let_5 _let_2)))))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub) _let_3)) _let_2))))))))))))))) (forall ((Q103249 $$unsorted) (Q103251 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q103251))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.cart tptp.real Q103249))) (let ((_let_5 (tptp.s _let_4 X))) (let ((_let_6 (tptp.fun _let_4 tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.vectoru_norm) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.dot) _let_5)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_2)) _let_2)))))))))))))) (forall ((Q103280 $$unsorted) (Q103282 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q103282))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.cart tptp.real Q103280))) (let ((_let_5 (tptp.s _let_4 X))) (let ((_let_6 (tptp.fun _let_4 tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.vectoru_norm) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.dot) _let_5)) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_2)) _let_2)))))))))))))) (forall ((Q103311 $$unsorted) (Q103313 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q103313))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.cart tptp.real Q103311))) (let ((_let_5 (tptp.s _let_4 X))) (let ((_let_6 (tptp.fun _let_4 tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.vectoru_norm) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.dot) _let_5)) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_2)) _let_2))))))))))) (forall ((Q103338 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.cart tptp.real Q103338))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun _let_3 tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.vectoru_norm) _let_4)) _let_2) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.dot) _let_4)) _let_4)) _let_2)))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_3) tptp.d_))) (let ((_let_5 (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.fun N tptp.bool))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dimindex) (tptp.s _let_7 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 X))) _let_1)))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_2 Y))) _let_1))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_2 (tptp.s _let_1 X))))) (tptp.s tptp.real (tptp.i _let_2 (tptp.s _let_1 Y))))))))))) (forall ((Q103415 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real Q103415))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.real))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.dot) _let_3)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.vectoru_norm) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.real tptp.a0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.s _let_6 X))) (let ((_let_8 (tptp.fun _let_6 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.vectoru_norm) _let_7)) _let_4) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.dot) _let_7)) _let_7)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.real tptp.a0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.s _let_6 X))) (let ((_let_8 (tptp.fun _let_6 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.vectoru_norm) _let_7)))) _let_4))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.dot) _let_7)) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.real tptp.a0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.s _let_6 X))) (let ((_let_8 (tptp.fun _let_6 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.s _let_10 tptp.realu_ge))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.vectoru_norm) _let_7)))) _let_4))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.realu_le) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.dot) _let_7)) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.real tptp.a0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.s _let_6 X))) (let ((_let_8 (tptp.fun _let_6 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_lt))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.vectoru_norm) _let_7)))) _let_4))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.dot) _let_7)) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.real tptp.a0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.s _let_6 X))) (let ((_let_8 (tptp.fun _let_6 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.s _let_10 tptp.realu_gt))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.vectoru_norm) _let_7)))) _let_4))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.realu_lt) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.dot) _let_7)) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.real tptp.a0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.s _let_6 X))) (let ((_let_8 (tptp.fun _let_6 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.s _let_10 tptp.realu_lt))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_8 tptp.vectoru_norm) _let_7)))) _let_4))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.dot) _let_7)) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1))))))))))))))))))))))))) (forall ((Q104506 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.cart tptp.real Q104506))) (let ((_let_5 (tptp.s _let_4 Y))) (let ((_let_6 (tptp.fun _let_4 tptp.real))) (let ((_let_7 (tptp.s _let_6 tptp.vectoru_norm))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_9 (tptp.s _let_4 X))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun tptp.real _let_11))) (let ((_let_13 (tptp.s _let_12 tptp.realu_sub))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.dot) _let_9)) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.realu_div) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.vectoru_add) _let_9)) _let_5)))))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_7 _let_9)))) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_7 _let_5)))) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) _let_2))))))))))))))))))) (forall ((Q104559 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.cart tptp.real Q104559))) (let ((_let_5 (tptp.s _let_4 Y))) (let ((_let_6 (tptp.s _let_4 X))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 tptp.real))) (let ((_let_9 (tptp.s _let_8 tptp.vectoru_norm))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun tptp.real _let_11))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.dot) _let_6)) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.realu_div) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_6)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_5)))) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.vectoru_sub) _let_6)) _let_5)))))) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) _let_2)))))))))))))))))) (forall ((Q104610 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.cart tptp.real Q104610))) (let ((_let_5 (tptp.s _let_4 Y))) (let ((_let_6 (tptp.s _let_4 X))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 tptp.real))) (let ((_let_9 (tptp.s _let_8 tptp.vectoru_norm))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_pow))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun tptp.real _let_11))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.dot) _let_6)) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.realu_div) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_6)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_5)))) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.vectoru_sub) _let_6)) _let_5)))))) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_ofu_num) _let_2)))))))))))))))))) (forall ((Q104636 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q104636))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.dot))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (let ((_let_6 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (let ((_let_7 (tptp.s _let_1 Y))) (= (= _let_2 _let_7) (and (= _let_6 (tptp.s tptp.real (tptp.i _let_5 _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_7)) _let_7)) _let_6))))))))))) (forall ((Q104658 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q104658))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.distance) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.c_) _let_2)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((Q104680 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q104680))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (= (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_3)))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))))))))))))) (forall ((Q104710 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q104710))) (let ((_let_2 (tptp.prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.distance) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.c_) (tptp.s _let_1 X))) (tptp.s _let_1 Y))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_8 (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 X))))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i _let_8 _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i _let_8 _let_3)))))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))))))))))))))))))) (forall ((Q104777 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q104777))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.c_))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 X))))) (let ((_let_7 (tptp.s (tptp.fun _let_3 tptp.real) tptp.distance))) (let ((_let_8 (tptp.s _let_1 Y))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_8)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_3 (tptp.i _let_6 _let_8)))))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_3 (tptp.i _let_6 _let_2)))))))))))))))))))) (forall ((Q104818 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q104818))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (= _let_3 _let_2)))))))) (forall ((Q104851 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q104851))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (not (= _let_3 _let_2)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2))))))))))))))) (forall ((Q104879 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q104879))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (= (not (= _let_3 _let_2)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2))))))))))))))) (forall ((Q104912 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.cart tptp.real Q104912))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.prod _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_2 _let_5) tptp.c_))) (let ((_let_7 (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_2 X))))) (let ((_let_8 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le))) (let ((_let_11 (tptp.s _let_2 Z0))) (let ((_let_12 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.real _let_12) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i _let_7 _let_11)))))) (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_11)))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i _let_7 _let_3)))))) _let_1))))))))))))))))) (forall ((Q104964 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real E0))) (let ((_let_2 (tptp.cart tptp.real Q104964))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.prod _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_2 _let_5) tptp.c_))) (let ((_let_7 (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_2 X))))) (let ((_let_8 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_lt))) (let ((_let_11 (tptp.s _let_2 Z0))) (let ((_let_12 (tptp.fun tptp.real tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.real _let_12) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i _let_7 _let_11)))))) (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_11)))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i _let_7 _let_3)))))) _let_1))))))))))))))))) (forall ((Q105011 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real tptp.e0))) (let ((_let_2 (tptp.cart tptp.real Q105011))) (let ((_let_3 (tptp.s _let_2 X2))) (let ((_let_4 (tptp.prod _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_2 _let_5) tptp.c_))) (let ((_let_7 (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_2 X1))))) (let ((_let_8 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_lt))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (let ((_let_12 (tptp.fun tptp.real tptp.real))) (let ((_let_13 (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.real _let_12) tptp.realu_div) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (let ((_let_14 (tptp.s _let_2 Y))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i _let_7 _let_14)))))) _let_13))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_14)))))) _let_13)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i _let_7 _let_3)))))) _let_1))))))))))))))))))) (forall ((Q105069 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real tptp.e0))) (let ((_let_2 (tptp.cart tptp.real Q105069))) (let ((_let_3 (tptp.s _let_2 X2))) (let ((_let_4 (tptp.s _let_2 X1))) (let ((_let_5 (tptp.prod _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_6) tptp.c_))) (let ((_let_8 (tptp.s (tptp.fun _let_5 tptp.real) tptp.distance))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_lt))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (let ((_let_12 (tptp.fun tptp.real tptp.real))) (let ((_let_13 (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.real _let_12) tptp.realu_div) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (let ((_let_14 (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_2 Y))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_5 (tptp.i _let_14 _let_4)))))) _let_13))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_5 (tptp.i _let_14 _let_3)))))) _let_13)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_3)))))) _let_1))))))))))))))))))) (forall ((Q105155 $$unsorted) (X $$unsorted) (XI_ $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105155))) (let ((_let_2 (tptp.s _let_1 YI_))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_8 (tptp.s _let_1 XI_))) (let ((_let_9 (tptp.s _let_1 X))) (let ((_let_10 (tptp.fun tptp.real tptp.real))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (let ((_let_12 (tptp.s (tptp.fun _let_1 _let_11) tptp.vectoru_add))) (let ((_let_13 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.real _let_13) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_9)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_8)) _let_2)))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_9)) _let_8)))))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))))))))))))))))))))))) (forall ((Q105190 $$unsorted) (X $$unsorted) (Y $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105190))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_8 (tptp.s tptp.real C0))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (let ((_let_11 (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_) _let_8)))) (= (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_11 _let_3)))) (tptp.s _let_1 (tptp.i _let_11 _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_9 tptp.realu_abs) _let_8)))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (XI_ $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.s tptp.real tptp.e0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 YI_))) (let ((_let_4 (tptp.s _let_2 XI_))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_2 _let_5) tptp.vectoru_add))) (let ((_let_7 (tptp.s _let_2 Y))) (let ((_let_8 (tptp.s _let_2 X))) (let ((_let_9 (tptp.prod _let_2 _let_2))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.s (tptp.fun _let_2 _let_10) tptp.c_))) (let ((_let_12 (tptp.s (tptp.fun _let_9 tptp.real) tptp.distance))) (let ((_let_13 (tptp.fun tptp.real tptp.bool))) (let ((_let_14 (tptp.s (tptp.fun tptp.real _let_13) tptp.realu_lt))) (let ((_let_15 (tptp.fun tptp.num tptp.num))) (let ((_let_16 (tptp.fun tptp.real tptp.real))) (let ((_let_17 (tptp.s tptp.real (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun tptp.real _let_16) tptp.realu_div) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_15 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_15 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_15 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.real (tptp.i _let_12 (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_8)) _let_4)))))) _let_17))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.real (tptp.i _let_12 (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_7)) _let_3)))))) _let_17)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.real (tptp.i _let_12 (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_8)) _let_7)))) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3)))))))) _let_1)))))))))))))))))))))) (forall ((Q105293 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105293))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (= _let_3 _let_2))))))))) (forall ((Q105328 $$unsorted) (Q105334 $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.cart tptp.real Q105334))) (let ((_let_4 (tptp.prod _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 _let_4))) (let ((_let_6 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.c_) (tptp.s _let_3 Y))) (tptp.s _let_3 Z0))))))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_pow))) (let ((_let_9 (tptp.cart tptp.real Q105328))) (let ((_let_10 (tptp.prod _let_9 _let_9))) (let ((_let_11 (tptp.fun _let_9 _let_10))) (let ((_let_12 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_10 tptp.real) tptp.distance) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.c_) (tptp.s _let_9 W))) (tptp.s _let_9 X))))))) (= (= _let_12 _let_6) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_12)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))))))))))))))))) (forall ((Q105385 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105385))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))) (let ((_let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_5 (tptp.prod _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.c_))) (let ((_let_8 (tptp.s (tptp.fun _let_5 tptp.real) tptp.distance))) (and (= (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_4)))) _let_3) (= (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2)))) _let_3))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun _let_1 _let_1)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.neutral) (tptp.s _let_2 tptp.vectoru_add))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 (tptp.fun _let_1 _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.monoidal) (tptp.s _let_2 tptp.vectoru_add))))))) (forall ((A $$unsorted) (N $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun A tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.d_) (tptp.s _let_3 (tptp.i _let_5 _let_2)))) _let_1)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun A (tptp.cart tptp.real N)))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.real))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_4 tptp.real))) (let ((_let_9 (tptp.fun tptp.num tptp.real))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.sum) _let_7)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_1) _let_3)) _let_1)))))))))))))))) (forall ((S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.vsum) _let_5)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_6 _let_1) tptp.lambda) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)) _let_3)))))))))))))))))) (forall ((Q105493 $$unsorted) (Q105495 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105495))) (let ((_let_2 (tptp.fun Q105493 _let_1))) (let ((_let_3 (tptp.fun Q105493 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.vsum) (tptp.s _let_3 tptp.empty))) (tptp.s _let_2 F0))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((Q105536 $$unsorted) (Q105541 $$unsorted) (X $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105541))) (let ((_let_2 (tptp.fun Q105536 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q105536 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum))) (let ((_let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)))) (let ((_let_9 (tptp.s Q105536 X))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun _let_4 tptp.bool))) (let ((_let_13 (tptp.fun _let_4 _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 tptp.finite) _let_5))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun Q105536 _let_13) tptp.insert) _let_9)) _let_5)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.bool _let_11) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun Q105536 _let_12) tptp.in) _let_9)) _let_5)))) _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.vectoru_add) (tptp.s _let_1 (tptp.i _let_3 _let_9)))) _let_8)))))))))))))))))))) (forall ((Q105555 $$unsorted) (Q105569 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105569))) (let ((_let_2 (tptp.fun Q105555 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q105555 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_1 (tptp.fun _let_1 _let_1)))) (let ((_let_7 (tptp.fun _let_2 _let_1))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.vsum) _let_5)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.iterate) (tptp.s _let_6 tptp.vectoru_add))) _let_5)) _let_3))))))))))))) (forall ((A $$unsorted) (Q105605 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105605))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105605))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) F0) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.vsum) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((Q105615 $$unsorted) (Q105619 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105619))) (let ((_let_2 (tptp.fun Q105615 _let_1))) (let ((_let_3 (tptp.fun Q105615 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105619))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q105615 _let_1) U_0) (tptp.s Q105615 X))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.vsum) (tptp.s _let_3 tptp.s0))) (tptp.s _let_2 U_0))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((Q105645 $$unsorted) (Q105652 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q105645 X))) (let ((_let_2 (tptp.cart tptp.real Q105652))) (let ((_let_3 (tptp.fun Q105645 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_5)) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))) (forall ((F0 $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105652))) (let ((_let_2 (tptp.fun Q105645 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q105645 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.vsum) (tptp.s _let_4 S0))))) (let ((_let_7 (tptp.s tptp.real C0))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) U_0) _let_7)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) _let_7)) (tptp.s _let_1 (tptp.i _let_6 _let_3))))))))))))))))) (forall ((Q105678 $$unsorted) (Q105681 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (V $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105681))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s Q105678 X))) (let ((_let_4 (tptp.fun Q105678 tptp.real))) (let ((_let_5 (tptp.s _let_4 C0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun Q105678 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) (tptp.s tptp.real (tptp.i _let_5 _let_3)))) _let_2)))))))))))) (forall ((C0 $$unsorted) (S0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105681))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun Q105678 tptp.real))) (let ((_let_4 (tptp.s _let_3 C0))) (let ((_let_5 (tptp.fun Q105678 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_3 tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (let ((_let_9 (tptp.fun Q105678 _let_1))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun _let_9 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_5 _let_11) tptp.vsum) _let_6)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_4)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.sum) _let_6)) _let_4)))) _let_2))))))))))))))))) (forall ((Q105715 $$unsorted) (Q105728 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q105715 X))) (let ((_let_2 (tptp.cart tptp.real Q105728))) (let ((_let_3 (tptp.fun Q105715 _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.s _let_3 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.vectoru_add) (tptp.s _let_2 (tptp.i _let_5 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105728))) (let ((_let_2 (tptp.fun Q105715 _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun Q105715 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)))) (let ((_let_8 (tptp.s _let_2 F0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) U_0) _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_add) (tptp.s _let_1 (tptp.i _let_7 _let_8)))) (tptp.s _let_1 (tptp.i _let_7 _let_3))))))))))))))))))) (forall ((Q105761 $$unsorted) (Q105774 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q105761 X))) (let ((_let_2 (tptp.cart tptp.real Q105774))) (let ((_let_3 (tptp.fun Q105761 _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.s _let_3 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.vectoru_sub) (tptp.s _let_2 (tptp.i _let_5 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105774))) (let ((_let_2 (tptp.fun Q105761 _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun Q105761 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)))) (let ((_let_8 (tptp.s _let_2 F0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) U_0) _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_sub) (tptp.s _let_1 (tptp.i _let_7 _let_8)))) (tptp.s _let_1 (tptp.i _let_7 _let_3))))))))))))))))))) (forall ((Q105798 $$unsorted) (Q105801 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105801))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.fun Q105798 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)) (tptp.s Q105798 N0))) _let_2))))) (forall ((C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105801))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.fun Q105798 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun Q105798 _let_1))) (let ((_let_7 (tptp.fun _let_6 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.vsum) _let_4)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.card) _let_4)))))) _let_2)))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun A tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.d_) (tptp.s _let_3 (tptp.i _let_5 _let_2)))) _let_1)))))))))))) (forall ((S0 $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.real))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (let ((_let_10 (tptp.fun _let_3 _let_2))) (let ((_let_11 (tptp.fun tptp.num tptp.real))) (let ((_let_12 (tptp.fun N tptp.bool))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.s (tptp.fun tptp.num _let_13) tptp.l_a_))) (let ((_let_15 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.num (tptp.i (tptp.s _let_15 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_15 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_12 tptp.num) tptp.dimindex) (tptp.s _let_12 tptp.univ))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_2 _let_11) tptp.d_) (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.vsum) _let_8)) _let_4)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_1)))))))))))))))))))))))) (forall ((Q105914 $$unsorted) (Q105918 $$unsorted) (Q105892 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q105918 Q105892))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.cart tptp.real Q105914))) (let ((_let_4 (tptp.fun Q105892 _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun Q105918 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun Q105918 tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_6 _let_3))) (let ((_let_11 (tptp.fun Q105892 tptp.bool))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (let ((_let_13 (tptp.fun _let_4 _let_3))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q105918 Y))) (let ((_let_2 (tptp.s Q105918 X))) (let ((_let_3 (tptp.s (tptp.fun Q105918 Q105892) F0))) (let ((_let_4 (tptp.fun Q105918 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q105918 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q105892 (tptp.i _let_3 _let_2)) (tptp.s Q105892 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.vsum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_1 _let_12) tptp.image) _let_2)) _let_9)))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.vsum) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.o) _let_5)) _let_2)))))))))))))))))))) (forall ((Q105942 $$unsorted) (Q105967 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q105967))) (let ((_let_2 (tptp.fun Q105942 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q105942 tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum))) (let ((_let_8 (tptp.s _let_4 S0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.fun _let_4 tptp.bool))) (let ((_let_12 (tptp.s _let_11 tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_12 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i _let_12 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_4 _let_11) tptp.disjoint) _let_8)) _let_5)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.union) _let_8)) _let_5)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3))))))))))))))))))) (forall ((Q105987 $$unsorted) (Q106012 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106012))) (let ((_let_2 (tptp.fun Q105987 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q105987 tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum))) (let ((_let_8 (tptp.s _let_4 S0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.fun _let_4 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 tptp.finite) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_4 _let_11) tptp.subset) _let_5)) _let_8)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.diff) _let_8)) _let_5)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_sub) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)))))))))))))))))) (forall ((Q106054 $$unsorted) (Q106053 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q106053 A5))) (let ((_let_2 (tptp.cart tptp.real Q106054))) (let ((_let_3 (tptp.fun Q106053 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q106053 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_3 _let_2))) (let ((_let_8 (tptp.s (tptp.fun _let_5 _let_7) tptp.vsum))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.fun Q106053 _let_5))) (let ((_let_11 (tptp.fun _let_5 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 tptp.finite) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q106053 _let_11) tptp.in) _let_1)) _let_6)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.delete) _let_6)) _let_1)))) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_2 _let_9) tptp.vectoru_sub) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_4)))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.s _let_4 S0))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (let ((_let_10 (tptp.s (tptp.fun _let_4 _let_9) tptp.vsum))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (let ((_let_12 (tptp.s (tptp.fun _let_1 _let_11) tptp.vectoru_add))) (let ((_let_13 (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_13 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_13 _let_5)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_6)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_5)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.union) _let_6)) _let_5)))) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.inter) _let_6)) _let_5)))) _let_3)))))))))))))))))))) (forall ((Q106132 $$unsorted) (Q106140 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q106132 X))) (let ((_let_2 (tptp.cart tptp.real Q106140))) (let ((_let_3 (tptp.fun Q106132 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_0) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.vectoru_neg) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106140))) (let ((_let_2 (tptp.fun Q106132 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q106132 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.vsum) (tptp.s _let_4 S0))))) (= (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) (tptp.s _let_1 (tptp.i _let_6 _let_3)))))))))))))) (forall ((Q106171 $$unsorted) (Q106182 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106182))) (let ((_let_2 (tptp.fun Q106171 _let_1))) (let ((_let_3 (tptp.fun Q106171 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.vsum) (tptp.s _let_3 S0))))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q106171 X))) (let ((_let_2 (tptp.cart tptp.real Q106182))) (let ((_let_3 (tptp.fun Q106171 _let_2))) (let ((_let_4 (tptp.fun Q106171 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q106171 _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 F0) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 G0) _let_1)))))))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_2 F0))) (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_2 G0))))))))))) (forall ((A $$unsorted) (N $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 U))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum))) (let ((_let_8 (tptp.s _let_4 V))) (let ((_let_9 (tptp.fun _let_4 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.subset) _let_5)) _let_8))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 V)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 U)))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) F0) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)))))))))))))) (forall ((A $$unsorted) (Q106306 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106306))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T0))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.vsum))) (let ((_let_7 (tptp.s _let_3 S0))) (let ((_let_8 (tptp.fun _let_3 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.subset) _let_4)) _let_7))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.cart tptp.real Q106306))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 T0)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 F0) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.g) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106306))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 S0)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 T0)))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) F0) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) (tptp.s _let_2 F0))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) (tptp.s _let_2 tptp.g)))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 U))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 V)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 U)))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) F0) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.union) _let_5)) (tptp.s _let_4 V))))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (F0 $$unsorted) (U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 V))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 U)))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_3 V)))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) F0) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.union) (tptp.s _let_4 U))) _let_5)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3))))))))))))) (forall ((Q106444 $$unsorted) (Q106450 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106450))) (let ((_let_2 (tptp.s Q106444 X))) (let ((_let_3 (tptp.fun Q106444 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q106444 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_0) _let_6)) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q106444 _let_7) tptp.in) _let_2)) _let_6)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106450))) (let ((_let_2 (tptp.fun Q106444 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q106444 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_3)))) (tptp.s _let_1 (tptp.i _let_7 _let_3))))))))))))))) (forall ((Q106500 $$unsorted) (Q106502 $$unsorted) (U_1 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106502))) (let ((_let_2 (tptp.s Q106500 X))) (let ((_let_3 (tptp.fun Q106500 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q106500 tptp.bool))) (let ((_let_6 (tptp.s _let_5 P0))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_1) _let_6)) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_278 $$unsorted)) (let ((_let_1 (tptp.fun Q106500 tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s Q106500 GENR_PVARR_278)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q106500 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q106500 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q106500 _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q106500 _let_4) tptp.setspec) (tptp.s Q106500 GENR_PVARR_278))) _let_2)) _let_1)))))))))))))) (forall ((P0 $$unsorted) (S0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106502))) (let ((_let_2 (tptp.fun Q106500 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q106500 tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.s _let_4 S0))) (let ((_let_8 (tptp.fun _let_2 _let_1))) (let ((_let_9 (tptp.s (tptp.fun _let_4 _let_8) tptp.vsum))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_4 (tptp.i (tptp.s _let_10 tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) U_0) _let_7)) _let_5)))))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_7)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_5)) _let_3)))))))))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (U_2 $$unsorted)) (=> (forall ((P0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 P0))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_2) _let_3)) _let_1))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_1))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (P0 $$unsorted) (GENR_PVARR_279 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_1) (tptp.s _let_1 S0))) (tptp.s _let_1 P0))) (tptp.s A GENR_PVARR_279)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 P0) _let_1))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_279))) _let_2)) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.s _let_3 F0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 P0))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_6 _let_11) U_0) _let_7)) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.bool _let_9) tptp.cond) (tptp.s tptp.bool (tptp.i _let_7 _let_1)))) (tptp.s _let_2 (tptp.i _let_5 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))))) (forall ((S0 $$unsorted) (P0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 P0))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.s _let_4 S0))) (let ((_let_8 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) _let_7)))) (let ((_let_9 (tptp.s _let_6 tptp.gspec))) (let ((_let_10 (tptp.fun _let_2 _let_1))) (let ((_let_11 (tptp.s (tptp.fun _let_4 _let_10) tptp.vsum))) (let ((_let_12 (tptp.s _let_2 F0))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (let ((_let_14 (tptp.fun _let_2 _let_2))) (let ((_let_15 (tptp.fun _let_2 _let_14))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_7)) (tptp.s _let_2 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_4 _let_15) U_0) _let_5)) _let_12)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_1 _let_13) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_4 (tptp.i _let_9 (tptp.s _let_4 (tptp.i _let_8 _let_5)))))) _let_12)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_4 (tptp.i _let_9 (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_6 U_2) _let_5)))))))) _let_3)))))))))))))))))))))))))))) (forall ((Q106605 $$unsorted) (Q106610 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q106610 X))) (let ((_let_2 (tptp.cart tptp.real Q106605))) (let ((_let_3 (tptp.fun Q106610 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q106610 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.vsum) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q106610 _let_6) tptp.insert) _let_1)) (tptp.s _let_5 tptp.empty))))) _let_4)) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))) (forall ((Q106640 $$unsorted) (Q106632 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q106640 X))) (let ((_let_2 (tptp.cart tptp.real Q106632))) (let ((_let_3 (tptp.fun Q106640 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q106640 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106632))) (let ((_let_2 (tptp.fun Q106640 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q106640 tptp.real))) (let ((_let_5 (tptp.fun Q106640 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_4 tptp.real))) (let ((_let_8 (tptp.fun _let_2 _let_1))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.vsum) _let_6)) _let_3)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.sum) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)))))))))))))))))))) (forall ((N $$unsorted) (A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun A _let_5))) (let ((_let_7 (tptp.fun _let_6 _let_5))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) _let_1)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun A tptp.real) G0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_5 tptp.real) tptp.vectoru_norm) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.vsum) _let_3)) (tptp.s _let_6 F0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.sum) _let_3)) (tptp.s _let_1 G0)))))))))))))))) (forall ((Q106736 $$unsorted) (Q106745 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q106736 A5))) (let ((_let_2 (tptp.cart tptp.real Q106745))) (let ((_let_3 (tptp.fun Q106736 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q106736 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))) (forall ((S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real B0))) (let ((_let_2 (tptp.cart tptp.real Q106745))) (let ((_let_3 (tptp.fun Q106736 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q106736 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_3 _let_2))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_le))) (let ((_let_10 (tptp.fun Q106736 tptp.real))) (let ((_let_11 (tptp.fun _let_10 tptp.real))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_5 _let_11) tptp.sum) _let_6)) (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_4)))))) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.vsum) _let_6)) _let_4)))))) _let_1)))))))))))))))))) (forall ((Q106792 $$unsorted) (A $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.cart tptp.real Q106792))) (let ((_let_5 (tptp.fun A _let_4))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.cart tptp.real Q106792))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) _let_1)))))) (tptp.s tptp.real B0)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.vectoru_norm) (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vsum) _let_2)) (tptp.s _let_5 F0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))))) (tptp.s tptp.real B0))))))))))))))) (forall ((Q106879 $$unsorted) (M0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q106879))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.f))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.s tptp.num M0))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun _let_3 _let_2))) (and (= (tptp.p _let_5) (= _let_8 _let_1)) (= (tptp.s _let_2 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.vsum) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_) _let_8)) _let_1)))) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_5)) (tptp.s _let_2 (tptp.i _let_4 _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.vec) _let_1))))))))))))))))))) (forall ((Q106879 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106879))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 tptp.f))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) _let_5)))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (let ((_let_10 (tptp.s (tptp.fun _let_6 _let_9) tptp.vsum))) (let ((_let_11 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i _let_8 _let_4)))) _let_3)))) (let ((_let_12 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.suc) _let_4)))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i _let_8 _let_12)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.bool _let_14) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_a_) _let_5)) _let_12)))) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 tptp.vectoru_add) _let_11)) (tptp.s _let_1 (tptp.i _let_3 _let_12)))))) _let_11)))))))))))))))))) (forall ((N $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.s tptp.num tptp.u_0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.s _let_6 tptp.numeral))) (let ((_let_8 (tptp.s tptp.num M0))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_) _let_8)))) (let ((_let_12 (tptp.fun _let_3 _let_2))) (let ((_let_13 (tptp.s (tptp.fun _let_9 _let_12) tptp.vsum))) (let ((_let_14 (tptp.fun _let_2 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.l_) (tptp.s tptp.num (tptp.i _let_7 _let_5)))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.l_a_) _let_8)) _let_1)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s _let_9 (tptp.i _let_11 _let_1)))) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_2 _let_14) tptp.vectoru_add) (tptp.s _let_2 (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.m_) _let_1)) (tptp.s tptp.num (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) _let_5)))))))))) _let_4)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))))))))) (forall ((Q106968 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.cart tptp.real Q106968))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_5)) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))) (forall ((F0 $$unsorted) (C0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q106968))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (let ((_let_8 (tptp.s tptp.real C0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) U_0) _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.r_) _let_8)) (tptp.s _let_1 (tptp.i _let_7 _let_3)))))))))))))))))) (forall ((Q107021 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107021))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.vsum) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num X))) (let ((_let_2 (tptp.cart tptp.real Q107021))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num M0))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s tptp.num N0))))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 F0) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 G0) _let_1)))))))))) (= (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_2 F0))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_2 G0)))))))))))) (forall ((B $$unsorted) (A $$unsorted) (Q107061 $$unsorted) (U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (Y $$unsorted) (GENR_PVARR_281 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_1) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B Y))) (tptp.s A GENR_PVARR_281)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_281))) _let_2)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107061))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s B Y))) (let ((_let_5 (tptp.fun A B))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun B _let_7))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.fun _let_2 _let_1))) (let ((_let_12 (tptp.fun B _let_1))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_5 _let_13))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_7 _let_14) U_0) _let_8)) _let_6)) _let_3)) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) tptp.vsum) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) U_1) _let_8)) _let_6)) _let_4)))))) _let_3)))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107061))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun A B))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun B _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (let ((_let_11 (tptp.fun B tptp.bool))) (let ((_let_12 (tptp.fun _let_6 _let_11))) (let ((_let_13 (tptp.fun _let_8 _let_1))) (let ((_let_14 (tptp.fun _let_2 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.finite) _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_6 _let_14) tptp.vsum) _let_7)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.vsum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.image) _let_5)) _let_7)))) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_5)) _let_3))))))))))))))))))))))))) (forall ((B $$unsorted) (A $$unsorted) (Q107150 $$unsorted) (U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (Y $$unsorted) (GENR_PVARR_282 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_1) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s B Y))) (tptp.s A GENR_PVARR_282)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) F0) _let_1)) (tptp.s B Y)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.setspec) (tptp.s A GENR_PVARR_282))) _let_2)) _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107150))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s B Y))) (let ((_let_5 (tptp.fun A B))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun A tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun B _let_7))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.fun _let_2 _let_1))) (let ((_let_12 (tptp.fun B _let_1))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_5 _let_13))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_7 _let_14) U_0) _let_8)) _let_6)) _let_3)) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) tptp.vsum) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) U_1) _let_8)) _let_6)) _let_4)))))) _let_3)))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107150))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun A B))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun B _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (let ((_let_12 (tptp.fun B tptp.bool))) (let ((_let_13 (tptp.s _let_12 T0))) (let ((_let_14 (tptp.fun _let_9 _let_1))) (let ((_let_15 (tptp.fun _let_4 _let_12))) (let ((_let_16 (tptp.fun _let_12 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) tptp.subset) (tptp.s _let_12 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_7 _let_15) tptp.image) _let_8)) _let_5)))) _let_13)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_12 _let_14) tptp.vsum) _let_13)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_4 _let_11) U_0) _let_5)) _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)) _let_3))))))))))))))))))))))))) (forall ((Q107186 $$unsorted) (Q107185 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (V $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107185))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s Q107186 X))) (let ((_let_4 (tptp.fun Q107186 tptp.real))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun Q107186 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) (tptp.s tptp.real (tptp.i _let_5 _let_3)))) _let_2)))))))))))) (forall ((F0 $$unsorted) (V $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107185))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun Q107186 tptp.real))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q107186 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun Q107186 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 _let_1))) (let ((_let_10 (tptp.fun _let_3 tptp.real))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.sum) _let_8)) _let_4)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.vsum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_2)))))))))))))))))))) (forall ((Q107219 $$unsorted) (Q107222 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107222))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s Q107219 X))) (let ((_let_6 (tptp.s Q107219 A5))) (let ((_let_7 (tptp.fun Q107219 _let_1))) (and (= (tptp.p _let_2) (= _let_5 _let_6)) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun Q107219 _let_7) U_0) _let_6)) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.bool _let_4) tptp.cond) _let_2)) (tptp.s _let_1 tptp.b0))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107222))) (let ((_let_2 (tptp.fun Q107219 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s Q107219 A5))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun Q107219 _let_1))) (let ((_let_9 (tptp.fun _let_8 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_2 _let_9) tptp.vsum) _let_3)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q107219 _let_8) U_0) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q107219 _let_5) tptp.in) _let_4)) _let_3)))) (tptp.s _let_1 tptp.b0))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))))) (forall ((Q107272 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real Q107272))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.s _let_3 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.vectoru_add) (tptp.s _let_2 (tptp.i _let_5 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107272))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (let ((_let_8 (tptp.s _let_2 F0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) U_0) _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_add) (tptp.s _let_1 (tptp.i _let_7 _let_8)))) (tptp.s _let_1 (tptp.i _let_7 _let_3)))))))))))))))))) (forall ((Q107324 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real Q107324))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.s _let_3 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.vectoru_sub) (tptp.s _let_2 (tptp.i _let_5 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107324))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.o_o_) (tptp.s tptp.num M0))) (tptp.s tptp.num N0))))))) (let ((_let_8 (tptp.s _let_2 F0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) U_0) _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_sub) (tptp.s _let_1 (tptp.i _let_7 _let_8)))) (tptp.s _let_1 (tptp.i _let_7 _let_3)))))))))))))))))) (forall ((Q107387 $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107387))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) _let_4)))) (let ((_let_7 (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num P0))))) (let ((_let_8 (tptp.s tptp.num (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_))) (let ((_let_12 (tptp.fun _let_2 _let_1))) (let ((_let_13 (tptp.s (tptp.fun _let_9 _let_12) tptp.vsum))) (let ((_let_14 (tptp.s tptp.num M0))) (let ((_let_15 (tptp.s _let_10 (tptp.i _let_11 _let_14)))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.l_a_) _let_14)) _let_8))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s _let_9 (tptp.i _let_15 _let_7)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_1 _let_16) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s _let_9 (tptp.i _let_15 _let_4)))) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_8)) _let_7)))) _let_3))))))))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (Q107444 $$unsorted) (U_2 $$unsorted)) (=> (forall ((X $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107444))) (let ((_let_2 (tptp.fun (tptp.prod A B) _let_1))) (let ((_let_3 (tptp.fun A (tptp.fun B _let_1)))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_2) (tptp.s _let_3 X))) (tptp.s _let_2 F0)))) (forall ((I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.cart tptp.real Q107444))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.prod A B))) (let ((_let_6 (tptp.fun B _let_5))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.geq) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_5 _let_3) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun A _let_6) tptp.c_) _let_2)) _let_1)))))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) X) _let_2)) _let_1))))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_283 $$unsorted)) (let ((_let_1 (tptp.prod A B))) (let ((_let_2 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) (tptp.s _let_3 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_283)))) (exists ((I0 $$unsorted) (J0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s B J0))) (let ((_let_2 (tptp.s A I0))) (let ((_let_3 (tptp.prod A B))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun B tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun A tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun A _let_11) tptp.in) _let_2)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun B _let_9) tptp.in) _let_1)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun A _let_8) T0) _let_2))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_283))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.c_) _let_2)) _let_1))))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.cart tptp.real Q107444))) (let ((_let_3 (tptp.fun B _let_2))) (let ((_let_4 (tptp.fun A _let_3))) (let ((_let_5 (tptp.s _let_4 X))) (let ((_let_6 (tptp.fun B tptp.bool))) (let ((_let_7 (tptp.fun A _let_6))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun _let_3 _let_2))) (let ((_let_10 (tptp.fun A _let_2))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) U_0) _let_8)) _let_5)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.vsum) (tptp.s _let_6 (tptp.i _let_8 _let_1)))) (tptp.s _let_3 (tptp.i _let_5 _let_1))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107444))) (let ((_let_2 (tptp.fun A (tptp.fun B _let_1)))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.prod A B))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun A (tptp.fun B tptp.bool)))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun A tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun _let_4 tptp.bool))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.fun _let_5 _let_1))) (let ((_let_14 (tptp.fun A _let_1))) (let ((_let_15 (tptp.fun _let_2 _let_14))) (let ((_let_16 (tptp.fun _let_14 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_9 tptp.bool) tptp.finite) _let_10))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s A I0))) (let ((_let_2 (tptp.fun B tptp.bool))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) T0) _let_1)))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_9 _let_16) tptp.vsum) _let_10)) (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_7 _let_15) U_0) _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.vsum) (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_11 _let_11) tptp.gspec) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) U_1) _let_10)) _let_8)))))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.gabs) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_2) _let_3))))))))))))))))))))))))))))))) (forall ((N $$unsorted) (A $$unsorted) (B $$unsorted) (D0 $$unsorted) (I0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A B))) (let ((_let_2 (tptp.s _let_1 I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun B _let_3))) (let ((_let_5 (tptp.s _let_4 D0))) (let ((_let_6 (tptp.fun A _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_6 _let_3))) (let ((_let_11 (tptp.fun B tptp.bool))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (let ((_let_13 (tptp.fun _let_4 _let_3))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s (tptp.fun A B) I0))) (let ((_let_4 (tptp.s B (tptp.i _let_3 _let_2)))) (let ((_let_5 (tptp.s A Y))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun A _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_7))) (not (= _let_2 _let_5)) (= _let_4 (tptp.s B (tptp.i _let_3 _let_5)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun B _let_1) D0) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.vsum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_1 _let_12) tptp.image) _let_2)) _let_9)))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.vsum) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.o) _let_5)) _let_2)))))))))))))))))))) (forall ((Q107636 $$unsorted) (Q107660 $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107660))) (let ((_let_2 (tptp.fun Q107636 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q107636 tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum))) (let ((_let_8 (tptp.s _let_4 S0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_5))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107660))) (let ((_let_2 (tptp.s Q107636 X))) (let ((_let_3 (tptp.fun Q107636 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q107636 _let_5) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.inter) (tptp.s _let_3 S0))) (tptp.s _let_3 T0)))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q107636 _let_1) F0) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.union) _let_8)) _let_5)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)))))))))))))))))) (forall ((A $$unsorted) (Q107754 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107754))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun _let_4 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) U_0) _let_3)) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)) _let_3))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107754))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_5 _let_1))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.finite) _let_7))) (forall ((T0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))))))))) (forall ((T1 $$unsorted) (T2 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107754))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 T2))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)))) (let ((_let_7 (tptp.s _let_3 T1))) (let ((_let_8 (tptp.s _let_5 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_3 _let_9) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_7)) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_4)) _let_8))) (not (= _let_7 _let_4)) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_4)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) F0) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.vsum) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.unions) _let_7)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.vsum) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3)))))))))))))))))) (forall ((Q107795 $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107795))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.o_o_))) (let ((_let_10 (tptp.fun _let_2 _let_1))) (let ((_let_11 (tptp.s (tptp.fun _let_7 _let_10) tptp.vsum))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.l_a_) _let_6)) _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_4)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_1 _let_12) tptp.vectoru_add) (tptp.s _let_1 (tptp.i _let_3 _let_6)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) _let_6)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_4)))) _let_3))))))))))))))))))) (forall ((Q107857 $$unsorted) (U_0 $$unsorted)) (=> (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.cart tptp.real Q107857))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.f))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_sub) (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real Q107857))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s tptp.num N0))) (let ((_let_7 (tptp.s _let_5 tptp.f))) (let ((_let_8 (tptp.s tptp.num M0))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_5 _let_4))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.vsum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) _let_8)) _let_6)))) (tptp.s _let_5 U_0))) (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.l_a_) _let_8)) _let_6)))) (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.vectoru_sub) (tptp.s _let_4 (tptp.i _let_7 _let_8)))) (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_6)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))) (forall ((Q107910 $$unsorted) (U_0 $$unsorted)) (=> (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.cart tptp.real Q107910))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.f))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 U_0) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.vectoru_sub) (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))) (forall ((M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real Q107910))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s tptp.num M0))) (let ((_let_7 (tptp.s _let_5 tptp.f))) (let ((_let_8 (tptp.s tptp.num N0))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_5 _let_4))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.vsum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) _let_6)) _let_8)))) (tptp.s _let_5 U_0))) (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.bool _let_10) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 tptp.l_a_) _let_6)) _let_8)))) (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.vectoru_sub) (tptp.s _let_4 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_8)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))) (tptp.s _let_4 (tptp.i _let_7 _let_6)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))) (forall ((A $$unsorted) (Q107975 $$unsorted) (X $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q107975))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum))) (let ((_let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)))) (let ((_let_9 (tptp.s A X))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun _let_4 tptp.bool))) (let ((_let_13 (tptp.fun A _let_4))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 tptp.finite) _let_5))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_4 _let_13) tptp.delete) _let_5)) _let_9)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.bool _let_11) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun A _let_12) tptp.in) _let_9)) _let_5)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 tptp.vectoru_sub) _let_8)) (tptp.s _let_1 (tptp.i _let_3 _let_9)))))) _let_8)))))))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun B _let_1))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (let ((_let_5 (tptp.fun A _let_1))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun B tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) tptp.in) (tptp.s B Y))) (tptp.s _let_1 T0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)) (tptp.s B Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s B Y))) (let ((_let_4 (tptp.s (tptp.fun A B) H0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s B (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_1)) (tptp.s _let_6 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) _let_3)) (tptp.s _let_4 T0)))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) G0) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) _let_1)))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.vsum) (tptp.s _let_6 S0))) (tptp.s _let_5 F0))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.vsum) (tptp.s _let_3 T0))) (tptp.s _let_2 G0))))))))))))) (forall ((A $$unsorted) (B $$unsorted) (N $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun B _let_1))) (let ((_let_3 (tptp.fun B tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (let ((_let_5 (tptp.fun A _let_1))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (=> (and (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s B Y))) (let ((_let_2 (tptp.s A (tptp.i (tptp.s (tptp.fun B A) K0) _let_1)))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun B tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun B _let_6) tptp.in) _let_1)) (tptp.s _let_5 T0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (= (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_2)) _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s B (tptp.i (tptp.s (tptp.fun A B) H0) _let_1)))) (let ((_let_4 (tptp.fun B tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun A _let_7) tptp.in) _let_1)) (tptp.s _let_6 S0)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun B _let_5) tptp.in) _let_3)) (tptp.s _let_4 T0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun B A) K0) _let_3)) _let_1) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun B _let_2) G0) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) _let_1)))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.vsum) (tptp.s _let_6 S0))) (tptp.s _let_5 F0))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.vsum) (tptp.s _let_3 T0))) (tptp.s _let_2 G0))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun A tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))) (forall ((F0 $$unsorted) (P0 $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun A (tptp.cart tptp.real N)))) (let ((_let_7 (tptp.fun A tptp.real))) (let ((_let_8 (tptp.fun A tptp.bool))) (let ((_let_9 (tptp.s _let_8 P0))) (let ((_let_10 (tptp.fun _let_7 tptp.real))) (let ((_let_11 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (forall ((Q0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 Q0))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.subset) _let_4)) (tptp.s _let_3 P0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.vsum) _let_4)) (tptp.s _let_2 F0))))))) (tptp.s tptp.real E0)))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.sum) _let_9)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) U_0) (tptp.s _let_6 F0))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))) (tptp.s tptp.real E0))))))))))))))))))))))) (forall ((Q108537 $$unsorted) (Q108528 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q108528))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s Q108537 X))) (let ((_let_4 (tptp.fun Q108537 _let_1))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (let ((_let_7 (tptp.fun Q108537 tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.dot) (tptp.s _let_1 (tptp.i _let_5 _let_3)))) _let_2)))))))))))) (forall ((S0 $$unsorted) (F0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q108528))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun Q108537 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q108537 tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun Q108537 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (let ((_let_10 (tptp.fun _let_3 _let_1))) (let ((_let_11 (tptp.fun _let_1 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.dot) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.vsum) _let_8)) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_2)))))))))))))))))))) (forall ((Q108573 $$unsorted) (Q108564 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (F0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q108573 Y))) (let ((_let_2 (tptp.cart tptp.real Q108564))) (let ((_let_3 (tptp.fun Q108573 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.s _let_2 X))) (let ((_let_6 (tptp.fun _let_2 tptp.real))) (let ((_let_7 (tptp.fun Q108573 tptp.real))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_0) _let_5)) _let_4)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.dot) _let_5)) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))) (forall ((S0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q108564))) (let ((_let_2 (tptp.fun Q108573 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun Q108573 tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun Q108573 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (let ((_let_10 (tptp.fun _let_2 _let_1))) (let ((_let_11 (tptp.fun _let_1 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.dot) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.vsum) _let_8)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_4)) _let_3)))))))))))))))))))) (forall ((Q108605 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (P0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.cart tptp.real Q108605))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun tptp.num _let_5))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) U_0) _let_6)) _let_1)) _let_2)) (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num P0))) (let ((_let_2 (tptp.cart tptp.real Q108605))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun tptp.num _let_3))) (let ((_let_6 (tptp.s tptp.num tptp.n))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_))) (let ((_let_11 (tptp.fun _let_3 _let_2))) (let ((_let_12 (tptp.s (tptp.fun _let_8 _let_11) tptp.vsum))) (let ((_let_13 (tptp.fun tptp.num tptp.num))) (let ((_let_14 (tptp.s (tptp.fun tptp.num _let_13) tptp.p_))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_14 _let_7)) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_13 (tptp.i _let_14 _let_6)) _let_1)))))) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_7)) _let_6)))) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_1)))))))))))))))))))))) (forall ((Q108650 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (M0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.cart tptp.real Q108650))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun tptp.num _let_5))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) U_0) _let_6)) _let_1)) _let_2)) (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.p_) _let_2)) _let_1))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num M0))) (let ((_let_2 (tptp.cart tptp.real Q108650))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun tptp.num _let_3))) (let ((_let_6 (tptp.s tptp.num N0))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_))) (let ((_let_11 (tptp.fun _let_3 _let_2))) (let ((_let_12 (tptp.s (tptp.fun _let_8 _let_11) tptp.vsum))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 tptp.l_a_) _let_1)) _let_6))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_1)) _let_6)))) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.m_) _let_6)) _let_1)))))) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_1))))))))))))))))))))) (forall ((Q108694 $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q108694))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.num M0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.l_) _let_3)) _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.vsum) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) _let_4)) _let_3)))) (tptp.s _let_2 F0))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((Q108721 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q108721))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.fun tptp.num _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)) (tptp.s tptp.num N0))) _let_2))))) (forall ((C0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q108721))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.s tptp.num M0))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s tptp.num N0))) (let ((_let_6 (tptp.fun tptp.num _let_4))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun tptp.num _let_1))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun _let_8 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.vsum) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_) _let_3)) _let_5)))) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) U_0) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 tptp.m_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_6 tptp.p_) _let_5)) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_3)))))) _let_2))))))))))))))))) (forall ((Q108775 $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 tptp.suc))) (let ((_let_3 (tptp.cart tptp.real Q108775))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_1 _let_4))) (let ((_let_7 (tptp.s tptp.num M0))) (let ((_let_8 (tptp.s tptp.num N0))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.o_o_))) (let ((_let_12 (tptp.fun _let_4 _let_3))) (let ((_let_13 (tptp.s (tptp.fun _let_9 _let_12) tptp.vsum))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.num (tptp.i _let_2 _let_8)))) (tptp.s tptp.num (tptp.i _let_2 _let_7)))))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_8)) _let_7)))) (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.o) _let_5)) _let_2))))))))))))))))))) (forall ((N $$unsorted) (A $$unsorted) (F0 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun A A))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun A _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.fun A tptp.bool))) (let ((_let_7 (tptp.fun _let_3 _let_2))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.vsum) (tptp.s _let_6 S0))))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s A X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_3)))) _let_2)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.fun A tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.in) (tptp.s A Y))) (tptp.s _let_1 S0)))) (and (exists ((X $$unsorted)) (let ((_let_1 (tptp.s A X))) (let ((_let_2 (tptp.fun A tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun A _let_3) tptp.in) _let_1)) (tptp.s _let_2 S0)))) (= (tptp.s A (tptp.i (tptp.s (tptp.fun A A) P0) _let_1)) (tptp.s A Y))))))) (forall ((X $$unsorted) (XI_ $$unsorted)) (let ((_let_1 (tptp.s A XI_))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.s A Y))) (let ((_let_4 (tptp.s (tptp.fun A A) P0))) (let ((_let_5 (tptp.fun A tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun A _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (= (tptp.s A (tptp.i _let_4 _let_2)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s A (tptp.i _let_4 _let_1)) _let_3)) (= _let_2 _let_1))))))))))))))))) (= (tptp.s _let_2 (tptp.i _let_8 _let_4)) (tptp.s _let_2 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.o) _let_4)) (tptp.s _let_1 P0)))))))))))))))) (forall ((N $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.fun _let_5 _let_5))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) U_1) _let_8)) _let_6)) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_8 _let_3)))) (tptp.s tptp.real (tptp.i _let_8 _let_2)))))) (tptp.s _let_4 (tptp.i _let_6 _let_3))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) U_0) _let_8)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) (tptp.s tptp.real (tptp.i _let_8 _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.vectoru_sub) (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_7 _let_9))) (let ((_let_11 (tptp.s tptp.num N0))) (let ((_let_12 (tptp.s tptp.num M0))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.fun tptp.num _let_13))) (let ((_let_15 (tptp.fun _let_5 _let_4))) (let ((_let_16 (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_13 _let_15) tptp.vsum) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.num _let_14) tptp.o_o_) _let_12)) _let_11)))))) (let ((_let_17 (tptp.fun _let_4 _let_4))) (let ((_let_18 (tptp.s (tptp.fun tptp.real _let_17) tptp.r_))) (let ((_let_19 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_11)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_20 (tptp.fun _let_4 _let_17))) (let ((_let_21 (tptp.s _let_20 tptp.vectoru_sub))) (= (tptp.s _let_4 (tptp.i _let_16 (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_0) _let_8)) _let_6)))) (tptp.s _let_4 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun tptp.bool _let_20) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 tptp.l_a_) _let_12)) _let_11)))) (tptp.s _let_4 (tptp.i (tptp.s _let_17 (tptp.i _let_21 (tptp.s _let_4 (tptp.i (tptp.s _let_17 (tptp.i _let_21 (tptp.s _let_4 (tptp.i (tptp.s _let_17 (tptp.i _let_18 (tptp.s tptp.real (tptp.i _let_8 _let_19)))) (tptp.s _let_4 (tptp.i _let_6 _let_19)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_17 (tptp.i _let_18 (tptp.s tptp.real (tptp.i _let_8 _let_12)))) (tptp.s _let_4 (tptp.i _let_6 _let_12)))))))) (tptp.s _let_4 (tptp.i _let_16 (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_1) _let_8)) _let_6)))))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))))))))))))) (forall ((N $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_1) _let_6)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s tptp.real (tptp.i _let_6 _let_1)))))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) U_0) _let_8)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) (tptp.s tptp.real (tptp.i _let_8 _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_sub) (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_7 _let_9))) (let ((_let_11 (tptp.s tptp.num N0))) (let ((_let_12 (tptp.s tptp.num M0))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.fun tptp.num _let_13))) (let ((_let_15 (tptp.fun _let_5 _let_4))) (let ((_let_16 (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_13 _let_15) tptp.vsum) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.num _let_14) tptp.o_o_) _let_12)) _let_11)))))) (let ((_let_17 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (let ((_let_18 (tptp.fun tptp.num _let_2))) (let ((_let_19 (tptp.fun _let_4 _let_4))) (let ((_let_20 (tptp.s (tptp.fun tptp.real _let_19) tptp.r_))) (let ((_let_21 (tptp.fun _let_4 _let_19))) (let ((_let_22 (tptp.s _let_21 tptp.vectoru_sub))) (= (tptp.s _let_4 (tptp.i _let_16 (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_0) _let_8)) _let_6)))) (tptp.s _let_4 (tptp.i (tptp.s _let_19 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun tptp.bool _let_21) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s _let_14 tptp.l_a_) _let_12)) _let_11)))) (tptp.s _let_4 (tptp.i (tptp.s _let_19 (tptp.i _let_22 (tptp.s _let_4 (tptp.i (tptp.s _let_19 (tptp.i _let_22 (tptp.s _let_4 (tptp.i (tptp.s _let_19 (tptp.i _let_20 (tptp.s tptp.real (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_18 tptp.p_) _let_11)) _let_17)))))) (tptp.s _let_4 (tptp.i _let_6 _let_11)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_19 (tptp.i _let_20 (tptp.s tptp.real (tptp.i _let_8 _let_12)))) (tptp.s _let_4 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_18 tptp.m_) _let_12)) _let_17)))))))))) (tptp.s _let_4 (tptp.i _let_16 (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 U_1) _let_8)) _let_6)))))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))))))))))))))))))) (forall ((Q109147 $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q109147))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num P0))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 _let_5)))) (let ((_let_10 (tptp.fun _let_2 _let_1))) (let ((_let_11 (tptp.s (tptp.fun _let_6 _let_10) tptp.vsum))) (let ((_let_12 (tptp.s tptp.num N0))) (let ((_let_13 (tptp.s tptp.num tptp.u_0))) (let ((_let_14 (tptp.fun tptp.num tptp.num))) (let ((_let_15 (tptp.s _let_14 tptp.numeral))) (let ((_let_16 (tptp.s tptp.num (tptp.i _let_15 (tptp.s tptp.num (tptp.i (tptp.s _let_14 tptp.bit1) _let_13)))))) (let ((_let_17 (tptp.fun tptp.num _let_14))) (let ((_let_18 (tptp.fun _let_1 _let_1))) (let ((_let_19 (tptp.s _let_7 tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.l_) (tptp.s tptp.num (tptp.i _let_15 _let_13)))) _let_12))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_19 _let_5)) _let_12))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_19 _let_12)) (tptp.s tptp.num (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_17 tptp.p_) _let_4)) _let_16)))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_1 _let_18) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_6 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_17 tptp.m_) _let_12)) _let_16)))))) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_12)) _let_4)))) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_6 (tptp.i _let_9 _let_4)))) _let_3)))))))))))))))))))))))) (forall ((Q109210 $$unsorted) (F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted) (P0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q109210))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num P0))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 _let_5)))) (let ((_let_10 (tptp.fun _let_2 _let_1))) (let ((_let_11 (tptp.s (tptp.fun _let_6 _let_10) tptp.vsum))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (let ((_let_13 (tptp.s tptp.num N0))) (let ((_let_14 (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.p_) _let_13)) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_15 (tptp.fun _let_1 _let_1))) (let ((_let_16 (tptp.s _let_7 tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_16 _let_5)) _let_14))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_16 _let_13)) _let_4)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_1 _let_15) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_6 (tptp.i _let_9 _let_13)))) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_14)) _let_4)))) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_6 (tptp.i _let_9 _let_4)))) _let_3))))))))))))))))))))) (forall ((Q109287 $$unsorted) (Q109292 $$unsorted) (F0 $$unsorted) (P0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q109292))) (let ((_let_2 (tptp.fun Q109287 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q109287 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)))) (let ((_let_8 (tptp.fun Q109287 Q109287))) (let ((_let_9 (tptp.fun _let_8 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun Q109287 tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s Q109287 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun Q109287 _let_4) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s Q109287 (tptp.i (tptp.s (tptp.fun Q109287 Q109287) P0) _let_3)))) _let_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s Q109287 Y))) (let ((_let_2 (tptp.s Q109287 X))) (let ((_let_3 (tptp.s (tptp.fun Q109287 Q109287) P0))) (let ((_let_4 (tptp.fun Q109287 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun Q109287 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_1)) _let_5))) (= (tptp.s Q109287 (tptp.i _let_3 _let_2)) (tptp.s Q109287 (tptp.i _let_3 _let_1)))) (= _let_2 _let_1))))))))))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_2 _let_9) tptp.o) _let_3)) (tptp.s _let_8 P0))))) (tptp.s _let_1 (tptp.i _let_7 _let_3)))))))))))))) (forall ((Q109341 $$unsorted) (Q109340 $$unsorted) (Q109337 $$unsorted) (U_2 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s Q109340 J0))) (let ((_let_2 (tptp.s Q109341 I0))) (let ((_let_3 (tptp.cart tptp.real Q109337))) (let ((_let_4 (tptp.fun Q109340 _let_3))) (let ((_let_5 (tptp.fun Q109341 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun Q109341 _let_3))) (let ((_let_8 (tptp.fun Q109340 _let_7))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_2) _let_6)) _let_1)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_2)) _let_1)))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s Q109340 J0))) (let ((_let_2 (tptp.cart tptp.real Q109337))) (let ((_let_3 (tptp.fun Q109340 _let_2))) (let ((_let_4 (tptp.fun Q109341 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q109341 _let_2))) (let ((_let_7 (tptp.fun Q109340 _let_6))) (let ((_let_8 (tptp.fun Q109341 tptp.bool))) (let ((_let_9 (tptp.s _let_8 S0))) (let ((_let_10 (tptp.fun _let_6 _let_2))) (let ((_let_11 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) U_1) _let_9)) _let_5)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.vsum) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_2) _let_5)) _let_1))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s Q109341 I0))) (let ((_let_2 (tptp.cart tptp.real Q109337))) (let ((_let_3 (tptp.fun Q109340 _let_2))) (let ((_let_4 (tptp.fun Q109341 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun Q109340 tptp.bool))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.fun _let_3 _let_2))) (let ((_let_9 (tptp.fun Q109341 _let_2))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_5)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.vsum) _let_7)) (tptp.s _let_3 (tptp.i _let_5 _let_1)))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q109337))) (let ((_let_2 (tptp.fun Q109340 _let_1))) (let ((_let_3 (tptp.fun Q109341 _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun Q109341 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_3 _let_2))) (let ((_let_8 (tptp.fun Q109340 tptp.bool))) (let ((_let_9 (tptp.s _let_8 T0))) (let ((_let_10 (tptp.fun _let_2 _let_1))) (let ((_let_11 (tptp.fun Q109341 _let_1))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun _let_11 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_5 _let_13) tptp.vsum) _let_6)) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_8 _let_12) U_0) _let_9)) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.vsum) _let_9)) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) U_1) _let_6)) _let_4)))))))))))))))))))))))))) (forall ((Q109392 $$unsorted) (U_2 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real Q109392))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) U_2) _let_6)) _let_1)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_2)) _let_1)))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.fun tptp.num (tptp.cart tptp.real Q109392)))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_1) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 U_2) _let_4)) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (D0 $$unsorted) (F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real Q109392))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s tptp.num D0))) (let ((_let_7 (tptp.s tptp.num C0))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun _let_3 _let_2))) (let ((_let_11 (tptp.fun _let_4 _let_3))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) U_0) _let_7)) _let_6)) _let_5)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.vsum) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) _let_7)) _let_6)))) (tptp.s _let_3 (tptp.i _let_5 _let_1)))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q109392))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.s tptp.num B0))) (let ((_let_6 (tptp.s tptp.num A5))) (let ((_let_7 (tptp.fun _let_3 _let_2))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) U_0))) (let ((_let_10 (tptp.s tptp.num D0))) (let ((_let_11 (tptp.s tptp.num C0))) (let ((_let_12 (tptp.fun tptp.num tptp.bool))) (let ((_let_13 (tptp.fun tptp.num _let_12))) (let ((_let_14 (tptp.s (tptp.fun tptp.num _let_13) tptp.o_o_))) (let ((_let_15 (tptp.fun _let_2 _let_1))) (let ((_let_16 (tptp.s (tptp.fun _let_12 _let_15) tptp.vsum))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_15 (tptp.i _let_16 (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i _let_14 _let_6)) _let_5)))) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_11)) _let_10)) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_15 (tptp.i _let_16 (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i _let_14 _let_11)) _let_10)))) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_1) _let_4)))))))))))))))))))))))))))))) (forall ((Q109481 $$unsorted) (Q109494 $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s Q109481 X))) (let ((_let_2 (tptp.cart tptp.real Q109494))) (let ((_let_3 (tptp.fun Q109481 _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.s _let_3 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_1) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.vectoru_add) (tptp.s _let_2 (tptp.i _let_5 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_286 $$unsorted)) (let ((_let_1 (tptp.fun Q109481 (tptp.cart tptp.real Q109494)))) (let ((_let_2 (tptp.fun Q109481 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 F0))) (tptp.s Q109481 GENR_PVARR_286)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s Q109481 X))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun Q109481 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (let ((_let_5 (tptp.cart tptp.real Q109494))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (and (= (tptp.p _let_2) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q109481 _let_6) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (not (= (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun Q109481 _let_5) F0) _let_1)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q109481 _let_4) tptp.setspec) (tptp.s Q109481 GENR_PVARR_286))) _let_2)) _let_1)))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q109494))) (let ((_let_2 (tptp.fun Q109481 _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun Q109481 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)))) (let ((_let_8 (tptp.s _let_2 F0))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.fun _let_2 _let_4))) (let ((_let_12 (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_4 _let_11) U_0) _let_5)))) (let ((_let_13 (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec))) (let ((_let_14 (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_14 (tptp.s _let_4 (tptp.i _let_13 (tptp.s _let_4 (tptp.i _let_12 _let_8))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_14 (tptp.s _let_4 (tptp.i _let_13 (tptp.s _let_4 (tptp.i _let_12 _let_3)))))))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) U_1) _let_8)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_add) (tptp.s _let_1 (tptp.i _let_7 _let_8)))) (tptp.s _let_1 (tptp.i _let_7 _let_3))))))))))))))))))))))))) (forall ((Q109577 $$unsorted) (Q109575 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s Q109575 X))) (let ((_let_2 (tptp.cart tptp.real Q109577))) (let ((_let_3 (tptp.fun Q109575 _let_2))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s Q109575 A5))) (and (= (tptp.p _let_4) (= _let_1 _let_7)) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q109575 _let_3) U_0) _let_7)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_4)) (tptp.s _let_2 tptp.y))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.f) _let_1))))))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s Q109575 A5))) (let ((_let_2 (tptp.cart tptp.real Q109577))) (let ((_let_3 (tptp.fun Q109575 _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.f))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun Q109575 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_3 _let_2))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.vsum) _let_8)))) (let ((_let_11 (tptp.fun _let_7 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 tptp.finite) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun Q109575 _let_11) tptp.in) _let_1)) _let_8)))) (= (tptp.s _let_2 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun Q109575 _let_3) U_0) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.vectoru_add) (tptp.s _let_2 (tptp.i _let_10 _let_4)))) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 tptp.vectoru_sub) (tptp.s _let_2 tptp.y))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))))))))))) (forall ((Q109587 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.n))) (let ((_let_2 (tptp.cart tptp.real Q109587))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 tptp.f))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.vsum) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) _let_1)) _let_1)))) _let_4)) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))) (forall ((Q109598 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.cart tptp.real Q109598))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.f))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.vsum) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) _let_2)) _let_2)))) _let_5)) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))))))))) (forall ((Q109622 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) (let ((_let_5 (tptp.cart tptp.real Q109622))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s _let_6 T0))) (let ((_let_8 (tptp.s tptp.num (tptp.i _let_3 _let_2)))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (let ((_let_12 (tptp.fun _let_6 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.vsum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.o_o_) _let_8)) _let_4)))) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.vectoru_add) (tptp.s _let_5 (tptp.i _let_7 _let_8)))) (tptp.s _let_5 (tptp.i _let_7 _let_4)))))))))))))))))) (forall ((Q109650 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s _let_1 tptp.bit1))) (let ((_let_3 (tptp.s tptp.num (tptp.i _let_2 (tptp.s tptp.num tptp.u_0))))) (let ((_let_4 (tptp.s _let_1 tptp.numeral))) (let ((_let_5 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_2 _let_3)))))) (let ((_let_6 (tptp.cart tptp.real Q109650))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s _let_7 T0))) (let ((_let_9 (tptp.fun _let_6 _let_6))) (let ((_let_10 (tptp.s (tptp.fun _let_6 _let_9) tptp.vectoru_add))) (let ((_let_11 (tptp.s tptp.num (tptp.i _let_4 _let_3)))) (let ((_let_12 (tptp.fun tptp.num tptp.bool))) (let ((_let_13 (tptp.fun tptp.num _let_12))) (let ((_let_14 (tptp.fun _let_7 _let_6))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_12 _let_14) tptp.vsum) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.num _let_13) tptp.o_o_) _let_11)) _let_5)))) _let_8)) (tptp.s _let_6 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i _let_8 _let_11)))) (tptp.s _let_6 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i _let_8 (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_3)))))))) (tptp.s _let_6 (tptp.i _let_8 _let_5)))))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.t_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) _let_4)))) (let ((_let_7 (tptp.cart tptp.real N))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s _let_8 F0))) (let ((_let_10 (tptp.fun _let_7 _let_7))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_8 _let_8) U_0) _let_9)) _let_4)) (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.vectoru_add) (tptp.s _let_7 (tptp.i _let_9 _let_6)))) (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.p_) _let_6)) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))))))))))) (forall ((F0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.s tptp.num M0))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (let ((_let_10 (tptp.s (tptp.fun _let_6 _let_9) tptp.vsum))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (let ((_let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_13 (tptp.s _let_11 tptp.numeral))) (let ((_let_14 (tptp.fun tptp.num _let_11))) (let ((_let_15 (tptp.s _let_11 (tptp.i (tptp.s _let_14 tptp.t_) (tptp.s tptp.num (tptp.i _let_13 (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit0) _let_12)))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i _let_15 _let_5)))) (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_14 tptp.p_) (tptp.s tptp.num (tptp.i _let_15 _let_4)))) (tptp.s tptp.num (tptp.i _let_13 _let_12)))))))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_4)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3))))))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.t_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) _let_4)))) (let ((_let_7 (tptp.cart tptp.real N))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s _let_8 F0))) (let ((_let_10 (tptp.fun _let_7 _let_7))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_8 _let_8) U_0) _let_9)) _let_4)) (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.vectoru_add) (tptp.s _let_7 (tptp.i _let_9 _let_6)))) (tptp.s _let_7 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.p_) _let_6)) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))))))))))) (forall ((F0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun tptp.num _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.s tptp.num N0))) (let ((_let_5 (tptp.s tptp.num tptp.u_0))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.s _let_6 tptp.numeral))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_7 _let_5)))))) (let ((_let_11 (tptp.fun _let_2 _let_1))) (let ((_let_12 (tptp.s (tptp.fun _let_8 _let_11) tptp.vsum))) (let ((_let_13 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) _let_5)))) (let ((_let_14 (tptp.fun tptp.num _let_6))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_14 tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_14 tptp.t_) (tptp.s tptp.num (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit0) _let_13)))))) _let_4)))) (tptp.s tptp.num (tptp.i _let_7 _let_13)))))))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s _let_8 (tptp.i _let_10 _let_4)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)))))))))))))))))))))) (forall ((Q109978 $$unsorted) (U_0 $$unsorted)) (=> (forall ((K0 $$unsorted) (I0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.realu_ofu_num))) (let ((_let_6 (tptp.s tptp.bool V))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.s tptp.num I0))) (let ((_let_10 (tptp.s tptp.num K0))) (and (= (tptp.p _let_6) (= _let_9 _let_10)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) U_0) _let_10)) _let_9)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) _let_6)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))))) (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.cart tptp.real Q109978))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.basis) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.lambda) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) _let_1))))))))))) (forall ((N $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s tptp.num K0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun N tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.vectoru_norm) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.basis) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_2)))))))))))) (forall ((Q110060 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.cart tptp.real Q110060))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.basis) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_2))))))) (forall ((N $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real C0)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) (tptp.s _let_1 X))) (tptp.s tptp.real C0))))))) (forall ((N $$unsorted) (X $$unsorted) (E0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real E0)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.distance) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.c_) (tptp.s _let_1 X))) (tptp.s _let_1 Y))))) (tptp.s tptp.real E0))))))))) (forall ((N $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.basis))) (let ((_let_5 (tptp.fun N tptp.bool))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (= (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_3 (tptp.i _let_4 _let_1)))) (= _let_2 _let_1))))))))))))) (forall ((N $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) tptp.basis))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun N tptp.bool))) (let ((_let_6 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dimindex) (tptp.s _let_5 tptp.univ))))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) _let_6))) (not (= _let_4 _let_1))) (not (= (tptp.s _let_2 (tptp.i _let_3 _let_4)) (tptp.s _let_2 (tptp.i _let_3 _let_1)))))))))))))))) (forall ((N $$unsorted) (K0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.realu_ofu_num))) (let ((_let_6 (tptp.s tptp.bool V))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.s tptp.num I0))) (let ((_let_10 (tptp.s tptp.num K0))) (let ((_let_11 (tptp.cart tptp.real N))) (and (= (tptp.p _let_6) (= _let_9 _let_10)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_11 _let_4) tptp.d_) (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.basis) _let_10)))) _let_9)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.bool _let_8) tptp.cond) _let_6)) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_2 X))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.d_) _let_4)) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.basis) _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num _let_1))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_3 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.vsum) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))) _let_2)))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) U_0) _let_5)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) (tptp.s tptp.real (tptp.i _let_5 _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.basis) _let_1)))))))))))) (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.fun tptp.num _let_1))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_3 _let_1))) (= (= (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.vsum) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 F0))))) (tptp.s _let_1 X)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 F0) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 X))) _let_1)))))))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.d_) _let_3)) _let_1)))) (let ((_let_6 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1)))) (let ((_let_7 (tptp.fun _let_2 tptp.real))) (let ((_let_8 (tptp.s (tptp.fun _let_2 _let_7) tptp.dot))) (let ((_let_9 (tptp.fun N tptp.bool))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.l_a_))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dimindex) (tptp.s _let_9 tptp.univ))))))) (and (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_3)) _let_5) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_6)) _let_5)))))))))))))))) (forall ((N $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))) (let ((_let_3 (tptp.s tptp.num J0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_8 (tptp.s tptp.num I0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_8)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.s tptp.num J0))) (let ((_let_9 (tptp.cart tptp.real N))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.basis))) (let ((_let_11 (tptp.s tptp.num I0))) (let ((_let_12 (tptp.fun _let_9 tptp.real))) (and (= (tptp.p _let_5) (= _let_11 _let_8)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.dot) (tptp.s _let_9 (tptp.i _let_10 _let_11)))) (tptp.s _let_9 (tptp.i _let_10 _let_8)))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) _let_5)) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (tptp.s tptp.real (tptp.i _let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))))))))))) (forall ((Q110508 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart tptp.real Q110508))) (let ((_let_3 (tptp.s (tptp.fun tptp.num _let_2) tptp.basis))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun _let_2 tptp.real))) (=> (not (= _let_4 _let_1)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.dot) (tptp.s _let_2 (tptp.i _let_3 _let_4)))) (tptp.s _let_2 (tptp.i _let_3 _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (forall ((N $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num tptp.u_0))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.s _let_3 tptp.numeral))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s tptp.num I0))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.cart tptp.real N))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (= (= (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.basis) _let_7)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 tptp.vec) (tptp.s tptp.num (tptp.i _let_4 _let_2))))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.in) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))))))))))))) (forall ((N $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s tptp.num K0))) (let ((_let_7 (tptp.fun N tptp.bool))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dimindex) (tptp.s _let_7 tptp.univ))))))) (not (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.basis) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))) (forall ((Q110589 $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110589))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110589))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.dot) (tptp.s _let_1 X))))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 Y))) (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 Z0)))))))) (= (tptp.s _let_1 Y) (tptp.s _let_1 Z0))))) (forall ((Q110616 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110616))) (= (forall ((Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110616))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.dot))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 X))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 Y))) _let_2)))))))) (= (tptp.s _let_1 X) (tptp.s _let_1 Y))))) (forall ((Q110633 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110633))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.orthogonal) _let_3)) _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.dot) _let_3)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (forall ((Q110652 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110652))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))) (forall ((Q110667 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110667))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) _let_2)) _let_2))) (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((Q110681 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110681))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q110704 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110704))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_3)))) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q110725 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110725))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))))) (= (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))) (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))) (forall ((N $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.num I0))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.s _let_6 X))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.fun N tptp.bool))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dimindex) (tptp.s _let_9 tptp.univ))))))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.orthogonal) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.basis) _let_5)))) _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.d_) _let_7)) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))) (forall ((N $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.basis))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_11 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) _let_7)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.orthogonal) (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (tptp.s _let_3 (tptp.i _let_4 _let_1))))) (not (= _let_2 _let_1)))))))))))))))) (forall ((Q110833 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110833))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.orthogonal) (tptp.s _let_1 A5))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))) (forall ((Q110858 $$unsorted) (A5 $$unsorted) (X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110858))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal) (tptp.s _let_1 A5))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) (tptp.s tptp.real C0))) _let_2)))))))))))) (forall ((Q111053 $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111053))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 A5))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2))))))))))) (forall ((Q111054 $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111054))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.orthogonal) (tptp.s _let_1 A5))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) _let_3)) _let_2))))))))))))) (forall ((Q111055 $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111055))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.orthogonal) (tptp.s _let_1 A5))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub) _let_3)) _let_2))))))))))))) (forall ((Q110949 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110949))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.orthogonal) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_1 A5))))))) (forall ((Q110968 $$unsorted) (A5 $$unsorted) (X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q110968))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.orthogonal))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.r_) (tptp.s tptp.real C0))) _let_3)))) _let_2))))))))))) (forall ((Q111056 $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111056))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_3)))) _let_2)))))))))) (forall ((Q111057 $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111057))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.orthogonal))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.vectoru_add) _let_4)) _let_3)))) _let_2)))))))))))) (forall ((Q111058 $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111058))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.orthogonal))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.vectoru_sub) _let_4)) _let_3)))) _let_2)))))))))))) (forall ((A $$unsorted) (N $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.s A Y))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_1)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.orthogonal) (tptp.s _let_2 X))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) F0) _let_1))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.orthogonal) (tptp.s _let_1 X))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.vsum) _let_4)) (tptp.s _let_2 F0)))))))))))))) (forall ((A $$unsorted) (N $$unsorted) (F0 $$unsorted) (S0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun A tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s A X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun A tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun A _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun A _let_1) F0) _let_2)))) (tptp.s _let_1 Y)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.orthogonal) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.vsum) _let_4)) (tptp.s _let_2 F0))))) (tptp.s _let_1 Y)))))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.x))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.list A))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.cart A tptp.n10))) (let ((_let_6 (tptp.fun tptp.num A))) (= (tptp.s A (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.d_) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.vector) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun A _let_4) tptp.cons) _let_1)) (tptp.s _let_3 tptp.nil))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.x))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.list A))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.cons))) (let ((_let_6 (tptp.cart A tptp.n20))) (let ((_let_7 (tptp.fun tptp.num A))) (= (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.d_) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vector) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A tptp.y))) (tptp.s _let_3 tptp.nil))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.y))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.list A))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.cons))) (let ((_let_6 (tptp.cart A tptp.n20))) (let ((_let_7 (tptp.fun tptp.num A))) (= (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.d_) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vector) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A tptp.x))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s _let_3 tptp.nil))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.x))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.list A))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.cons))) (let ((_let_6 (tptp.cart A tptp.n3))) (let ((_let_7 (tptp.fun tptp.num A))) (= (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.d_) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vector) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A tptp.y))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A tptp.z))) (tptp.s _let_3 tptp.nil))))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.y))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.list A))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.s (tptp.fun A _let_4) tptp.cons))) (let ((_let_6 (tptp.cart A tptp.n3))) (let ((_let_7 (tptp.fun tptp.num A))) (= (tptp.s A (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.d_) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vector) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A tptp.x))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_1)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s A tptp.z))) (tptp.s _let_3 tptp.nil))))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_1))))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.s A tptp.z))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.bit1))) (let ((_let_4 (tptp.list A))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.s (tptp.fun A _let_5) tptp.cons))) (let ((_let_7 (tptp.cart A tptp.n3))) (let ((_let_8 (tptp.fun tptp.num A))) (= (tptp.s A (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) tptp.d_) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.vector) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s A tptp.x))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s A tptp.y))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_1)) (tptp.s _let_4 tptp.nil))))))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num tptp.u_0))))))))) _let_1)))))))))) (forall ((A $$unsorted)) (= (forall ((V $$unsorted)) (let ((_let_1 (tptp.cart A tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 V)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.cart A tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.p0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vector) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.cons) (tptp.s A X))) (tptp.s _let_1 tptp.nil)))))))))))))) (forall ((A $$unsorted)) (= (forall ((V $$unsorted)) (let ((_let_1 (tptp.cart A tptp.n20))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 V)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s (tptp.fun A _let_2) tptp.cons))) (let ((_let_4 (tptp.cart A tptp.n20))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.p0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vector) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A X))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A Y))) (tptp.s _let_1 tptp.nil))))))))))))))))) (forall ((A $$unsorted)) (= (forall ((V $$unsorted)) (let ((_let_1 (tptp.cart A tptp.n3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 V)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s (tptp.fun A _let_2) tptp.cons))) (let ((_let_4 (tptp.cart A tptp.n3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.p0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vector) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A X))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A Y))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A Z0))) (tptp.s _let_1 tptp.nil))))))))))))))))))) (forall ((A $$unsorted)) (= (exists ((V $$unsorted)) (let ((_let_1 (tptp.cart A tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 V)))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.cart A tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.p0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vector) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun A _let_2) tptp.cons) (tptp.s A X))) (tptp.s _let_1 tptp.nil)))))))))))))) (forall ((A $$unsorted)) (= (exists ((V $$unsorted)) (let ((_let_1 (tptp.cart A tptp.n20))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 V)))))) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s (tptp.fun A _let_2) tptp.cons))) (let ((_let_4 (tptp.cart A tptp.n20))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.p0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vector) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A X))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A Y))) (tptp.s _let_1 tptp.nil))))))))))))))))) (forall ((A $$unsorted)) (= (exists ((V $$unsorted)) (let ((_let_1 (tptp.cart A tptp.n3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 V)))))) (exists ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.list A))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s (tptp.fun A _let_2) tptp.cons))) (let ((_let_4 (tptp.cart A tptp.n3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.p0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vector) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A X))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A Y))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i _let_3 (tptp.s A Z0))) (tptp.s _let_1 tptp.nil))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) F0))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_add) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) F0))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_5)) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))))))) (forall ((Q111564 $$unsorted) (Q111562 $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111564))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q111562))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s tptp.real C0))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) U_0) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) _let_6)) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))))))))))) (forall ((F0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q111564) (tptp.cart tptp.real Q111562)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) U_0) (tptp.s tptp.real C0))) _let_2))))))))))))) (forall ((Q111583 $$unsorted) (Q111590 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111583))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q111590))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) U_0) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q111583) (tptp.cart tptp.real Q111590)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_3 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)))))))))))) (forall ((Q111612 $$unsorted) (Q111621 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111612))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q111621))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.s _let_4 F0))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_6 _let_2)))) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q111612) (tptp.cart tptp.real Q111621)))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s _let_1 F0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_3)) _let_2)))))))))))))) (forall ((Q111643 $$unsorted) (Q111652 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111643))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q111652))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.s _let_4 F0))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.vectoru_sub) (tptp.s _let_3 (tptp.i _let_6 _let_2)))) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q111643) (tptp.cart tptp.real Q111652)))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s _let_1 F0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_3)) _let_2)))))))))))))) (forall ((Q111672 $$unsorted) (Q111668 $$unsorted) (Q111669 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111669))) (let ((_let_2 (tptp.cart tptp.real Q111668))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.cart tptp.real Q111672))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 G0))) (let ((_let_8 (tptp.fun _let_2 _let_5))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.linear) _let_7)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.linear) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.o) _let_7)) _let_4)))))))))))))))) (forall ((Q111683 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111683))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111683))) (let ((_let_2 (tptp.s _let_1 X))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 U_0)))))))) (forall ((Q111690 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111690))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 tptp.i1))))))) (forall ((Q111694 $$unsorted) (Q111699 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q111694) (tptp.cart tptp.real Q111699)))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111699))) (let ((_let_2 (tptp.cart tptp.real Q111694))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) U_0) (tptp.s _let_2 X))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 U_0))))))) (forall ((Q111705 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111705))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 tptp.vectoru_neg))))))) (forall ((Q111747 $$unsorted) (Q111736 $$unsorted) (Q111733 $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111736))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s Q111747 A5))) (let ((_let_4 (tptp.cart tptp.real Q111733))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun Q111747 _let_5))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun Q111747 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) U_1) _let_7)) _let_2)) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_7 _let_3)) _let_2))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111736))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q111733))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun Q111747 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun Q111747 _let_3))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun Q111747 tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun _let_7 _let_3))) (let ((_let_12 (tptp.fun _let_5 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) U_0) _let_10)) _let_6)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.vsum) _let_10)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_6)) _let_2)))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q111736) (tptp.cart tptp.real Q111733)))) (let ((_let_2 (tptp.fun Q111747 _let_1))) (let ((_let_3 (tptp.fun Q111747 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) _let_4))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.s Q111747 A5))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real Q111736) (tptp.cart tptp.real Q111733)))) (let ((_let_3 (tptp.fun Q111747 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q111747 _let_4) tptp.in) _let_1)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q111747 _let_2) F0) _let_1)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) (tptp.s _let_2 F0))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (Q111786 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (K0 $$unsorted) (V $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111786))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s tptp.num K0))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.s _let_4 X))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun tptp.num tptp.real))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (let ((_let_11 (tptp.fun _let_4 _let_1))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun tptp.num _let_12))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_7 _let_13) U_0) _let_8)) _let_3)) _let_2)) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.d_) (tptp.s _let_6 (tptp.i _let_8 _let_5)))) _let_3)))) _let_2))))))))))))))))) (forall ((F0 $$unsorted) (V $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111786))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 (tptp.cart tptp.real N)))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun N tptp.bool))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun tptp.num _let_10) tptp.l_a_))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dimindex) (tptp.s _let_9 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.linear) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_2)) (tptp.s _let_1 V)))))))))))))))))))))) (forall ((Q111807 $$unsorted) (Q111809 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q111809))) (let ((_let_3 (tptp.cart tptp.real Q111807))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.s _let_4 F0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (= (tptp.s _let_2 (tptp.i _let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))))) (forall ((Q111837 $$unsorted) (Q111834 $$unsorted) (F0 $$unsorted) (C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111834))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q111837))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s tptp.real C0))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (= (tptp.s _let_3 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) _let_6)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) _let_6)) (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))))))) (forall ((Q111863 $$unsorted) (Q111862 $$unsorted) (F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111862))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q111863))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (= (tptp.s _let_3 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))))))))) (forall ((Q111897 $$unsorted) (Q111896 $$unsorted) (F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111896))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q111897))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s _let_1 X))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (= (tptp.s _let_3 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.vectoru_add) _let_6)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_5 _let_6)))) (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))))))) (forall ((Q111931 $$unsorted) (Q111930 $$unsorted) (F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111930))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q111931))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s _let_1 X))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (= (tptp.s _let_3 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.vectoru_sub) _let_6)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.vectoru_sub) (tptp.s _let_3 (tptp.i _let_5 _let_6)))) (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))))))) (forall ((Q111967 $$unsorted) (Q111971 $$unsorted) (Q111963 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q111963))) (let ((_let_2 (tptp.fun Q111971 _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.cart tptp.real Q111967))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun Q111971 _let_4))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun Q111971 tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun _let_7 _let_4))) (let ((_let_12 (tptp.fun _let_2 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_9 tptp.bool) tptp.finite) _let_10)))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.vsum) _let_10)) _let_3)))) (tptp.s _let_4 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.vsum) _let_10)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.o) _let_6)) _let_3))))))))))))))))))) (forall ((Q112022 $$unsorted) (Q112025 $$unsorted) (Q112011 $$unsorted) (U_1 $$unsorted)) (=> (forall ((C0 $$unsorted) (F0 $$unsorted) (V $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s Q112025 I0))) (let ((_let_2 (tptp.cart tptp.real Q112011))) (let ((_let_3 (tptp.fun Q112025 _let_2))) (let ((_let_4 (tptp.s _let_3 V))) (let ((_let_5 (tptp.cart tptp.real Q112022))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun Q112025 tptp.real))) (let ((_let_9 (tptp.s _let_8 C0))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun Q112025 _let_5))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun _let_6 _let_12))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_8 _let_13) U_1) _let_9)) _let_7)) _let_4)) _let_1)) (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_) (tptp.s tptp.real (tptp.i _let_9 _let_1)))) (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (V $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s Q112025 I0))) (let ((_let_2 (tptp.cart tptp.real Q112011))) (let ((_let_3 (tptp.fun Q112025 _let_2))) (let ((_let_4 (tptp.s _let_3 V))) (let ((_let_5 (tptp.fun Q112025 tptp.real))) (let ((_let_6 (tptp.s _let_5 C0))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) _let_6)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) (tptp.s tptp.real (tptp.i _let_6 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted) (C0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112011))) (let ((_let_2 (tptp.fun Q112025 _let_1))) (let ((_let_3 (tptp.s _let_2 V))) (let ((_let_4 (tptp.cart tptp.real Q112022))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun Q112025 tptp.real))) (let ((_let_8 (tptp.s _let_7 C0))) (let ((_let_9 (tptp.fun Q112025 _let_4))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun Q112025 tptp.bool))) (let ((_let_13 (tptp.s _let_12 S0))) (let ((_let_14 (tptp.fun _let_9 _let_4))) (let ((_let_15 (tptp.fun _let_2 _let_2))) (let ((_let_16 (tptp.fun _let_2 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_12 tptp.bool) tptp.finite) _let_13)))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) tptp.vsum) _let_13)) (tptp.s _let_2 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_7 _let_15) U_0) _let_8)) _let_3)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_12 _let_14) tptp.vsum) _let_13)) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) U_1) _let_8)) _let_6)) _let_3))))))))))))))))))))))))))) (forall ((Q112067 $$unsorted) (Q112072 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q112072) (tptp.cart tptp.real Q112067)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112072))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real Q112067))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q112072))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.cart tptp.real Q112067))) (=> (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) F0) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.vec) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (exists ((B0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.vectoru_norm) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) F0) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real B0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.vectoru_norm) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) F0) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))))))) (forall ((Q112240 $$unsorted) (Q112239 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q112239) (tptp.cart tptp.real Q112240)))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112239))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_4)))) _let_3))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112239))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.cart tptp.real Q112240))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.image) (tptp.s _let_4 F0))) (tptp.s _let_2 S0))))) (let ((_let_8 (tptp.s _let_3 X))) (let ((_let_9 (tptp.fun _let_5 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_3 _let_9) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_8)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) _let_8)))) _let_7)))))))))))))))))) (forall ((Q112265 $$unsorted) (Q112255 $$unsorted) (Q112254 $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112254))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q112265))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real Q112255))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.fun _let_3 _let_5))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) U_1) _let_8)) _let_2)) _let_4)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_4)) _let_2)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112254))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q112265))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real Q112255))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 F0))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) U_0) _let_8)) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_4)) _let_2)))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q112265) (tptp.fun (tptp.cart tptp.real Q112254) (tptp.cart tptp.real Q112255))))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.bilinear) (tptp.s _let_1 F0)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112265))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real Q112254) (tptp.cart tptp.real Q112255)))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) U_0) (tptp.s _let_3 F0))) (tptp.s _let_1 X)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112254))) (let ((_let_2 (tptp.cart tptp.real Q112255))) (let ((_let_3 (tptp.cart tptp.real Q112265))) (let ((_let_4 (tptp.fun _let_3 (tptp.fun _let_1 _let_2)))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_1) (tptp.s _let_4 F0))) (tptp.s _let_1 Y))))))))))))))))))))) (forall ((Q112310 $$unsorted) (Q112309 $$unsorted) (Q112292 $$unsorted) (H0 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112292))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.cart tptp.real Q112309))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.cart tptp.real Q112310))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 H0))) (let ((_let_9 (tptp.s _let_3 X))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.bilinear) _let_8))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.vectoru_add) _let_9)) _let_4)))) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.vectoru_add) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_9)) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_4)) _let_2)))))))))))))))))) (forall ((Q112352 $$unsorted) (Q112333 $$unsorted) (Q112351 $$unsorted) (H0 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112351))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.cart tptp.real Q112333))) (let ((_let_4 (tptp.cart tptp.real Q112352))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_6 H0))) (let ((_let_8 (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_3 X))))) (let ((_let_9 (tptp.s _let_1 Y))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.bilinear) _let_7))) (= (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.vectoru_add) _let_9)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.vectoru_add) (tptp.s _let_4 (tptp.i _let_8 _let_9)))) (tptp.s _let_4 (tptp.i _let_8 _let_2)))))))))))))))))) (forall ((Q112388 $$unsorted) (Q112385 $$unsorted) (Q112376 $$unsorted) (H0 $$unsorted) (C0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112376))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q112385))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real Q112388))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 H0))) (let ((_let_9 (tptp.s tptp.real C0))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.bilinear) _let_8))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.r_) _let_9)) _let_4)))) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_) _let_9)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_4)) _let_2)))))))))))))))))) (forall ((Q112424 $$unsorted) (Q112411 $$unsorted) (Q112421 $$unsorted) (H0 $$unsorted) (C0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112421))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q112411))) (let ((_let_4 (tptp.cart tptp.real Q112424))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_6 H0))) (let ((_let_8 (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_3 X))))) (let ((_let_9 (tptp.s tptp.real C0))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.bilinear) _let_7))) (= (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.r_) _let_9)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_) _let_9)) (tptp.s _let_4 (tptp.i _let_8 _let_2)))))))))))))))))) (forall ((Q112458 $$unsorted) (Q112457 $$unsorted) (Q112444 $$unsorted) (H0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112444))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q112457))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real Q112458))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 H0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.bilinear) _let_8))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) _let_4)))) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.vectoru_neg) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_4)) _let_2))))))))))))))) (forall ((Q112492 $$unsorted) (Q112477 $$unsorted) (Q112491 $$unsorted) (H0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112491))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q112477))) (let ((_let_4 (tptp.cart tptp.real Q112492))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_6 H0))) (let ((_let_8 (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_3 X))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.bilinear) _let_7))) (= (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.vectoru_neg) (tptp.s _let_4 (tptp.i _let_8 _let_2))))))))))))))) (forall ((Q112532 $$unsorted) (Q112524 $$unsorted) (Q112534 $$unsorted) (H0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q112534))) (let ((_let_3 (tptp.cart tptp.real Q112524))) (let ((_let_4 (tptp.cart tptp.real Q112532))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (let ((_let_7 (tptp.s _let_6 H0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.bilinear) _let_7))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.vec) _let_1)))) (tptp.s _let_3 X))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))))))) (forall ((Q112563 $$unsorted) (Q112572 $$unsorted) (Q112574 $$unsorted) (H0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q112574))) (let ((_let_3 (tptp.cart tptp.real Q112572))) (let ((_let_4 (tptp.cart tptp.real Q112563))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (let ((_let_7 (tptp.s _let_6 H0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.bilinear) _let_7))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_4 X))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))))))) (forall ((Q112614 $$unsorted) (Q112613 $$unsorted) (Q112596 $$unsorted) (H0 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112596))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.cart tptp.real Q112613))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.cart tptp.real Q112614))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.s _let_7 H0))) (let ((_let_9 (tptp.s _let_3 X))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun _let_3 _let_3))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.bilinear) _let_8))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_3 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.vectoru_sub) _let_9)) _let_4)))) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.vectoru_sub) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_9)) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_8 _let_4)) _let_2)))))))))))))))))) (forall ((Q112656 $$unsorted) (Q112637 $$unsorted) (Q112655 $$unsorted) (H0 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112655))) (let ((_let_2 (tptp.s _let_1 Z0))) (let ((_let_3 (tptp.cart tptp.real Q112637))) (let ((_let_4 (tptp.cart tptp.real Q112656))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_6 H0))) (let ((_let_8 (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_3 X))))) (let ((_let_9 (tptp.s _let_1 Y))) (let ((_let_10 (tptp.fun _let_4 _let_4))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.bilinear) _let_7))) (= (tptp.s _let_4 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.vectoru_sub) _let_9)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_4 _let_10) tptp.vectoru_sub) (tptp.s _let_4 (tptp.i _let_8 _let_9)))) (tptp.s _let_4 (tptp.i _let_8 _let_2)))))))))))))))))) (forall ((Q112722 $$unsorted) (Q112723 $$unsorted) (M $$unsorted) (N $$unsorted) (P $$unsorted) (U_0 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.fun (tptp.prod Q112722 Q112723) _let_1))) (let ((_let_3 (tptp.fun (tptp.cart tptp.real M) (tptp.fun (tptp.cart tptp.real N) _let_1)))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) (tptp.s _let_3 H0))) (tptp.s _let_2 F0)))) (forall ((I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s Q112723 J0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s Q112722 I0))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.cart tptp.real P))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.prod Q112722 Q112723))) (let ((_let_8 (tptp.fun Q112723 _let_7))) (let ((_let_9 (tptp.fun _let_5 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.geq) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_7 _let_5) F0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun Q112722 _let_8) tptp.c_) _let_3)) _let_1)))))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) H0) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun Q112722 _let_4) tptp.f) _let_3)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun Q112723 _let_2) tptp.g) _let_1))))))))))))))))))))))) (forall ((H0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.s _let_5 H0))) (let ((_let_7 (tptp.prod Q112722 Q112723))) (let ((_let_8 (tptp.fun _let_7 _let_1))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun Q112723 tptp.bool))) (let ((_let_11 (tptp.s _let_10 tptp.t0))) (let ((_let_12 (tptp.fun Q112722 tptp.bool))) (let ((_let_13 (tptp.s _let_12 tptp.s0))) (let ((_let_14 (tptp.fun _let_7 tptp.bool))) (let ((_let_15 (tptp.fun _let_10 _let_14))) (let ((_let_16 (tptp.fun _let_8 _let_1))) (let ((_let_17 (tptp.fun Q112723 _let_2))) (let ((_let_18 (tptp.fun _let_17 _let_2))) (let ((_let_19 (tptp.fun Q112722 _let_4))) (let ((_let_20 (tptp.fun _let_19 _let_4))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.bilinear) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_12 tptp.bool) tptp.finite) _let_13))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_10 tptp.bool) tptp.finite) _let_11)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_4 (tptp.i (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_12 _let_20) tptp.vsum) _let_13)) (tptp.s _let_19 tptp.f))))) (tptp.s _let_2 (tptp.i (tptp.s _let_18 (tptp.i (tptp.s (tptp.fun _let_10 _let_18) tptp.vsum) _let_11)) (tptp.s _let_17 tptp.g))))) (tptp.s _let_1 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_14 _let_16) tptp.vsum) (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_12 _let_15) tptp.cross0) _let_13)) _let_11)))) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_9 _let_8) tptp.gabs) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_0) _let_6))))))))))))))))))))))))))))))) (forall ((P $$unsorted) (M $$unsorted) (N $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.fun (tptp.cart tptp.real N) (tptp.cart tptp.real P))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.bilinear) (tptp.s _let_1 H0)))) (exists ((B0 $$unsorted)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul))) (let ((_let_7 (tptp.cart tptp.real P))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_7 tptp.real) tptp.vectoru_norm) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) H0) _let_4)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))))))))))) (forall ((Q112837 $$unsorted) (Q112835 $$unsorted) (Q112836 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q112835) (tptp.fun (tptp.cart tptp.real Q112836) (tptp.cart tptp.real Q112837))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.bilinear) (tptp.s _let_1 H0)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real B0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q112836))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q112835))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul))) (let ((_let_7 (tptp.cart tptp.real Q112837))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_7 tptp.real) tptp.vectoru_norm) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) H0) _let_4)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (P $$unsorted) (U_1 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.p_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.cart tptp.real M))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s _let_8 F0))) (let ((_let_10 (tptp.fun _let_7 _let_7))) (let ((_let_11 (tptp.cart tptp.real P))) (let ((_let_12 (tptp.fun _let_4 _let_11))) (let ((_let_13 (tptp.fun _let_7 _let_12))) (let ((_let_14 (tptp.s _let_13 H0))) (let ((_let_15 (tptp.fun tptp.num _let_11))) (let ((_let_16 (tptp.fun _let_5 _let_15))) (let ((_let_17 (tptp.fun _let_8 _let_16))) (= (tptp.s _let_11 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_13 _let_17) U_1) _let_14)) _let_9)) _let_6)) _let_2)) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_14 (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.vectoru_sub) (tptp.s _let_7 (tptp.i _let_9 _let_3)))) (tptp.s _let_7 (tptp.i _let_9 _let_2)))))) (tptp.s _let_4 (tptp.i _let_6 _let_3))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.cart tptp.real M))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s _let_8 F0))) (let ((_let_10 (tptp.cart tptp.real P))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.s _let_12 H0))) (let ((_let_14 (tptp.fun tptp.num _let_10))) (let ((_let_15 (tptp.fun _let_3 _let_14))) (let ((_let_16 (tptp.fun _let_8 _let_15))) (= (tptp.s _let_10 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) U_0) _let_13)) _let_9)) _let_4)) _let_1)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_7 (tptp.i _let_9 _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.vectoru_sub) (tptp.s _let_2 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real P))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s _let_7 G0))) (let ((_let_9 (tptp.cart tptp.real M))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.s _let_10 F0))) (let ((_let_12 (tptp.fun _let_6 _let_4))) (let ((_let_13 (tptp.fun _let_9 _let_12))) (let ((_let_14 (tptp.s _let_13 H0))) (let ((_let_15 (tptp.fun _let_7 _let_5))) (let ((_let_16 (tptp.fun _let_10 _let_15))) (let ((_let_17 (tptp.fun _let_13 _let_16))) (let ((_let_18 (tptp.s tptp.num N0))) (let ((_let_19 (tptp.s tptp.num M0))) (let ((_let_20 (tptp.fun tptp.num tptp.bool))) (let ((_let_21 (tptp.fun tptp.num _let_20))) (let ((_let_22 (tptp.fun _let_5 _let_4))) (let ((_let_23 (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_20 _let_22) tptp.vsum) (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun tptp.num _let_21) tptp.o_o_) _let_19)) _let_18)))))) (let ((_let_24 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.p_) _let_18)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))) (let ((_let_25 (tptp.fun _let_4 _let_4))) (let ((_let_26 (tptp.fun _let_4 _let_25))) (let ((_let_27 (tptp.s _let_26 tptp.vectoru_sub))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_13 tptp.bool) tptp.bilinear) _let_14))) (= (tptp.s _let_4 (tptp.i _let_23 (tptp.s _let_5 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 U_0) _let_14)) _let_11)) _let_8)))) (tptp.s _let_4 (tptp.i (tptp.s _let_25 (tptp.i (tptp.s _let_26 (tptp.i (tptp.s (tptp.fun tptp.bool _let_26) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 tptp.l_a_) _let_19)) _let_18)))) (tptp.s _let_4 (tptp.i (tptp.s _let_25 (tptp.i _let_27 (tptp.s _let_4 (tptp.i (tptp.s _let_25 (tptp.i _let_27 (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i _let_14 (tptp.s _let_9 (tptp.i _let_11 _let_24)))) (tptp.s _let_6 (tptp.i _let_8 _let_24)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i _let_14 (tptp.s _let_9 (tptp.i _let_11 _let_19)))) (tptp.s _let_6 (tptp.i _let_8 _let_19)))))))) (tptp.s _let_4 (tptp.i _let_23 (tptp.s _let_5 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 U_1) _let_14)) _let_11)) _let_8)))))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1)))))))))))))))))))))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (P $$unsorted) (U_1 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.cart tptp.real P))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_11))) (let ((_let_13 (tptp.s _let_12 H0))) (let ((_let_14 (tptp.fun tptp.num _let_10))) (let ((_let_15 (tptp.fun _let_3 _let_14))) (let ((_let_16 (tptp.fun _let_6 _let_15))) (= (tptp.s _let_10 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) U_1) _let_13)) _let_7)) _let_4)) _let_1)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.vectoru_sub) (tptp.s _let_5 (tptp.i _let_7 (tptp.s tptp.num (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.p_) _let_1)) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.s _let_5 (tptp.i _let_7 _let_1)))))) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((H0 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.cart tptp.real M))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.s _let_8 F0))) (let ((_let_10 (tptp.cart tptp.real P))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (let ((_let_12 (tptp.fun _let_7 _let_11))) (let ((_let_13 (tptp.s _let_12 H0))) (let ((_let_14 (tptp.fun tptp.num _let_10))) (let ((_let_15 (tptp.fun _let_4 _let_14))) (let ((_let_16 (tptp.fun _let_8 _let_15))) (= (tptp.s _let_10 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_12 _let_16) U_0) _let_13)) _let_9)) _let_5)) _let_2)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_13 (tptp.s _let_7 (tptp.i _let_9 _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_sub) (tptp.s _let_3 (tptp.i _let_5 _let_2)))) (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted) (M0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real P))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.s _let_7 G0))) (let ((_let_9 (tptp.cart tptp.real M))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.s _let_10 F0))) (let ((_let_12 (tptp.fun _let_6 _let_4))) (let ((_let_13 (tptp.fun _let_9 _let_12))) (let ((_let_14 (tptp.s _let_13 H0))) (let ((_let_15 (tptp.fun _let_7 _let_5))) (let ((_let_16 (tptp.fun _let_10 _let_15))) (let ((_let_17 (tptp.fun _let_13 _let_16))) (let ((_let_18 (tptp.s tptp.num N0))) (let ((_let_19 (tptp.s tptp.num M0))) (let ((_let_20 (tptp.fun tptp.num tptp.bool))) (let ((_let_21 (tptp.fun tptp.num _let_20))) (let ((_let_22 (tptp.fun _let_5 _let_4))) (let ((_let_23 (tptp.s _let_22 (tptp.i (tptp.s (tptp.fun _let_20 _let_22) tptp.vsum) (tptp.s _let_20 (tptp.i (tptp.s _let_21 (tptp.i (tptp.s (tptp.fun tptp.num _let_21) tptp.o_o_) _let_19)) _let_18)))))) (let ((_let_24 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (let ((_let_25 (tptp.fun tptp.num _let_2))) (let ((_let_26 (tptp.fun _let_4 _let_4))) (let ((_let_27 (tptp.fun _let_4 _let_26))) (let ((_let_28 (tptp.s _let_27 tptp.vectoru_sub))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_13 tptp.bool) tptp.bilinear) _let_14))) (= (tptp.s _let_4 (tptp.i _let_23 (tptp.s _let_5 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 U_0) _let_14)) _let_11)) _let_8)))) (tptp.s _let_4 (tptp.i (tptp.s _let_26 (tptp.i (tptp.s _let_27 (tptp.i (tptp.s (tptp.fun tptp.bool _let_27) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_20 (tptp.i (tptp.s _let_21 tptp.l_a_) _let_19)) _let_18)))) (tptp.s _let_4 (tptp.i (tptp.s _let_26 (tptp.i _let_28 (tptp.s _let_4 (tptp.i (tptp.s _let_26 (tptp.i _let_28 (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i _let_14 (tptp.s _let_9 (tptp.i _let_11 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_25 tptp.p_) _let_18)) _let_24)))))) (tptp.s _let_6 (tptp.i _let_8 _let_18)))))) (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i _let_14 (tptp.s _let_9 (tptp.i _let_11 _let_19)))) (tptp.s _let_6 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_25 tptp.m_) _let_19)) _let_24)))))))))) (tptp.s _let_4 (tptp.i _let_23 (tptp.s _let_5 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 U_1) _let_14)) _let_11)) _let_8)))))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (FI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) U_0) (tptp.s _let_4 F0))) (tptp.s _let_3 FI_)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun _let_3 tptp.real))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.dot) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) F0) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.dot) _let_4)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) FI_) _let_2))))))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_1 _let_2))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (= (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.adjoint) _let_4)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_6 _let_5) tptp.h_) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_1 _let_3))) (let ((_let_7 (tptp.s _let_3 X))) (let ((_let_8 (tptp.fun _let_3 tptp.real))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.dot) (tptp.s _let_1 (tptp.i _let_5 _let_7)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.dot) _let_7)) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.adjoint) _let_5)) _let_2)))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_1 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.adjoint) _let_4)))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_1 tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_3))) (let ((_let_9 (tptp.fun _let_3 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.dot) _let_4)) (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.adjoint) _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.dot) (tptp.s _let_1 (tptp.i _let_6 _let_4)))) _let_2))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s _let_3 Y))) (let ((_let_7 (tptp.fun _let_3 tptp.real))) (let ((_let_8 (tptp.fun _let_3 _let_1))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.dot) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.adjoint) _let_5)) _let_6)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.dot) _let_6)) (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_1 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_5 _let_3) tptp.adjoint) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.adjoint) _let_4)))) _let_4)))))))) (forall ((Q113333 $$unsorted) (Q113332 $$unsorted) (F0 $$unsorted) (FI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q113332))) (let ((_let_2 (tptp.cart tptp.real Q113333))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_1 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q113333))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q113332))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun _let_3 tptp.real))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.dot) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) FI_) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.dot) _let_4)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2))))))))))))) (= (tptp.s _let_5 FI_) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.adjoint) _let_4)))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_1 $$unsorted)) (=> (forall ((C0 $$unsorted) (A5 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s tptp.real C0))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.num _let_7))) (let ((_let_11 (tptp.fun _let_4 _let_10))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) U_1) _let_8)) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_mul) _let_8)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_2)))) _let_1))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun tptp.num _let_2))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_6 _let_2) tptp.lambda) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) U_1) _let_5)) _let_4)) _let_1)))))))))))))))) (forall ((C0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.s tptp.real C0))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_r_) _let_4)) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) U_0) _let_4)) _let_3))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_2)))) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun tptp.num _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_1) _let_4)) _let_1))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun tptp.num _let_1))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.matrixu_neg) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.d_))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_3 _let_8) tptp.d_))) (let ((_let_10 (tptp.s _let_4 A5))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun tptp.num _let_8))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_4 _let_13) U_1) _let_10)) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_10)) _let_2)))) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.s _let_3 B0))) (let ((_let_5 (tptp.s _let_3 A5))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun tptp.num _let_2))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_6 _let_2) tptp.lambda) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_1) _let_5)) _let_4)) _let_1)))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.s _let_2 A5))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.matrixu_add) _let_4)) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_4)) _let_3))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.d_))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_3 _let_8) tptp.d_))) (let ((_let_10 (tptp.s _let_4 A5))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun tptp.num _let_8))) (let ((_let_13 (tptp.fun _let_4 _let_12))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_4 _let_13) U_1) _let_10)) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_10)) _let_2)))) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.s _let_3 B0))) (let ((_let_5 (tptp.s _let_3 A5))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun tptp.num _let_2))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) U_0) _let_5)) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_6 _let_2) tptp.lambda) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_1) _let_5)) _let_4)) _let_1)))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.s _let_2 A5))) (let ((_let_5 (tptp.fun tptp.num _let_1))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.matrixu_sub) _let_4)) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) U_0) _let_4)) _let_3))))))))))))))))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (U_2 $$unsorted)) (=> (forall ((A5 $$unsorted) (I0 $$unsorted) (B0 $$unsorted) (J0 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num K0))) (let ((_let_3 (tptp.cart tptp.real P))) (let ((_let_4 (tptp.cart _let_3 N))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s tptp.num I0))) (let ((_let_9 (tptp.cart tptp.real N))) (let ((_let_10 (tptp.cart _let_9 M))) (let ((_let_11 (tptp.s _let_10 A5))) (let ((_let_12 (tptp.fun tptp.num _let_9))) (let ((_let_13 (tptp.fun tptp.real tptp.real))) (let ((_let_14 (tptp.fun tptp.num _let_7))) (let ((_let_15 (tptp.fun _let_4 _let_14))) (let ((_let_16 (tptp.fun tptp.num _let_15))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_10 _let_16) U_2) _let_11)) _let_8)) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.real _let_13) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_9 _let_7) tptp.d_) (tptp.s _let_9 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.d_) _let_11)) _let_8)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_2)))) _let_1)))))))))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (I0 $$unsorted) (B0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real P) N))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.s _let_5 A5))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.fun tptp.num _let_9))) (let ((_let_11 (tptp.fun N tptp.bool))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.fun tptp.num _let_13))) (let ((_let_15 (tptp.fun _let_7 tptp.real))) (let ((_let_16 (tptp.fun _let_2 _let_7))) (let ((_let_17 (tptp.fun tptp.num _let_16))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_5 _let_17) U_1) _let_6)) _let_4)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_13 _let_15) tptp.sum) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.num _let_14) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_12 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_11 tptp.num) tptp.dimindex) (tptp.s _let_11 tptp.univ))))))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) U_2) _let_6)) _let_4)) _let_3)) _let_1))))))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.s _let_5 A5))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun tptp.num _let_1))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_5 _let_11) U_0) _let_6)) _let_3)) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.lambda) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_1) _let_6)) _let_4)) _let_3))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_1))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.cart _let_1 M))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.matrixu_mul) _let_5)) _let_3)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.lambda) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)) _let_3))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (I0 $$unsorted) (X $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s _let_5 tptp.d_))) (let ((_let_7 (tptp.s tptp.num I0))) (let ((_let_8 (tptp.cart _let_2 M))) (let ((_let_9 (tptp.s _let_8 A5))) (let ((_let_10 (tptp.fun tptp.num _let_2))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun tptp.num _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_8 _let_12) U_1) _let_9)) _let_7)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.d_) _let_9)) _let_7)))) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_6 _let_3)) _let_1)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.cart _let_1 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun N tptp.bool))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_6 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)) _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dimindex) (tptp.s _let_9 tptp.univ))))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) _let_5)) _let_3)) _let_2))))))))))))))))))) (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.cart tptp.real M))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.matrixu_vectoru_mul) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_2)))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (J0 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.s tptp.num J0))) (let ((_let_7 (tptp.cart tptp.real N))) (let ((_let_8 (tptp.cart _let_7 M))) (let ((_let_9 (tptp.s _let_8 A5))) (let ((_let_10 (tptp.fun tptp.num _let_7))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun tptp.num _let_5))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_8 _let_12) U_1) _let_9)) _let_6)) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_7 _let_4) tptp.d_) (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.d_) _let_9)) _let_1)))) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.d_) _let_3)) _let_1)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.num J0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun M tptp.bool))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.fun tptp.num _let_11))) (let ((_let_13 (tptp.fun _let_6 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)) _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_11 _let_13) tptp.sum) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dimindex) (tptp.s _let_9 tptp.univ))))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) _let_5)) _let_3)) _let_2))))))))))))))))))) (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.vectoru_matrixu_mul) _let_2)) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_6 _let_3) tptp.lambda) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) U_0) _let_5)) _let_2)))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_1 $$unsorted)) (=> (forall ((I0 $$unsorted) (K0 $$unsorted) (J0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 tptp.realu_ofu_num))) (let ((_let_3 (tptp.s tptp.num K0))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s tptp.num J0))) (let ((_let_8 (tptp.s tptp.num I0))) (let ((_let_9 (tptp.fun tptp.num _let_1))) (and (= (tptp.p _let_4) (= _let_8 _let_7)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) U_1) _let_8)) _let_3)) _let_7)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_4)) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((K0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) U_0) _let_1)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) U_1) _let_2)) _let_1)))))))))))) (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.cart _let_2 M))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mat) _let_1)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) U_0) _let_1)))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_1 $$unsorted)) (=> (forall ((A5 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.num J0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_1) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_2)))) _let_1)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.cart tptp.real M))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) U_0) _let_3)) _let_1)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_1) _let_3)) _let_1))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.cart _let_3 N))) (= (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.transp) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_2)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_2)))) _let_1)))))))))))) (forall ((A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.row) _let_1)) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_1))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_2)))) _let_1)))))))))))) (forall ((A5 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.cart tptp.real M))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.column) _let_1)) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3)) _let_1))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_291 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 A5))) (tptp.s _let_1 GENR_PVARR_291)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun M tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dimindex) (tptp.s _let_8 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.setspec) (tptp.s _let_1 GENR_PVARR_291))) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.row) _let_3)) (tptp.s _let_2 A5)))))))))))))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.rows) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_292 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 A5))) (tptp.s _let_1 GENR_PVARR_292)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun N tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dimindex) (tptp.s _let_8 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.setspec) (tptp.s _let_3 GENR_PVARR_292))) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.column) _let_2)) (tptp.s _let_1 A5)))))))))))))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun (tptp.cart tptp.real M) tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.columns) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)))))))))))) (forall ((N $$unsorted) (M $$unsorted) (C0 $$unsorted) (A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.j))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.d_))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_3 _let_8) tptp.d_))) (let ((_let_10 (tptp.s tptp.real C0))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun _let_4 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.real _let_12) tptp.r_r_) _let_10)) _let_5)))) _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_mul) _let_10)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1)))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.d_))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_3 _let_8) tptp.d_))) (let ((_let_10 (tptp.s _let_4 A5))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun _let_4 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.matrixu_add) _let_10)) _let_5)))) _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_10)) _let_2)))) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1)))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.d_))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_3 _let_8) tptp.d_))) (let ((_let_10 (tptp.s _let_4 A5))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun _let_4 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_4 _let_12) tptp.matrixu_sub) _let_10)) _let_5)))) _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_10)) _let_2)))) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1)))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_6) tptp.d_))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.s (tptp.fun _let_3 _let_8) tptp.d_))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.matrixu_neg) _let_5)))) _let_2)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))) _let_1))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.num J0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_3))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.cart tptp.real M))) (let ((_let_9 (tptp.cart _let_8 N))) (let ((_let_10 (tptp.fun tptp.num _let_8))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_8 _let_7) tptp.d_) (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_9 _let_10) tptp.d_) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.transp) _let_5)))) _let_1)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_2)))) _let_1)))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (N0 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num J0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_7 (tptp.fun M tptp.bool))) (let ((_let_8 (tptp.s tptp.num I0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_8)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dimindex) (tptp.s _let_7 tptp.univ)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.real))) (let ((_let_2 (tptp.s _let_1 tptp.realu_ofu_num))) (let ((_let_3 (tptp.s tptp.num N0))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s tptp.num J0))) (let ((_let_8 (tptp.s tptp.num I0))) (let ((_let_9 (tptp.cart tptp.real N))) (let ((_let_10 (tptp.cart _let_9 M))) (let ((_let_11 (tptp.fun tptp.num _let_9))) (and (= (tptp.p _let_4) (= _let_8 _let_7)) (= (tptp.s tptp.real (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_9 _let_1) tptp.d_) (tptp.s _let_9 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_10 _let_11) tptp.d_) (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) tptp.mat) _let_3)))) _let_8)))) _let_7)) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_4)) (tptp.s tptp.real (tptp.i _let_2 _let_3)))) (tptp.s tptp.real (tptp.i _let_2 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.real B0))) (let ((_let_4 (tptp.s tptp.real A5))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.r_r_))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) _let_4)) _let_3)))) _let_2))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.r_r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)) _let_2)))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.matrixu_add))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.matrixu_add))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 A5))))) (= (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)))))))))) (forall ((Q114603 $$unsorted) (Q114604 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real Q114603) Q114604))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_add) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2)) _let_2))))) (forall ((Q114621 $$unsorted) (Q114622 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real Q114621) Q114622))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_add) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))))) (forall ((Q114643 $$unsorted) (Q114644 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real Q114643) Q114644))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_add) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.matrixu_neg) _let_2)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((Q114667 $$unsorted) (Q114668 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real Q114667) Q114668))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_add) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.matrixu_neg) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_1 A5))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.matrixu_sub) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_5 tptp.matrixu_add) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.matrixu_neg) _let_2))))))))))) (forall ((Q114719 $$unsorted) (Q114720 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real Q114719) Q114720))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_sub) _let_2)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 C0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.cart _let_1 M))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrixu_mul) (tptp.s _let_4 A5))))) (let ((_let_8 (tptp.s _let_2 B0))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) tptp.matrixu_add) _let_8)) _let_3)))) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.matrixu_add) (tptp.s _let_5 (tptp.i _let_7 _let_8)))) (tptp.s _let_5 (tptp.i _let_7 _let_3)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real M) M))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.matrixu_mul) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)) _let_2))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.cart _let_1 N))) (let ((_let_6 (tptp.fun _let_5 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.matrixu_mul) _let_3)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_3)))))))) (forall ((M $$unsorted) (N $$unsorted) (Q $$unsorted) (P $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q))) (let ((_let_2 (tptp.cart _let_1 P))) (let ((_let_3 (tptp.s _let_2 C0))) (let ((_let_4 (tptp.cart tptp.real P))) (let ((_let_5 (tptp.cart _let_4 N))) (let ((_let_6 (tptp.s _let_5 B0))) (let ((_let_7 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_8 (tptp.s _let_7 A5))) (let ((_let_9 (tptp.cart _let_4 M))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.cart _let_1 M))) (let ((_let_12 (tptp.fun _let_2 _let_11))) (let ((_let_13 (tptp.cart _let_1 N))) (let ((_let_14 (tptp.fun _let_2 _let_13))) (let ((_let_15 (tptp.fun _let_13 _let_11))) (= (tptp.s _let_11 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_7 _let_15) tptp.matrixu_mul) _let_8)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_5 _let_14) tptp.matrixu_mul) _let_6)) _let_3)))) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.matrixu_mul) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.matrixu_mul) _let_8)) _let_6)))) _let_3))))))))))))))))))) (forall ((N $$unsorted) (P $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real P))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.cart _let_2 N))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.mat) _let_1)))) (tptp.s _let_4 A5))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) _let_1)))))))))) (forall ((N $$unsorted) (P $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real P))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.cart _let_2 N))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 A5))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mat) _let_1)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) _let_1)))))))))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 C0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.cart _let_1 M))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.s (tptp.fun _let_4 _let_7) tptp.matrixu_mul))) (let ((_let_9 (tptp.s _let_4 A5))) (let ((_let_10 (tptp.fun _let_6 _let_6))) (let ((_let_11 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_4 _let_11) tptp.matrixu_add) _let_9)) _let_5)))) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.matrixu_add) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_9)) _let_3)))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))))))))))))))))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 C0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.cart _let_1 M))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrixu_mul) (tptp.s _let_4 A5))))) (let ((_let_8 (tptp.s _let_2 B0))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) tptp.matrixu_sub) _let_8)) _let_3)))) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.matrixu_sub) (tptp.s _let_5 (tptp.i _let_7 _let_8)))) (tptp.s _let_5 (tptp.i _let_7 _let_3)))))))))))))))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 C0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.s _let_4 B0))) (let ((_let_6 (tptp.cart _let_1 M))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.s (tptp.fun _let_4 _let_7) tptp.matrixu_mul))) (let ((_let_9 (tptp.s _let_4 A5))) (let ((_let_10 (tptp.fun _let_6 _let_6))) (let ((_let_11 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_4 _let_11) tptp.matrixu_sub) _let_9)) _let_5)))) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.matrixu_sub) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_9)) _let_3)))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))))))))))))))))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.cart _let_1 M))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.s (tptp.fun _let_4 _let_7) tptp.matrixu_mul))) (let ((_let_9 (tptp.s tptp.real C0))) (let ((_let_10 (tptp.fun _let_6 _let_6))) (let ((_let_11 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.r_r_) _let_9)) _let_5)))) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_r_) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))))))))))))))))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.cart _let_1 M))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrixu_mul) (tptp.s _let_4 A5))))) (let ((_let_8 (tptp.s tptp.real C0))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_5 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_r_) _let_8)) _let_3)))) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.r_r_) _let_8)) (tptp.s _let_5 (tptp.i _let_7 _let_3)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_r_) (tptp.s tptp.real C0))))) (let ((_let_5 (tptp.s _let_1 A5))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_add))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_5)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_r_) (tptp.s tptp.real C0))))) (let ((_let_5 (tptp.s _let_1 A5))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_sub))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_5)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s tptp.real C0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.r_r_))) (let ((_let_6 (tptp.s tptp.real B0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_add) _let_6)) _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.matrixu_add) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s tptp.real C0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.r_r_))) (let ((_let_6 (tptp.s tptp.real B0))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_sub) _let_6)) _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.matrixu_sub) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))) (forall ((Q115612 $$unsorted) (Q115613 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real Q115612) Q115613))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_r_) (tptp.s tptp.real C0))) _let_2)) _let_2))))) (forall ((Q115629 $$unsorted) (Q115630 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real Q115629) Q115630))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (tptp.s _let_2 A5))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mat) _let_1))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.matrixu_neg) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.r_r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) _let_2)))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 tptp.a))) (let ((_let_3 (tptp.s _let_1 tptp.b))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.matrixu_add))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 tptp.c0))) (let ((_let_3 (tptp.s _let_1 tptp.b))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.matrixu_add))) (let ((_let_6 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 tptp.a))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) _let_2)) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 tptp.c0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_add))) (let ((_let_5 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 tptp.a))))) (let ((_let_6 (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 tptp.b))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_2)))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_5 _let_2)))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_3 tptp.matrixu_neg))) (let ((_let_5 (tptp.s _let_1 A5))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_add))) (= (tptp.s _let_1 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 _let_5)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_4 _let_5)))) (tptp.s _let_1 (tptp.i _let_4 _let_2)))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.matrixu_sub))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.matrixu_neg) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((Q115825 $$unsorted) (Q115826 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real Q115825) Q115826))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.matrixu_neg) _let_2)) _let_2)))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_sub) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_sub) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.matrixu_neg) _let_2))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s _let_1 A5))) (= (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.matrixu_neg) _let_3)) _let_2) (= _let_3 _let_2)))))) (forall ((M $$unsorted) (N $$unsorted) (P $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.s _let_3 B0))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.cart _let_5 M))) (let ((_let_7 (tptp.s _let_6 A5))) (let ((_let_8 (tptp.cart _let_1 M))) (let ((_let_9 (tptp.fun _let_3 _let_8))) (let ((_let_10 (tptp.cart tptp.real M))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.fun _let_1 _let_5))) (let ((_let_13 (tptp.fun _let_5 _let_10))) (= (tptp.s _let_10 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_6 _let_13) tptp.matrixu_vectoru_mul) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_3 _let_12) tptp.matrixu_vectoru_mul) _let_4)) _let_2)))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.matrixu_vectoru_mul) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.matrixu_mul) _let_7)) _let_4)))) _let_2))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.cart _let_1 N))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.matrixu_vectoru_mul) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)) _let_2))))))) (forall ((N $$unsorted) (Q116015 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q116015))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 Q116015))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.matrixu_vectoru_mul) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mat) _let_1)))) (tptp.s _let_3 X))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.cart _let_3 N))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.matrixu_vectoru_mul) (tptp.s _let_4 A5))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.matrixu_vectoru_mul) (tptp.s _let_3 A5))))) (let ((_let_7 (tptp.s _let_1 X))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_add) _let_7)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.vectoru_add) (tptp.s _let_4 (tptp.i _let_6 _let_7)))) (tptp.s _let_4 (tptp.i _let_6 _let_2))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.matrixu_vectoru_mul) (tptp.s _let_3 A5))))) (let ((_let_7 (tptp.s _let_1 X))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_sub) _let_7)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.vectoru_sub) (tptp.s _let_4 (tptp.i _let_6 _let_7)))) (tptp.s _let_4 (tptp.i _let_6 _let_2))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.s _let_3 B0))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_3 _let_6) tptp.matrixu_vectoru_mul))) (let ((_let_8 (tptp.s _let_3 A5))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.matrixu_add) _let_8)) _let_4)))) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.vectoru_add) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.s _let_3 B0))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_3 _let_6) tptp.matrixu_vectoru_mul))) (let ((_let_8 (tptp.s _let_3 A5))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.matrixu_sub) _let_8)) _let_4)))) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.vectoru_sub) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.matrixu_vectoru_mul) (tptp.s _let_3 A5))))) (let ((_let_7 (tptp.s tptp.real C0))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.r_) _let_7)) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) _let_7)) (tptp.s _let_4 (tptp.i _let_6 _let_2))))))))))))))) (forall ((Q116425 $$unsorted) (Q116423 $$unsorted) (Q116424 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q116423))) (let ((_let_2 (tptp.cart _let_1 Q116424))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.cart tptp.real Q116424))) (let ((_let_5 (tptp.cart _let_4 Q116423))) (let ((_let_6 (tptp.cart tptp.real Q116425))) (let ((_let_7 (tptp.cart _let_6 Q116423))) (let ((_let_8 (tptp.s _let_7 B0))) (let ((_let_9 (tptp.cart _let_1 Q116425))) (let ((_let_10 (tptp.cart _let_4 Q116425))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.cart _let_6 Q116424))) (let ((_let_13 (tptp.fun _let_7 _let_12))) (= (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_12 _let_10) tptp.transp) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_2 _let_13) tptp.matrixu_mul) _let_3)) _let_8)))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.matrixu_mul) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.transp) _let_8)))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.transp) _let_3))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (= (= (tptp.s _let_1 A5) (tptp.s _let_1 B0)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 M))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.matrixu_vectoru_mul))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 A5))) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 B0))) _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (X $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.num K0))) (let ((_let_4 (tptp.cart _let_1 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.real))) (let ((_let_8 (tptp.cart tptp.real M))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun tptp.num tptp.real))) (let ((_let_11 (tptp.fun M tptp.bool))) (let ((_let_12 (tptp.fun tptp.num tptp.bool))) (let ((_let_13 (tptp.s (tptp.fun tptp.num _let_12) tptp.l_a_))) (let ((_let_14 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s tptp.num (tptp.i (tptp.s _let_14 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_14 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_11 tptp.num) tptp.dimindex) (tptp.s _let_11 tptp.univ))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.d_) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.matrixu_vectoru_mul) _let_5)) _let_2)))) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.dot) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_3)))) _let_2))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart _let_1 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_5 X))) (let ((_let_8 (tptp.fun _let_5 tptp.real))) (let ((_let_9 (tptp.fun _let_3 _let_1))) (let ((_let_10 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_1 _let_10) tptp.dot) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.vectoru_matrixu_mul) _let_7)) _let_4)))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.dot) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.matrixu_vectoru_mul) _let_4)) _let_2)))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.transp))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_r_) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_r_) _let_5)) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.transp))) (let ((_let_5 (tptp.s _let_1 A5))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.matrixu_add) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.matrixu_add) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.transp))) (let ((_let_5 (tptp.s _let_1 A5))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.matrixu_sub) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.matrixu_sub) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.transp))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.matrixu_neg) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.matrixu_neg) (tptp.s _let_3 (tptp.i _let_4 _let_2)))))))))) (forall ((Q116735 $$unsorted) (Q116736 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real Q116735) Q116736))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real Q116736) Q116735))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.transp) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mat) _let_1))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real M) N))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.transp) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.transp) _let_2)))) _let_2))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.transp))) (= (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2)))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.cart _let_4 N))) (let ((_let_7 (tptp.fun _let_6 _let_4))) (let ((_let_8 (tptp.fun N tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dimindex) (tptp.s _let_8 tptp.univ))))))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.row) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.transp) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.column) _let_3)) _let_2)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_7 (tptp.fun _let_6 _let_1))) (let ((_let_8 (tptp.fun M tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dimindex) (tptp.s _let_8 tptp.univ))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.column) _let_4)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.transp) _let_3)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.row) _let_4)) _let_3)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.cart _let_3 N))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.rows) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.transp) _let_2)))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.columns) _let_2))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real M) N))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.columns) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.transp) _let_3)))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.rows) _let_3))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.cart _let_3 N))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.cart _let_1 M))) (let ((_let_7 (tptp.fun _let_1 _let_3))) (let ((_let_8 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.vectoru_matrixu_mul) _let_2)) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.matrixu_vectoru_mul) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.transp) _let_5)))) _let_2)))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.cart _let_4 M))) (let ((_let_6 (tptp.s _let_1 X))) (let ((_let_7 (tptp.fun _let_5 _let_4))) (let ((_let_8 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.matrixu_vectoru_mul) _let_3)) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_matrixu_mul) _let_6)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.transp) _let_3)))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.finite) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.rows) (tptp.s _let_2 A5)))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real M) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.columns) (tptp.s _let_1 A5))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (= (= (tptp.s _let_1 A5) (tptp.s _let_1 B0)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.row) _let_3)))) (let ((_let_6 (tptp.fun M tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (= (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_2 A5))) (tptp.s _let_1 (tptp.i _let_5 (tptp.s _let_2 B0)))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (= (= (tptp.s _let_1 A5) (tptp.s _let_1 B0)) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.column) _let_2)))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (= (tptp.s _let_3 (tptp.i _let_5 (tptp.s _let_1 A5))) (tptp.s _let_3 (tptp.i _let_5 (tptp.s _let_1 B0)))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.cart _let_1 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun tptp.num _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.real))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) U_0) _let_5)) _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.dot) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.d_) _let_5)) _let_3)))) _let_2))))))))))))) (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.cart tptp.real M))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.matrixu_vectoru_mul) _let_4)) _let_2)) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_2)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s _let_1 X))) (let ((_let_8 (tptp.fun tptp.num tptp.real))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun tptp.num _let_5))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) U_0) _let_7)) _let_3)) _let_4)) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.d_) _let_7)) _let_4)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.column) _let_4)) _let_3))))))))))))))))) (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun N tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (let ((_let_12 (tptp.fun _let_6 _let_5))) (let ((_let_13 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_2 _let_13) tptp.matrixu_vectoru_mul) _let_3)) _let_4)) (tptp.s _let_5 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.vsum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dimindex) (tptp.s _let_8 tptp.univ))))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) U_0) _let_4)) _let_3))))))))))))))))))))) (forall ((N $$unsorted) (U_1 $$unsorted)) (=> (forall ((X $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s (tptp.fun _let_3 _let_4) tptp.d_))) (let ((_let_6 (tptp.s _let_3 X))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) U_1) _let_6)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.basis) _let_2)))) _let_1)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun _let_4 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.sum) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_1) _let_3)) _let_1)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (F0 $$unsorted) (J0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.s tptp.num I0))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_3 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s _let_3 X))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.num _let_7))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) U_0) _let_8)) _let_6)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.d_) _let_8)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.d_) (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.basis) _let_2)))))) _let_1))))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.s _let_3 X))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun M tptp.bool))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (let ((_let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (let ((_let_14 (tptp.fun tptp.num _let_13))) (let ((_let_15 (tptp.fun _let_7 tptp.real))) (let ((_let_16 (tptp.fun N tptp.bool))) (let ((_let_17 (tptp.s _let_14 tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_17 _let_12)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_17 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_16 tptp.num) tptp.dimindex) (tptp.s _let_16 tptp.univ))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.d_) (tptp.s _let_2 (tptp.i _let_5 _let_6)))) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_13 _let_15) tptp.sum) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.num _let_14) tptp.o_o_) _let_12)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_10 tptp.num) tptp.dimindex) (tptp.s _let_10 tptp.univ))))))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) U_0) _let_6)) _let_5)) _let_1))))))))))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.invertible) (tptp.s _let_1 A5)))) (exists ((AI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 N))) (let ((_let_5 (tptp.cart _let_3 M))) (let ((_let_6 (tptp.s _let_5 A5))) (let ((_let_7 (tptp.cart tptp.real M))) (let ((_let_8 (tptp.cart _let_7 N))) (let ((_let_9 (tptp.s _let_8 AI_))) (let ((_let_10 (tptp.fun _let_5 _let_4))) (let ((_let_11 (tptp.cart _let_7 M))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (and (= (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) tptp.matrixu_mul) _let_6)) _let_9)) (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.mat) _let_2))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.matrixu_mul) _let_9)) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mat) _let_2)))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (AI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 N))) (let ((_let_5 (tptp.cart _let_3 M))) (let ((_let_6 (tptp.s _let_5 A5))) (let ((_let_7 (tptp.cart tptp.real M))) (let ((_let_8 (tptp.cart _let_7 N))) (let ((_let_9 (tptp.s _let_8 AI_))) (let ((_let_10 (tptp.fun _let_5 _let_4))) (let ((_let_11 (tptp.cart _let_7 M))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (let ((_let_13 (tptp.fun _let_8 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_5 _let_13) U_0) _let_6)) _let_9))) (and (= (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) tptp.matrixu_mul) _let_6)) _let_9)) (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.mat) _let_2))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.matrixu_mul) _let_9)) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mat) _let_2))))))))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.matrixu_inv) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.h_) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2)))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 N))) (let ((_let_5 (tptp.cart _let_3 M))) (let ((_let_6 (tptp.s _let_5 A5))) (let ((_let_7 (tptp.cart tptp.real M))) (let ((_let_8 (tptp.cart _let_7 N))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.matrixu_inv) _let_6)))) (let ((_let_10 (tptp.fun _let_5 _let_4))) (let ((_let_11 (tptp.cart _let_7 M))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.invertible) _let_6))) (and (= (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) tptp.matrixu_mul) _let_6)) _let_9)) (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.mat) _let_2))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.matrixu_mul) _let_9)) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.mat) _let_2)))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.s tptp.num J0))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_3 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun tptp.num _let_7))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_1) _let_6)) _let_1)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.d_) (tptp.s _let_4 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.basis) _let_2)))))) _let_1)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.fun _let_2 (tptp.cart tptp.real N)))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun tptp.num _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) U_0) _let_4)) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) tptp.lambda) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_1) _let_4)) _let_1))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real N)))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun tptp.num _let_1))) (let ((_let_5 (tptp.cart _let_1 N))) (= (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.matrix) _let_3)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.matrixu_vectoru_mul) _let_4)) _let_2))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.fun _let_1 (tptp.cart tptp.real M)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 A5)))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.cart _let_1 N))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.matrixu_vectoru_mul) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrix) _let_5)))) _let_2)) (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.cart _let_1 N))) (= (tptp.s _let_3 (tptp.i _let_5 _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.matrixu_vectoru_mul) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrix) _let_5)))) _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.matrixu_vectoru_mul) _let_4)) _let_2))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun _let_1 (tptp.cart tptp.real M)))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_4 _let_2) tptp.matrix) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3)))) _let_3)))))))) (forall ((Q117654 $$unsorted) (Q117653 $$unsorted) (Q117652 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q117652))) (let ((_let_2 (tptp.cart tptp.real Q117653))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.cart _let_2 Q117652))) (let ((_let_6 (tptp.cart tptp.real Q117654))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s _let_7 G0))) (let ((_let_9 (tptp.cart _let_1 Q117654))) (let ((_let_10 (tptp.cart _let_2 Q117654))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun _let_2 _let_6))) (let ((_let_13 (tptp.fun _let_3 _let_12))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.linear) _let_8)))) (= (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_12 _let_10) tptp.matrix) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_7 _let_13) tptp.o) _let_8)) _let_4)))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.matrixu_mul) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.matrix) _let_8)))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.matrix) _let_4)))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.cart _let_5 N))) (let ((_let_7 (tptp.fun tptp.num _let_5))) (let ((_let_8 (tptp.s _let_2 X))) (let ((_let_9 (tptp.fun tptp.num tptp.real))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun _let_3 _let_7))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_2 _let_11) U_0) _let_8)) _let_4)) _let_1)) (tptp.s _let_5 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_2 _let_9) tptp.d_) _let_8)) _let_1)))) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.d_) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.transp) _let_4)))) _let_1))))))))))))))))) (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun tptp.num _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun N tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (let ((_let_12 (tptp.fun _let_6 _let_5))) (let ((_let_13 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_2 _let_13) tptp.matrixu_vectoru_mul) _let_3)) _let_4)) (tptp.s _let_5 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.vsum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dimindex) (tptp.s _let_8 tptp.univ))))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) U_0) _let_4)) _let_3))))))))))))))))))))) (forall ((N $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.s _let_3 tptp.a))) (let ((_let_5 (tptp.fun tptp.num _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_3 _let_5) tptp.d_))) (let ((_let_7 (tptp.s _let_3 tptp.b))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.fun N tptp.bool))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.s (tptp.fun tptp.num _let_11) tptp.l_a_))) (let ((_let_13 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_13 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_13 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_10 tptp.num) tptp.dimindex) (tptp.s _let_10 tptp.univ))))))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.matrixu_mul) _let_4)) _let_7)))) _let_1)) (tptp.s _let_2 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.matrixu_vectoru_mul) (tptp.s _let_3 (tptp.i (tptp.s _let_8 tptp.transp) _let_7)))) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_1)))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 M))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.matrixu_vectoru_mul) _let_4)) _let_2))))))))))) (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart _let_3 M))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.cart _let_1 N))) (let ((_let_7 (tptp.fun _let_1 _let_3))) (let ((_let_8 (tptp.fun _let_3 _let_1))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_8 _let_7) tptp.adjoint) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_5)))) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.matrixu_vectoru_mul) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.transp) _let_5)))) _let_2)))))))))))))) (forall ((Q117843 $$unsorted) (Q117844 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q117844))) (let ((_let_2 (tptp.cart tptp.real Q117843))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.cart _let_2 Q117844))) (let ((_let_6 (tptp.cart _let_1 Q117843))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4))) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.matrix) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.adjoint) _let_4)))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.transp) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.matrix) _let_4)))))))))))))) (forall ((Q117856 $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real Q117856))) (let ((_let_3 (tptp.cart _let_2 Q117856))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q117856))) (let ((_let_2 (tptp.s _let_1 X))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)) _let_2)))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.matrix) (tptp.s _let_4 U_0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((Q117867 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real Q117867))) (let ((_let_3 (tptp.cart _let_2 Q117867))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.matrix) (tptp.s _let_4 tptp.i1))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (forall ((Q117887 $$unsorted) (Q117888 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q117887))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real Q117888)))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.cart _let_1 Q117888))) (let ((_let_6 (tptp.s (tptp.fun _let_2 _let_5) tptp.matrix))) (let ((_let_7 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_3))) (= (tptp.s _let_5 (tptp.i _let_6 _let_4)) (tptp.s _let_5 (tptp.i _let_6 _let_3)))) (= _let_4 _let_3)))))))))) (forall ((Q117930 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q117930))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.cart _let_1 Q117930))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.matrix) _let_3)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) _let_3))) (= (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.adjoint) _let_3)) _let_3) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.transp) _let_5)) _let_5))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (exists ((A5 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 F0) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.matrixu_vectoru_mul) (tptp.s _let_3 A5))) _let_2))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (exists ((C0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 F0) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) (tptp.s tptp.real C0))) _let_2)))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (GENR_PVARR_293 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 F0))) (tptp.s tptp.real GENR_PVARR_293)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_4) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.setspec) (tptp.s tptp.real GENR_PVARR_293))) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))))))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.onorm) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.sup) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (=> (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))))) (tptp.s tptp.real B0))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.vectoru_norm) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) F0) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.onorm) _let_5)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.vectoru_norm) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) F0) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_mul) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.onorm) (tptp.s _let_1 F0))))) (tptp.s tptp.real B0)))))))))))) (forall ((Q118203 $$unsorted) (Q118204 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q118203) (tptp.cart tptp.real Q118204)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.onorm) _let_2)))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_2 (tptp.s _let_1 F0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) _let_2))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.onorm) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) (tptp.s _let_2 X))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2)) (tptp.s _let_3 X))) _let_2)))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun (tptp.cart tptp.real M) _let_1))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.onorm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))) (forall ((Q118333 $$unsorted) (Q118355 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q118333) (tptp.cart tptp.real Q118355)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.onorm) _let_2))))) (not (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q118355))) (let ((_let_2 (tptp.cart tptp.real Q118333))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) (tptp.s _let_2 X))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))) (forall ((Q118371 $$unsorted) (Q118373 $$unsorted) (Q118374 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q118374))) (let ((_let_2 (tptp.cart tptp.real Q118373))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.cart tptp.real Q118371))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun _let_2 _let_5))) (let ((_let_10 (tptp.fun _let_3 _let_9))) (let ((_let_11 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.linear) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_9 tptp.real) tptp.onorm) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.o) _let_7)) _let_4)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_6 tptp.real) tptp.onorm) _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.onorm) _let_4)))))))))))))))))))) (forall ((Q118409 $$unsorted) (Q118421 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q118409))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q118421))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) U_0) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q118409) (tptp.cart tptp.real Q118421)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.onorm))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)))))) (tptp.s tptp.real (tptp.i _let_3 _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) U_0) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.onorm))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) _let_2))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)))) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.s _let_4 F0))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_6 _let_2)))) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.onorm))) (let ((_let_4 (tptp.s _let_1 F0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_4)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2))))))))))))))))))) (forall ((Q118562 $$unsorted) (Q118573 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q118562))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q118573))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.s _let_4 F0))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_6 _let_2)))) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real tptp.e0))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real Q118562) (tptp.cart tptp.real Q118573)))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_2 tptp.real) tptp.onorm))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_6 _let_4)))) (tptp.s tptp.real (tptp.i _let_6 _let_3)))))) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_4)) _let_3)))))) _let_1))))))))))))))))) (forall ((Q118614 $$unsorted) (Q118625 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (G0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q118614))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q118625))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.s _let_4 F0))) (let ((_let_7 (tptp.fun _let_3 _let_3))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) U_0) _let_6)) _let_5)) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_6 _let_2)))) (tptp.s _let_3 (tptp.i _let_5 _let_2)))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real tptp.e0))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real Q118614) (tptp.cart tptp.real Q118625)))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_2 tptp.real) tptp.onorm))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_lt))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_6 _let_4)))) (tptp.s tptp.real (tptp.i _let_6 _let_3)))))) _let_1)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_4)) _let_3)))))) _let_1))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (=> (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) U_0) _let_2)) _let_2)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.onorm) (tptp.s _let_3 U_0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.onorm) (tptp.s _let_3 tptp.i1))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) _let_1)) (tptp.s tptp.num I0))) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.lift) _let_1)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.lambda) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) U_0) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.drop) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.d_) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.d_) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.lift) _let_1)))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 X))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.lift) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop) _let_2)))) _let_2)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.drop) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.lift) _let_1)))) _let_1)))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.o) (tptp.s _let_5 tptp.lift))) (tptp.s _let_4 tptp.drop))))) _let_3)) _let_3)))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.o) (tptp.s _let_5 tptp.drop))) (tptp.s _let_4 tptp.lift))))) _let_2)) _let_2)))))))))) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun tptp.real _let_3))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_3 _let_9) tptp.in) _let_4)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 tptp.lift))) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.in) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.drop) _let_4)))) _let_2))))))))))))) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.in) _let_4)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 tptp.drop))) _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.lift) _let_4)))) _let_3))))))))))))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 X)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.lift) (tptp.s tptp.real X))))))))) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 X)))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.p0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.lift) (tptp.s tptp.real X))))))))) (= (forall ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) tptp.p0) (tptp.s tptp.real X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) tptp.p0) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop) (tptp.s _let_1 X))))))))) (= (exists ((X $$unsorted)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) tptp.p0) (tptp.s tptp.real X))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) tptp.p0) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop) (tptp.s _let_1 X))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.cart tptp.real tptp.n10)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 F0)))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.o) (tptp.s _let_3 tptp.lift))) (tptp.s _let_1 F0)))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 F0)))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun A tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.o) (tptp.s _let_3 tptp.drop))) (tptp.s _let_2 F0)))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A (tptp.cart tptp.real tptp.n10)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 F0)))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun A _let_2))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.o) (tptp.s _let_3 tptp.lift))) (tptp.s _let_1 F0)))))))))))))) (forall ((A $$unsorted) (P0 $$unsorted)) (= (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun A tptp.real))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 F0)))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun A _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun A tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.o) (tptp.s _let_3 tptp.drop))) (tptp.s _let_2 F0)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.lift))) (= (= (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_3 (tptp.i _let_4 _let_1))) (= _let_2 _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop))) (= (= (tptp.s tptp.real (tptp.i _let_4 _let_3)) (tptp.s tptp.real (tptp.i _let_4 _let_2))) (= _let_3 _let_2))))))) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.cart tptp.real tptp.n10))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.s _let_6 tptp.lift))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_8 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.in) (tptp.s _let_5 (tptp.i _let_7 _let_3)))) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.image) _let_7)) _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.in) _let_3)) _let_2)))))))))))))) (forall ((P0 $$unsorted)) (= (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real tptp.n10) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 S0)))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 tptp.lift))) (tptp.s _let_1 S0)))))))))))))) (forall ((P0 $$unsorted)) (= (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real tptp.n10) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 S0)))))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 tptp.lift))) (tptp.s _let_1 S0)))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.cart tptp.real tptp.n10))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 tptp.lift))))) (let ((_let_10 (tptp.fun _let_7 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.subset) (tptp.s _let_7 (tptp.i _let_9 _let_3)))) (tptp.s _let_7 (tptp.i _let_9 _let_2)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)) _let_2)))))))))))))) (forall ((P0 $$unsorted)) (= (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 S0)))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 tptp.drop))) (tptp.s _let_2 S0)))))))))))))) (forall ((P0 $$unsorted)) (= (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) P0) (tptp.s _let_1 S0)))))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) P0) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 tptp.drop))) (tptp.s _let_2 S0)))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.s _let_2 S0))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 tptp.drop))))) (let ((_let_10 (tptp.fun _let_7 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.subset) (tptp.s _let_7 (tptp.i _let_9 _let_4)))) (tptp.s _let_7 (tptp.i _let_9 _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.subset) _let_4)) _let_3)))))))))))))) (forall ((X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (let ((_let_7 (tptp.s _let_6 tptp.drop))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.fun _let_8 tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.in) (tptp.s tptp.real (tptp.i _let_7 _let_4)))) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.image) _let_7)) _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_4)) _let_3)))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.lift) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.lift))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_add) _let_4)) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.vectoru_add) (tptp.s _let_2 (tptp.i _let_3 _let_4)))) (tptp.s _let_2 (tptp.i _let_3 _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.lift))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_sub) _let_4)) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.vectoru_sub) (tptp.s _let_2 (tptp.i _let_3 _let_4)))) (tptp.s _let_2 (tptp.i _let_3 _let_1)))))))))))) (forall ((X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.lift))) (let ((_let_4 (tptp.s tptp.real C0))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (= (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_mul) _let_4)) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) _let_4)) (tptp.s _let_2 (tptp.i _let_3 _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s (tptp.fun tptp.real _let_2) tptp.lift))) (= (tptp.s _let_2 (tptp.i _let_3 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.vectoru_neg) (tptp.s _let_2 (tptp.i _let_3 _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s tptp.real X))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.lift) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.r_) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((Q119381 $$unsorted) (K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun Q119381 tptp.real))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.s _let_4 tptp.lift))) (let ((_let_6 (tptp.fun Q119381 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun Q119381 tptp.bool))) (let ((_let_9 (tptp.s _let_8 K0))) (let ((_let_10 (tptp.fun _let_6 _let_3))) (let ((_let_11 (tptp.fun _let_1 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (= (tptp.s _let_3 (tptp.i _let_5 (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.sum) _let_9)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.vsum) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.o) _let_5)) _let_2)))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 X))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i _let_3 _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.fun tptp.num tptp.real))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.cart tptp.real tptp.n10))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.drop) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.lambda) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) _let_3)))))) (tptp.s tptp.real (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.drop) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_sub) _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))) (forall ((X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop))) (let ((_let_4 (tptp.s tptp.real C0))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) _let_4)) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_neg) (tptp.s tptp.real (tptp.i _let_3 _let_2))))))))) (forall ((Q119533 $$unsorted) (K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun Q119533 _let_1))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.drop))) (let ((_let_6 (tptp.fun Q119533 tptp.real))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun Q119533 tptp.bool))) (let ((_let_9 (tptp.s _let_8 K0))) (let ((_let_10 (tptp.fun _let_6 tptp.real))) (let ((_let_11 (tptp.fun _let_2 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_8 tptp.bool) tptp.finite) _let_9))) (= (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_8 _let_11) tptp.vsum) _let_9)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.sum) _let_9)) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.o) _let_5)) _let_3)))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.drop) _let_2))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.drop) _let_2)))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2)) _let_4)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.real X))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.lift) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.real Y))) (let ((_let_2 (tptp.s tptp.real X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.cart tptp.real tptp.n10))) (let ((_let_5 (tptp.s (tptp.fun tptp.real _let_4) tptp.lift))) (let ((_let_6 (tptp.prod _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 _let_6))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_6 tptp.real) tptp.distance) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.c_) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (tptp.s _let_4 (tptp.i _let_5 _let_1)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.realu_sub) _let_2)) _let_1))))))))))))) (forall ((Q119643 $$unsorted) (Q119649 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (V $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q119649))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.cart tptp.real Q119643))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real tptp.n10))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (let ((_let_9 (tptp.fun _let_3 _let_1))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_2)) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_5 tptp.real) tptp.drop) (tptp.s _let_5 (tptp.i _let_7 _let_4)))))) _let_2)))))))))))))) (forall ((F0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q119649))) (let ((_let_2 (tptp.cart tptp.real Q119643))) (let ((_let_3 (tptp.fun _let_2 (tptp.cart tptp.real tptp.n10)))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) (tptp.s _let_1 V)))))))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real tptp.n10) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 F0))) (let ((_let_5 (tptp.cart _let_2 N))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun _let_5 _let_1))) (let ((_let_8 (tptp.s _let_2 X))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i _let_4 _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.drop) _let_8)))) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.column) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.matrix) _let_4)))))))))))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) (tptp.cart tptp.real tptp.n10)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.cart _let_1 tptp.n10))) (let ((_let_7 (tptp.fun tptp.num tptp.num))) (let ((_let_8 (tptp.fun _let_6 _let_1))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (= (tptp.s _let_3 (tptp.i _let_5 _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.lift) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.dot) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.row) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_7 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrix) _let_5)))))) _let_2)))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real tptp.n10))) (let ((_let_3 (tptp.s _let_2 X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.drop) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))) (forall ((Q119749 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun Q119749 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun Q119749 tptp.real))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun Q119749 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 tptp.real))) (let ((_let_10 (tptp.fun _let_2 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.vsum) _let_8)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.lift) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.sum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.o) (tptp.s _let_4 tptp.drop))) _let_3))))))))))))))))))) (=> (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.p0))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.real) tptp.drop))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_5 _let_3)))) (tptp.s tptp.real (tptp.i _let_5 _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.p0) _let_3)) _let_2)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n10))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.p0) (tptp.s _let_1 X))) (tptp.s _let_1 Y)))))))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_10 _let_11) tptp.image) (tptp.s _let_10 tptp.lift))) _let_4)) _let_7) (= (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_8 _let_9) tptp.image) (tptp.s _let_8 tptp.drop))) _let_7)) _let_4) (forall ((Q119844 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun Q119844 tptp.real))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.fun Q119844 _let_3))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun Q119844 tptp.bool))) (let ((_let_8 (tptp.s _let_7 S0))) (let ((_let_9 (tptp.fun _let_5 _let_3))) (let ((_let_10 (tptp.fun _let_1 tptp.real))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.finite) _let_8))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.sum) _let_8)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.drop) (tptp.s _let_3 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.vsum) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.o) (tptp.s _let_4 tptp.lift))) _let_2))))))))))))))))))) (forall ((Q119852 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q119852))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.cart tptp.real tptp.n10))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_3)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.lift) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.dot) _let_3)) _let_2)))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q119852))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real tptp.n10)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 A5))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.cart tptp.real tptp.n10))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) U_0) _let_1)) _let_3)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.lift) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.d_) _let_3)) _let_1)))))))))))) (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) (tptp.cart tptp.real tptp.n10)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num K0)))))))))) (forall ((Q119933 $$unsorted) (Q119935 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real (tptp.finite_sum Q119935 Q119933)) (tptp.cart tptp.real Q119935)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 tptp.fstcart)))))) (forall ((Q119985 $$unsorted) (Q119987 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real (tptp.finite_sum Q119985 Q119987)) (tptp.cart tptp.real Q119987)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 tptp.sndcart)))))) (forall ((Q120015 $$unsorted) (Q120021 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.cart tptp.real Q120021))) (let ((_let_3 (tptp.cart tptp.real (tptp.finite_sum Q120021 Q120015)))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.fstcart) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.fstcart))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_add) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.fstcart))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_5)) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.fstcart))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.fstcart))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_sub) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_sub) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((Q120217 $$unsorted) (Q120216 $$unsorted) (Q120214 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s Q120217 I0))) (let ((_let_2 (tptp.cart tptp.real (tptp.finite_sum Q120216 Q120214)))) (let ((_let_3 (tptp.fun Q120217 _let_2))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real Q120216))) (let ((_let_6 (tptp.fun Q120217 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_1)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.fstcart) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))) (forall ((K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum Q120216 Q120214)))) (let ((_let_2 (tptp.fun Q120217 _let_1))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.cart tptp.real Q120216))) (let ((_let_5 (tptp.fun Q120217 _let_4))) (let ((_let_6 (tptp.fun Q120217 tptp.bool))) (let ((_let_7 (tptp.s _let_6 K0))) (let ((_let_8 (tptp.fun _let_5 _let_4))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.finite) _let_7))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.fstcart) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.vsum) _let_7)) _let_3)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.vsum) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3)))))))))))))))))) (forall ((Q120272 $$unsorted) (Q120278 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.cart tptp.real Q120278))) (let ((_let_3 (tptp.cart tptp.real (tptp.finite_sum Q120272 Q120278)))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.sndcart) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.sndcart))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_add) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.sndcart))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_5)) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.sndcart))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) (tptp.s _let_3 (tptp.i _let_4 _let_2)))) (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.sndcart))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_sub) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_sub) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2))))))))))))) (forall ((Q120474 $$unsorted) (Q120471 $$unsorted) (Q120473 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s Q120474 I0))) (let ((_let_2 (tptp.cart tptp.real (tptp.finite_sum Q120471 Q120473)))) (let ((_let_3 (tptp.fun Q120474 _let_2))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real Q120473))) (let ((_let_6 (tptp.fun Q120474 _let_5))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)) _let_1)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.sndcart) (tptp.s _let_2 (tptp.i _let_4 _let_1)))))))))))) (forall ((K0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum Q120471 Q120473)))) (let ((_let_2 (tptp.fun Q120474 _let_1))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.cart tptp.real Q120473))) (let ((_let_5 (tptp.fun Q120474 _let_4))) (let ((_let_6 (tptp.fun Q120474 tptp.bool))) (let ((_let_7 (tptp.s _let_6 K0))) (let ((_let_8 (tptp.fun _let_5 _let_4))) (let ((_let_9 (tptp.fun _let_2 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.finite) _let_7))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.sndcart) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.vsum) _let_7)) _let_3)))) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.vsum) _let_7)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) _let_3)))))))))))))))))) (forall ((Q120489 $$unsorted) (Q120491 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.cart tptp.real (tptp.finite_sum Q120489 Q120491)))) (let ((_let_3 (tptp.cart tptp.real Q120491))) (let ((_let_4 (tptp.cart tptp.real Q120489))) (let ((_let_5 (tptp.fun _let_3 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.pastecart) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.vec) _let_1)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))) (forall ((M $$unsorted) (N $$unsorted) (X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y2))) (let ((_let_3 (tptp.s _let_1 Y1))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.s _let_5 X2))) (let ((_let_7 (tptp.s _let_5 X1))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (let ((_let_9 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.s (tptp.fun _let_5 _let_10) tptp.pastecart))) (let ((_let_12 (tptp.fun _let_9 _let_9))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.vectoru_add) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_7)) _let_3)))) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_6)) _let_2)))) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.vectoru_add) _let_7)) _let_6)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) _let_3)) _let_2)))))))))))))))))) (forall ((Q120589 $$unsorted) (Q120590 $$unsorted) (X1 $$unsorted) (Y1 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q120590))) (let ((_let_2 (tptp.s _let_1 Y1))) (let ((_let_3 (tptp.cart tptp.real Q120589))) (let ((_let_4 (tptp.s _let_3 X1))) (let ((_let_5 (tptp.cart tptp.real (tptp.finite_sum Q120589 Q120590)))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_3 _let_6) tptp.pastecart))) (let ((_let_8 (tptp.s tptp.real C0))) (let ((_let_9 (tptp.fun _let_5 _let_5))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (let ((_let_11 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.r_) _let_8)) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.r_) _let_8)) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.r_) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_3 _let_6) tptp.pastecart))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.vectoru_neg) _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.vectoru_neg) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y2))) (let ((_let_3 (tptp.s _let_1 Y1))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.s _let_5 X2))) (let ((_let_7 (tptp.s _let_5 X1))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (let ((_let_9 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.s (tptp.fun _let_5 _let_10) tptp.pastecart))) (let ((_let_12 (tptp.fun _let_9 _let_9))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_9 _let_12) tptp.vectoru_sub) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_7)) _let_3)))) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_6)) _let_2)))) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i _let_11 (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.vectoru_sub) _let_7)) _let_6)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub) _let_3)) _let_2)))))))))))))))))) (forall ((Q120760 $$unsorted) (Q120763 $$unsorted) (Q120761 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (Y $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s Q120763 I0))) (let ((_let_2 (tptp.cart tptp.real Q120761))) (let ((_let_3 (tptp.fun Q120763 _let_2))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.cart tptp.real Q120760))) (let ((_let_6 (tptp.fun Q120763 _let_5))) (let ((_let_7 (tptp.s _let_6 X))) (let ((_let_8 (tptp.cart tptp.real (tptp.finite_sum Q120760 Q120761)))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.fun Q120763 _let_8))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (= (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_6 _let_11) U_0) _let_7)) _let_4)) _let_1)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.pastecart) (tptp.s _let_5 (tptp.i _let_7 _let_1)))) (tptp.s _let_2 (tptp.i _let_4 _let_1))))))))))))))))) (forall ((K0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q120761))) (let ((_let_2 (tptp.fun Q120763 _let_1))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.cart tptp.real Q120760))) (let ((_let_5 (tptp.fun Q120763 _let_4))) (let ((_let_6 (tptp.s _let_5 X))) (let ((_let_7 (tptp.cart tptp.real (tptp.finite_sum Q120760 Q120761)))) (let ((_let_8 (tptp.fun Q120763 _let_7))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (let ((_let_10 (tptp.fun Q120763 tptp.bool))) (let ((_let_11 (tptp.s _let_10 K0))) (let ((_let_12 (tptp.fun _let_8 _let_7))) (let ((_let_13 (tptp.fun _let_2 _let_1))) (let ((_let_14 (tptp.fun _let_5 _let_4))) (let ((_let_15 (tptp.fun _let_1 _let_7))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_10 tptp.bool) tptp.finite) _let_11))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_4 _let_15) tptp.pastecart) (tptp.s _let_4 (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_10 _let_14) tptp.vsum) _let_11)) _let_6)))) (tptp.s _let_1 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_10 _let_13) tptp.vsum) _let_11)) _let_3)))) (tptp.s _let_7 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.vsum) _let_11)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) U_0) _let_6)) _let_3)))))))))))))))))))))))) (forall ((Q120795 $$unsorted) (Q120800 $$unsorted) (X $$unsorted) (Y $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num N0))) (let ((_let_2 (tptp.cart tptp.real Q120800))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.cart tptp.real Q120795))) (let ((_let_5 (tptp.s _let_4 X))) (let ((_let_6 (tptp.cart tptp.real (tptp.finite_sum Q120795 Q120800)))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (= (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.pastecart) _let_5)) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) _let_1))) (and (= _let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.vec) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))))))) (forall ((Q120851 $$unsorted) (Q120849 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum Q120851 Q120849)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q120851))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.fstcart) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))))))))) (forall ((Q120883 $$unsorted) (Q120881 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum Q120883 Q120881)))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.cart tptp.real Q120883))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.fstcart))) (let ((_let_8 (tptp.prod _let_6 _let_6))) (let ((_let_9 (tptp.fun _let_6 _let_8))) (let ((_let_10 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_8 tptp.real) tptp.distance) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.c_) (tptp.s _let_6 (tptp.i _let_7 _let_3)))) (tptp.s _let_6 (tptp.i _let_7 _let_2)))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2)))))))))))))))))) (forall ((Q120961 $$unsorted) (Q120963 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum Q120961 Q120963)))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q120963))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.sndcart) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))))))))) (forall ((Q120993 $$unsorted) (Q120995 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum Q120993 Q120995)))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.cart tptp.real Q120995))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.sndcart))) (let ((_let_8 (tptp.prod _let_6 _let_6))) (let ((_let_9 (tptp.fun _let_6 _let_8))) (let ((_let_10 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_8 tptp.real) tptp.distance) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_6 _let_9) tptp.c_) (tptp.s _let_6 (tptp.i _let_7 _let_3)))) (tptp.s _let_6 (tptp.i _let_7 _let_2)))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2)))))))))))))))))) (forall ((Q121075 $$unsorted) (Q121076 $$unsorted) (X1 $$unsorted) (X2 $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121076))) (let ((_let_2 (tptp.s _let_1 Y2))) (let ((_let_3 (tptp.s _let_1 X2))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.cart tptp.real Q121075))) (let ((_let_6 (tptp.s _let_5 Y1))) (let ((_let_7 (tptp.s _let_5 X1))) (let ((_let_8 (tptp.fun _let_5 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.cart tptp.real (tptp.finite_sum Q121075 Q121076)))) (let ((_let_11 (tptp.fun _let_1 _let_10))) (let ((_let_12 (tptp.s (tptp.fun _let_5 _let_11) tptp.pastecart))) (let ((_let_13 (tptp.fun _let_10 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_10 _let_13) tptp.dot) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_7)) _let_3)))) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_6)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.dot) _let_7)) _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.dot) _let_3)) _let_2))))))))))))))))))) (forall ((Q121103 $$unsorted) (Q121104 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_3 (tptp.cart tptp.real Q121104))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_pow))) (let ((_let_7 (tptp.cart tptp.real Q121103))) (let ((_let_8 (tptp.s _let_7 X))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.cart tptp.real (tptp.finite_sum Q121103 Q121104)))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_10 tptp.real) tptp.vectoru_norm) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) tptp.pastecart) _let_8)) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 tptp.sqrt) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_7 tptp.real) tptp.vectoru_norm) _let_8)))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) _let_4)))) _let_2))))))))))))))))))) (forall ((Q121142 $$unsorted) (Q121143 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121143))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q121142))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.cart tptp.real (tptp.finite_sum Q121142 Q121143)))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_6 tptp.real) tptp.vectoru_norm) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.pastecart) _let_4)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_5 tptp.real) tptp.vectoru_norm) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.pastecart) _let_4)) _let_2)))))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_le))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) _let_4)))) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))) _let_7)))))))))))))) (forall ((Q121218 $$unsorted) (Q121215 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121215))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q121218))) (let ((_let_4 (tptp.cart tptp.real (tptp.finite_sum Q121215 Q121218)))) (let ((_let_5 (tptp.fun _let_3 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.vectoru_norm) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.pastecart) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))) (forall ((Q121236 $$unsorted) (Q121234 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121234))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real Q121236))) (let ((_let_4 (tptp.cart tptp.real (tptp.finite_sum Q121236 Q121234)))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.vectoru_norm) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.pastecart) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))) (forall ((Q121280 $$unsorted) (Q121279 $$unsorted) (X $$unsorted) (XI_ $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121279))) (let ((_let_2 (tptp.s _let_1 XI_))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.cart tptp.real Q121280))) (let ((_let_7 (tptp.s _let_6 Y))) (let ((_let_8 (tptp.cart tptp.real (tptp.finite_sum Q121279 Q121280)))) (let ((_let_9 (tptp.fun _let_6 _let_8))) (let ((_let_10 (tptp.s (tptp.fun _let_1 _let_9) tptp.pastecart))) (let ((_let_11 (tptp.prod _let_8 _let_8))) (let ((_let_12 (tptp.fun _let_8 _let_11))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_11 tptp.real) tptp.distance) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_8 _let_12) tptp.c_) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) _let_7)))) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_2)) _let_7)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2)))))))))))))))))) (forall ((Q121316 $$unsorted) (Q121317 $$unsorted) (X $$unsorted) (Y $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121317))) (let ((_let_2 (tptp.s _let_1 YI_))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.cart tptp.real Q121316))) (let ((_let_7 (tptp.cart tptp.real (tptp.finite_sum Q121316 Q121317)))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.pastecart) (tptp.s _let_6 X))))) (let ((_let_10 (tptp.prod _let_7 _let_7))) (let ((_let_11 (tptp.fun _let_7 _let_10))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_10 tptp.real) tptp.distance) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) tptp.c_) (tptp.s _let_7 (tptp.i _let_9 _let_3)))) (tptp.s _let_7 (tptp.i _let_9 _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2))))))))))))))))) (forall ((Q121390 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121390))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.subspace) _let_3))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121390))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_5)) _let_4)))) _let_3))))))))))))) (forall ((C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121390))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real C0))) _let_4)))) _let_3))))))))))))))))))) (forall ((Q121402 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q121402) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.span) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.hull) (tptp.s _let_3 tptp.subspace))) _let_2)))))))) (forall ((Q121420 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q121420) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.dependent) (tptp.s _let_1 S0)))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121420))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) _let_2)))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.delete) _let_4)) _let_2))))))))))))))))))) (forall ((Q121430 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q121430) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.independent) _let_2))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.dependent) _let_2))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 tptp.univ)))))) (forall ((Q121443 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q121443) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) _let_2))) (not (= _let_2 (tptp.s _let_1 tptp.empty))))))) (forall ((Q121453 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121453))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.s0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.subspace) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3))))))))) (forall ((Q121494 $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121494))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.subspace) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_5)) _let_4)))) _let_3))))))))))))) (forall ((Q121516 $$unsorted) (X $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121516))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.subspace) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real C0))) _let_4)))) _let_3)))))))))))) (forall ((Q121570 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121570))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.subspace) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_4)))) _let_3))))))))))) (forall ((Q121609 $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121609))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.subspace) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_sub) _let_5)) _let_4)))) _let_3))))))))))))) (forall ((Q121648 $$unsorted) (Q121655 $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121655))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun Q121648 _let_1))) (let ((_let_5 (tptp.fun Q121648 tptp.bool))) (let ((_let_6 (tptp.s _let_5 T0))) (let ((_let_7 (tptp.fun _let_4 _let_1))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 tptp.subspace) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.finite) _let_6))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121655))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s Q121648 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun Q121648 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q121648 _let_6) tptp.in) _let_3)) (tptp.s _let_5 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q121648 _let_1) F0) _let_3)))) (tptp.s _let_2 S0))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.vsum) _let_6)) (tptp.s _let_4 F0))))) _let_3))))))))))))) (forall ((Q121671 $$unsorted) (Q121673 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121673))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real Q121671))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.subspace) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.subspace) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))))))))))))) (forall ((Q121694 $$unsorted) (Q121697 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (S0 $$unsorted) (GENR_PVARR_297 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121694))) (let ((_let_2 (tptp.cart tptp.real Q121697))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 F0))) (tptp.s _let_3 S0))) (tptp.s _let_1 GENR_PVARR_297)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121694))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q121697))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.setspec) (tptp.s _let_1 GENR_PVARR_297))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.in) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))) (tptp.s _let_4 S0))))) _let_2))))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121697))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real Q121694))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.subspace) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.subspace) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.gspec) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) _let_6)) _let_3))))))))))))))))))) (forall ((Q121723 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q121723))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.subspace) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.insert) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_2 tptp.empty)))))))))) (forall ((Q121741 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q121741) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.inter) _let_3)) _let_2)))))))))))) (forall ((Q121764 $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q121764) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q121764) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.subspace) _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 tptp.subspace) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.inters) (tptp.s _let_2 F0)))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 (tptp.cart tptp.real N)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) (tptp.s _let_3 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.subspace) (tptp.s _let_2 S0))))) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (= _let_3 _let_2)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.in) _let_3)) (tptp.s _let_5 S0)))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) F0) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.vec) _let_1)))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s _let_1 T0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s _let_4 tptp.subspace))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.union) _let_2)) _let_3)))))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))) (forall ((Q121985 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q121985) tptp.bool))) (let ((_let_2 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (let ((_let_3 (tptp.s _let_1 (tptp.i _let_2 (tptp.s _let_1 S0))))) (= (tptp.s _let_1 (tptp.i _let_2 _let_3)) _let_3))))) (forall ((Q122006 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122006) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.subset))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i _let_3 _let_4)))) (tptp.s _let_1 (tptp.i _let_3 _let_2))))))))))))) (forall ((Q122015 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122015) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) (tptp.s _let_1 S0)))))))) (forall ((Q122036 $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122036))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 A5))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)))))))))))) (forall ((Q122045 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122045))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 tptp.s0)))))))))) (forall ((Q122111 $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122111))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_5)) _let_4)))) _let_3))))))))))))) (forall ((Q122108 $$unsorted) (X $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122108))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real C0))) _let_4)))) _let_3)))))))))))) (forall ((Q122152 $$unsorted) (S0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122152) tptp.bool))) (=> (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122152))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.in) (tptp.s _let_1 X))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 (tptp.s _let_2 H0)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 H0))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122152))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 H0) _let_2)))))))))))) (forall ((Q122165 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122165))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.empty))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_4 tptp.span) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3)))))))) (forall ((Q122169 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122169) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.independent) (tptp.s _let_1 tptp.empty)))))) (forall ((Q122179 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122179))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_3))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3)))))))))) (forall ((Q122205 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122205) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.independent))) (let ((_let_5 (tptp.s _let_1 T0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.dependent))) (let ((_let_5 (tptp.s _let_1 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_5)) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))) (forall ((Q122268 $$unsorted) (B0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122268) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_3)))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.subspace) _let_2)))) (= _let_4 _let_2))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) H0) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (forall ((C0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 H0))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.in) _let_3)) (tptp.s _let_5 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.r_) (tptp.s tptp.real C0))) _let_3)))) _let_2))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 H0) _let_2)))))))))))) (forall ((Q122358 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122358))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.s0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 X))))) (=> (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)))))))))))) (forall ((Q122368 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122368) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2))))))))) (forall ((Q122389 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122389) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.union))) (let ((_let_6 (tptp.s _let_4 tptp.span))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.subset) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i _let_6 _let_3)))) (tptp.s _let_1 (tptp.i _let_6 _let_2)))))) (tptp.s _let_1 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))))))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 tptp.univ))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2)) _let_2)))) (forall ((Q122419 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122419))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 tptp.s0)))))))))) (forall ((Q122457 $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122457))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_5)) _let_4)))) _let_3))))))))))))) (forall ((Q122488 $$unsorted) (X $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122488))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real C0))) _let_4)))) _let_3)))))))))))) (forall ((N $$unsorted) (X $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (let ((_let_7 (tptp.s tptp.real C0))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (=> (not (= _let_7 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) _let_7)) _let_4)))) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))))))))))))) (forall ((Q122563 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122563))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_4)))) _let_3))))))))))) (forall ((Q122592 $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122592))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_4)))) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3)))))))))) (forall ((Q122633 $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122633))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_sub) _let_5)) _let_4)))) _let_3))))))))))))) (forall ((Q122668 $$unsorted) (Q122679 $$unsorted) (S0 $$unsorted) (F0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122679))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun Q122668 _let_1))) (let ((_let_4 (tptp.fun Q122668 tptp.bool))) (let ((_let_5 (tptp.s _let_4 T0))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.finite) _let_5))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122679))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s Q122668 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun Q122668 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun Q122668 _let_6) tptp.in) _let_3)) (tptp.s _let_5 T0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun Q122668 _let_1) F0) _let_3)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)) (tptp.s _let_3 F0))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))))))))))))) (forall ((Q122739 $$unsorted) (S0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122739))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (let ((_let_7 (tptp.s _let_1 X))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_3))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.vectoru_add) _let_7)) _let_4)))) _let_3)) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))))))))))))) (forall ((Q122754 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122754) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (= (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2)) _let_2) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) _let_2))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.subspace) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_3)))) _let_2)))))))))) (forall ((Q122839 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122839))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vectoru_add) _let_3)) _let_2))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122839))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 A5))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.subspace) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.in) _let_4)) _let_3)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.image) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_4)))) _let_3)) _let_3)))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vectoru_add) _let_3)) _let_2))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 A5))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.subspace) _let_3))) (= (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.image) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) U_0) _let_4)))) _let_3)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_4)) _let_3))))))))))))))) (forall ((Q122994 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_298 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122994))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_298)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q122994))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.in))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) (tptp.s _let_6 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) (tptp.s _let_6 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.setspec) (tptp.s _let_1 GENR_PVARR_298))) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) _let_3)) _let_2))))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q122994) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_3)) _let_2)))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_299 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_299)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.s (tptp.fun _let_6 _let_6) tptp.span))) (let ((_let_9 (tptp.fun _let_6 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_1 _let_9) tptp.in))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_3)) (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_6 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_2)) (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_6 T0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.setspec) (tptp.s _let_1 GENR_PVARR_299))) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) _let_3)) _let_2)))))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.span) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.union) _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_0) _let_3)) _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (= (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.span) (tptp.s _let_7 (tptp.i _let_9 _let_3)))) (tptp.s _let_7 (tptp.i _let_9 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.dependent) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.dependent) _let_3))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (= _let_3 _let_2)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.dependent) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.dependent) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.independent) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.independent) _let_3))))))))))))) (forall ((N $$unsorted) (B0 $$unsorted) (S0 $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 B0))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 A5))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)))))) (exists ((K0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.vectoru_sub) (tptp.s _let_1 A5))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real K0))) _let_2)))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.delete) (tptp.s _let_3 S0))) _let_2))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 tptp.x))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.span) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.insert) (tptp.s _let_1 A5))) (tptp.s _let_2 S0)))))))) (exists ((K0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_sub) (tptp.s _let_1 tptp.x))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) (tptp.s tptp.real K0))) (tptp.s _let_1 A5))))))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 S0))))))))))))))))) (forall ((Q123623 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123623))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s _let_4 tptp.span))) (= (tptp.s _let_2 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3)))) (tptp.s _let_2 (tptp.i _let_5 _let_3))))))))) (forall ((Q123656 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_301 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123656))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 A5))) (tptp.s _let_1 GENR_PVARR_301)))) (exists ((U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123656))) (let ((_let_2 (tptp.s tptp.real U))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.setspec) (tptp.s _let_1 GENR_PVARR_301))) (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.in) _let_2)) (tptp.s _let_4 tptp.univ))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) _let_2)) (tptp.s _let_1 A5)))))))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123656))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.span) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) _let_2)) (tptp.s _let_3 tptp.empty))))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))) (forall ((Q123742 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (GENR_PVARR_302 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123742))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) (tptp.s _let_1 A5))) (tptp.s _let_1 B0))) (tptp.s _let_1 GENR_PVARR_302)))) (exists ((U $$unsorted) (V $$unsorted) (V0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123742))) (let ((_let_2 (tptp.s tptp.real V))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.r_))) (let ((_let_5 (tptp.s tptp.real U))) (let ((_let_6 (tptp.s tptp.bool V0))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool _let_7))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (let ((_let_10 (tptp.s _let_9 tptp.univ))) (let ((_let_11 (tptp.fun _let_9 tptp.bool))) (let ((_let_12 (tptp.s (tptp.fun tptp.real _let_11) tptp.in))) (and (= (tptp.p _let_6) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_5)) _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_2)) _let_10))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.setspec) (tptp.s _let_1 GENR_PVARR_302))) _let_6)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s _let_1 A5))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_1 B0))))))))))))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123742))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.insert))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_6 tptp.span) (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s _let_4 tptp.empty))))))) (tptp.s _let_4 (tptp.i (tptp.s _let_6 tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_3)) _let_2))))))))))))))) (forall ((Q123857 $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (GENR_PVARR_303 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123857))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) (tptp.s _let_1 A5))) (tptp.s _let_1 B0))) (tptp.s _let_1 C0))) (tptp.s _let_1 GENR_PVARR_303)))) (exists ((U $$unsorted) (V $$unsorted) (W $$unsorted) (V0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123857))) (let ((_let_2 (tptp.s tptp.real W))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s (tptp.fun tptp.real _let_3) tptp.r_))) (let ((_let_5 (tptp.s tptp.real V))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add))) (let ((_let_7 (tptp.s tptp.real U))) (let ((_let_8 (tptp.s tptp.bool V0))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.fun tptp.bool _let_9))) (let ((_let_11 (tptp.fun tptp.real tptp.bool))) (let ((_let_12 (tptp.s _let_11 tptp.univ))) (let ((_let_13 (tptp.fun _let_11 tptp.bool))) (let ((_let_14 (tptp.s (tptp.fun tptp.real _let_13) tptp.in))) (and (= (tptp.p _let_8) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 _let_7)) _let_12))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 _let_5)) _let_12))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 _let_2)) _let_12))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_1 _let_10) tptp.setspec) (tptp.s _let_1 GENR_PVARR_303))) _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_7)) (tptp.s _let_1 A5))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_5)) (tptp.s _let_1 B0))))) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s _let_1 C0)))))))))))))))))))))))))))))))) (forall ((A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q123857))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.s _let_1 A5))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.insert))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_8 tptp.span) (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_4)) (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) (tptp.s _let_5 tptp.empty))))))))) (tptp.s _let_5 (tptp.i (tptp.s _let_8 tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) U_0) _let_4)) _let_3)) _let_2))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 A5))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.insert))) (let ((_let_7 (tptp.s _let_5 tptp.span))) (let ((_let_8 (tptp.s _let_1 B0))) (let ((_let_9 (tptp.fun _let_2 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_1 _let_9) tptp.in))) (let ((_let_11 (tptp.s _let_9 (tptp.i _let_10 _let_4)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_11 (tptp.s _let_2 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_8)) _let_3))))))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_11 (tptp.s _let_2 (tptp.i _let_7 _let_3))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_8)) (tptp.s _let_2 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3)))))))))))))))))))) (forall ((Q124006 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q124006))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_1 _let_3))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.delete) _let_4)) _let_2)))) (let ((_let_7 (tptp.s _let_1 A5))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (let ((_let_9 (tptp.s _let_8 tptp.span))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun _let_1 _let_10) tptp.in))) (let ((_let_12 (tptp.s _let_10 (tptp.i _let_11 _let_7)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_12 (tptp.s _let_3 (tptp.i _let_9 _let_4))))) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_12 (tptp.s _let_3 (tptp.i _let_9 _let_6))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_2)) (tptp.s _let_3 (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.insert) _let_7)) _let_6))))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.insert))) (let ((_let_7 (tptp.s _let_5 tptp.span))) (let ((_let_8 (tptp.s _let_1 X))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_1 _let_10) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.vectoru_sub) _let_8)) _let_4)))) (tptp.s _let_2 (tptp.i _let_7 _let_3))))) (= (tptp.s _let_2 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_8)) _let_3)))) (tptp.s _let_2 (tptp.i _let_7 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_3))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s _let_4 tptp.span))) (let ((_let_6 (tptp.s _let_2 (tptp.i _let_5 _let_3)))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.in))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 Y))))) (let ((_let_10 (tptp.s _let_1 X))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_10)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 (tptp.s _let_2 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) _let_10)) _let_3)))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_6))))))))))))))) (forall ((N $$unsorted) (U_1 $$unsorted)) (=> (forall ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_2))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((P0 $$unsorted) (GENR_PVARR_304 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 P0))) (tptp.s _let_1 GENR_PVARR_304)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (exists ((S0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.subset) _let_5)) (tptp.s _let_4 P0)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_1) (tptp.s _let_2 U))))) (tptp.s _let_1 Y)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_304))) _let_2)) (tptp.s _let_1 Y)))))))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 P0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.span) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_3 U_0) _let_2))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_2))))))))) (forall ((P0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.dependent) (tptp.s _let_1 P0)))) (exists ((S0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s _let_4 S0))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.finite) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.subset) _let_5)) (tptp.s _let_4 P0)))) (exists ((V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (not (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) U) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.vsum) _let_5)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 U))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_2))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.dependent) _let_2))) (exists ((U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (and (exists ((V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (not (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) U) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.vsum) (tptp.s _let_4 S0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 U))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))))))) (forall ((N $$unsorted) (U_1 $$unsorted)) (=> (forall ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 U))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_1) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_2))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_307 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_307)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (exists ((U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.vsum) (tptp.s _let_4 S0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_1) (tptp.s _let_2 U))))) (tptp.s _let_1 Y))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_307))) _let_2)) (tptp.s _let_1 Y)))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.span) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_3 U_0) _let_2)))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (forall ((GENR_PVARR_308 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 GENR_PVARR_308)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.setspec) (tptp.s _let_2 GENR_PVARR_308))) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1))))))))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.span) (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.gspec) (tptp.s _let_1 U_0))))) (tptp.s _let_1 tptp.univ)))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (forall ((GENR_PVARR_311 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 GENR_PVARR_311)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.setspec) (tptp.s _let_2 GENR_PVARR_311))) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.hasu_size) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 U_0))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (forall ((GENR_PVARR_312 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 GENR_PVARR_312)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.setspec) (tptp.s _let_2 GENR_PVARR_312))) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 U_0))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (forall ((GENR_PVARR_313 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 GENR_PVARR_313)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.setspec) (tptp.s _let_2 GENR_PVARR_313))) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1))))))))))))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 U_0))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))) (forall ((N $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.bool))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.in) (tptp.s _let_2 X))) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.span) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.image) (tptp.s _let_3 tptp.basis))) (tptp.s _let_1 S0)))))))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.num I0))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.fun N tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_10 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_10 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dimindex) (tptp.s _let_9 tptp.univ)))))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.in) _let_5)) (tptp.s _let_7 S0)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_6 _let_4) tptp.d_) (tptp.s _let_6 X))) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (forall ((GENR_PVARR_318 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_0) (tptp.s _let_1 GENR_PVARR_318)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.setspec) (tptp.s _let_2 GENR_PVARR_318))) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.independent) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 U_0))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (S0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (let ((_let_6 (tptp.s _let_5 tptp.independent))) (let ((_let_7 (tptp.s tptp.bool (tptp.i _let_6 _let_4)))) (let ((_let_8 (tptp.s _let_2 A5))) (let ((_let_9 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_8)))) (let ((_let_10 (tptp.fun tptp.bool tptp.bool))) (let ((_let_11 (tptp.fun tptp.bool _let_10))) (let ((_let_12 (tptp.fun _let_3 _let_3))) (and (= (tptp.p _let_1) (and (tptp.p _let_7) (not (tptp.p (tptp.s tptp.bool (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_12 tptp.span) _let_4)))))))) (= (tptp.s tptp.bool (tptp.i _let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_2 _let_12) tptp.insert) _let_8)) _let_4)))) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.bool _let_11) tptp.cond) (tptp.s tptp.bool (tptp.i _let_9 _let_4)))) _let_7)) _let_1)))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2)))))) (= _let_3 _let_2)))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s _let_1 S0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2)))))) (exists ((TI_ $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 TI_))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.subset))) (let ((_let_7 (tptp.s _let_5 (tptp.i _let_6 _let_4)))) (let ((_let_8 (tptp.s _let_1 T0))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.hasu_size) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_8))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.union) _let_4)) _let_8))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_7 (tptp.s _let_1 (tptp.i (tptp.s _let_3 tptp.span) _let_2)))))))))))))))))))))) (forall ((Q125545 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q125545) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.card))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s _let_6 tptp.finite))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.independent) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2)))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_7 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.independent) _let_3))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.card) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.g_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.dependent) _let_2)))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.independent) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2)))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 C0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_2))))))))) (forall ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.independent) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (forall ((C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (=> (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.vsum) (tptp.s _let_4 B0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 C0))))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 B0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) C0) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))))))))))))) (forall ((Q125680 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q125680))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.independent) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) _let_2)) (tptp.s _let_3 tptp.empty)))))) (not (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))) (forall ((Q125698 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q125698))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.dependent) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) _let_2)) (tptp.s _let_3 tptp.empty)))))) (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (exists ((V $$unsorted)) (and (= (tptp.p (tptp.s tptp.bool V)) (exists ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_5 _let_5))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.r_))) (and (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.vectoru_add) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) (tptp.s _let_5 A5))))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s _let_5 B0))))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.vec) _let_1))) (not (and (= _let_4 _let_2) (= _let_3 _let_2))))))))))))) (exists ((VI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (and (= (tptp.p (tptp.s tptp.bool VI_)) (= (tptp.s _let_1 A5) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (exists ((VI_I_ $$unsorted)) (let ((_let_1 (tptp.s tptp.bool VI_I_))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.bool _let_2))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.s _let_4 B0))) (let ((_let_7 (tptp.fun _let_5 _let_5))) (let ((_let_8 (tptp.s (tptp.fun _let_4 _let_7) tptp.insert))) (let ((_let_9 (tptp.s _let_4 A5))) (and (= (tptp.p _let_1) (= _let_9 _let_6)) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.dependent) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_9)) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) (tptp.s _let_5 tptp.empty))))))) (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.bool _let_3) tptp.cond) _let_1)) (tptp.s tptp.bool VI_))) (tptp.s tptp.bool V))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 C0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_1 B0))) (let ((_let_7 (tptp.s _let_1 A5))) (=> (and (not (= _let_7 _let_6)) (not (= _let_7 _let_3)) (not (= _let_6 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.dependent) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_2 tptp.empty)))))))))) (exists ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (let ((_let_3 (tptp.s tptp.real Z0))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.fun _let_6 _let_6))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.r_))) (let ((_let_9 (tptp.s (tptp.fun _let_6 _let_7) tptp.vectoru_add))) (and (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) (tptp.s _let_6 A5))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_9 (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) (tptp.s _let_6 B0))))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) (tptp.s _let_6 C0))))))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) _let_1))) (not (and (= _let_5 _let_2) (= _let_4 _let_2) (= _let_3 _let_2)))))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (let ((_let_3 (tptp.s tptp.real Y))) (let ((_let_4 (tptp.s tptp.real X))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.s _let_5 B0))) (let ((_let_7 (tptp.fun _let_5 _let_5))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.r_))) (let ((_let_9 (tptp.s _let_5 A5))) (let ((_let_10 (tptp.fun _let_5 tptp.bool))) (let ((_let_11 (tptp.fun _let_10 _let_10))) (let ((_let_12 (tptp.s (tptp.fun _let_5 _let_11) tptp.insert))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_10 tptp.bool) tptp.independent) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_9)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_6)) (tptp.s _let_10 tptp.empty)))))))) (not (= _let_9 _let_6))) (= (= (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.vectoru_add) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_4)) _let_9)))) (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) _let_6)))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.vec) _let_1))) (and (= _let_4 _let_2) (= _let_3 _let_2))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (let ((_let_3 (tptp.s tptp.real Z0))) (let ((_let_4 (tptp.s tptp.real Y))) (let ((_let_5 (tptp.s tptp.real X))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.s _let_6 C0))) (let ((_let_8 (tptp.fun _let_6 _let_6))) (let ((_let_9 (tptp.s (tptp.fun tptp.real _let_8) tptp.r_))) (let ((_let_10 (tptp.s _let_6 B0))) (let ((_let_11 (tptp.s (tptp.fun _let_6 _let_8) tptp.vectoru_add))) (let ((_let_12 (tptp.s _let_6 A5))) (let ((_let_13 (tptp.fun _let_6 tptp.bool))) (let ((_let_14 (tptp.fun _let_13 _let_13))) (let ((_let_15 (tptp.s (tptp.fun _let_6 _let_14) tptp.insert))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_13 tptp.bool) tptp.independent) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i _let_15 _let_12)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i _let_15 _let_10)) (tptp.s _let_13 (tptp.i (tptp.s _let_14 (tptp.i _let_15 _let_7)) (tptp.s _let_13 tptp.empty)))))))))) (not (= _let_12 _let_10)) (not (= _let_12 _let_7)) (not (= _let_10 _let_7))) (= (= (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i _let_11 (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_12)))) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i _let_11 (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_4)) _let_10)))) (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_7)))))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) _let_1))) (and (= _let_5 _let_2) (= _let_4 _let_2) (= _let_3 _let_2)))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) (tptp.s _let_1 V)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.independent) _let_2)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 S0))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2))))))))))))))))) (forall ((N $$unsorted) (V $$unsorted)) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (GENR_PVARR_319 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_319)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.cart tptp.real (tptp.finite_sum M N)))) (let ((_let_5 (tptp.fun _let_3 _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (let ((_let_9 (tptp.fun tptp.bool _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.setspec) (tptp.s _let_4 GENR_PVARR_319))) (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.in) _let_2)) (tptp.s _let_6 tptp.univ))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.pastecart) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))))))))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_2 (tptp.s _let_1 F0))) (let ((_let_3 (tptp.fun (tptp.cart tptp.real (tptp.finite_sum M N)) tptp.bool))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.subspace) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))))) (forall ((Q126331 $$unsorted) (U_0 $$unsorted)) (=> (forall ((V $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126331) tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 V))) (tptp.s tptp.num N0)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126331) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s _let_1 V))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.subset))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.independent) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.hasu_size) _let_2)) (tptp.s tptp.num N0)))))))))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126331) tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.h_) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))) (forall ((Q126364 $$unsorted) (V $$unsorted)) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126364) tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.subset))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.hasu_size) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2)))))))))))))) (forall ((Q126398 $$unsorted) (V $$unsorted)) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126398) tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.subset))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.hasu_size) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2)))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 S0)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.subset) _let_3)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.independent) _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_3)) _let_2) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.hasu_size) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2))))))))))))))) (forall ((N $$unsorted) (V $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.s _let_1 B0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.independent) _let_4)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.card) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.dim) _let_2)))))))))))))) (forall ((N $$unsorted) (V $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.s _let_1 V))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.finite) _let_2)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.dim) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.card) _let_2))))))))))))) (forall ((Q126529 $$unsorted) (V $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126529) tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.s _let_1 B0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.independent) _let_4)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_4))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.card) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.dim) _let_2)))))))))))) (forall ((Q126544 $$unsorted) (V $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126544) tptp.bool))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.independent) _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_3)) _let_2)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.hasu_size) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2))))))))))) (forall ((Q126589 $$unsorted) (V $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.n))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real Q126589) tptp.bool))) (let ((_let_3 (tptp.s _let_2 V))) (let ((_let_4 (tptp.s _let_2 B0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_6) tptp.subset))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.independent) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.hasu_size) _let_4)) _let_1)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) _let_3)) _let_1)))))))))) (forall ((Q126603 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126603) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.dim) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.card) _let_2))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) (tptp.s _let_2 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) (tptp.s _let_2 S0))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))) (forall ((N $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.independent) _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)) (tptp.s _let_2 tptp.univ))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.hasu_size) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))))) (forall ((N $$unsorted) (V $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.fun _let_1 tptp.num))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.dim) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s _let_6 tptp.card) _let_2)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2)))))))))))))) (forall ((N $$unsorted) (V $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_1 V))) (let ((_let_5 (tptp.fun _let_1 tptp.num))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.card) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.dim) _let_4)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.independent) _let_2))))))))))) (forall ((Q126884 $$unsorted) (V $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q126884) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.subset))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.hasu_size) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_3)))))) (= (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_2)) (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.independent) _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.card) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.dim) _let_2))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 tptp.num))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.g_) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.card) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.dim) _let_2)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.dependent) _let_2)))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (= (tptp.s tptp.num (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.insert) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3)))) (tptp.s tptp.num (tptp.i _let_4 _let_3))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.num))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.independent) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.dim) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.card) _let_2)))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.subset) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))) (forall ((Q127017 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q127017) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (=> (= (tptp.s _let_1 (tptp.i _let_5 _let_4)) (tptp.s _let_1 (tptp.i _let_5 _let_2))) (= (tptp.s tptp.num (tptp.i _let_3 _let_4)) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))) (forall ((Q127058 $$unsorted) (Q127043 $$unsorted) (F0 $$unsorted) (B0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q127043))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.cart tptp.real Q127058))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)))) (let ((_let_10 (tptp.s _let_2 V))) (let ((_let_11 (tptp.fun _let_7 tptp.bool))) (let ((_let_12 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_2 _let_12) tptp.subset) _let_10)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) tptp.subset) (tptp.s _let_7 (tptp.i _let_9 _let_10)))) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.span) (tptp.s _let_7 (tptp.i _let_9 _let_3))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dim) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) _let_3)))))))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) (tptp.s _let_1 tptp.empty))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (forall ((N $$unsorted) (X $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (let ((_let_5 (tptp.s (tptp.fun _let_3 tptp.num) tptp.dim))) (let ((_let_6 (tptp.s tptp.num (tptp.i _let_5 _let_4)))) (let ((_let_7 (tptp.fun tptp.num _let_1))) (let ((_let_8 (tptp.fun _let_3 _let_3))) (let ((_let_9 (tptp.s _let_2 X))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (= (tptp.s tptp.num (tptp.i _let_5 (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.insert) _let_9)) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.cond) (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) tptp.in) _let_9)) (tptp.s _let_3 (tptp.i (tptp.s _let_8 tptp.span) _let_4)))))) _let_6)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s _let_7 tptp.p_) _let_6)) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))))))) (forall ((Q127174 $$unsorted) (X $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 _let_1)))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun tptp.num _let_2))) (let ((_let_7 (tptp.cart tptp.real Q127174))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.s _let_7 X))) (let ((_let_10 (tptp.fun _let_8 _let_8))) (and (= (tptp.p _let_5) (= _let_9 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.vec) _let_4)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dim) (tptp.s _let_8 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.insert) _let_9)) (tptp.s _let_8 tptp.empty))))) (tptp.s tptp.num (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.bool _let_6) tptp.cond) _let_5)) _let_4)) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s _let_2 S0))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) _let_5)) _let_3) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.subset) _let_5)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) _let_3)))) (tptp.s _let_2 tptp.empty)))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_7 tptp.bool))) (let ((_let_10 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) tptp.subset) (tptp.s _let_2 tptp.univ))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) (tptp.s _let_2 X))) (tptp.s _let_1 Y))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_7 _let_9) tptp.subset) (tptp.s _let_7 tptp.univ))) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_7 _let_7) tptp.span) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.span) (tptp.s _let_6 S0))))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (= _let_3 _let_2))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.independent) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.independent) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))))))))))))) (forall ((N $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_2)))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_sub) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_div) (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_2)))))) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((N $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 B0)))) (exists ((C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 C0))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s _let_2 B0))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_2) tptp.span))) (let ((_let_8 (tptp.s (tptp.fun _let_2 tptp.num) tptp.card))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_8 _let_3)))) (tptp.s tptp.num (tptp.i _let_8 _let_6))))) (= (tptp.s _let_2 (tptp.i _let_7 _let_3)) (tptp.s _let_2 (tptp.i _let_7 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.pairwise) (tptp.s _let_4 tptp.orthogonal))) _let_3))))))))))))))))) (forall ((N $$unsorted) (V $$unsorted)) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.s _let_2 V))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_2 _let_2) tptp.span))) (let ((_let_9 (tptp.s (tptp.fun _let_2 _let_5) tptp.subset))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_9 _let_3)) (tptp.s _let_2 (tptp.i _let_8 _let_6))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_9 _let_6)) (tptp.s _let_2 (tptp.i _let_8 _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.hasu_size) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) _let_6))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.pairwise) (tptp.s _let_4 tptp.orthogonal))) _let_3))))))))))))))) (forall ((Q127738 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q127738) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (let ((_let_4 (tptp.s _let_1 (tptp.i _let_3 _let_2)))) (let ((_let_5 (tptp.s _let_1 T0))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.subset))) (let ((_let_8 (tptp.s _let_1 (tptp.i _let_3 _let_5)))) (= (= _let_4 _let_8) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_8))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_4)))))))))))))) (forall ((Q127771 $$unsorted) (S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q127771))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s _let_4 tptp.span))) (let ((_let_6 (tptp.s _let_2 (tptp.i _let_5 _let_3)))) (let ((_let_7 (tptp.s _let_1 X))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (= (= (tptp.s _let_2 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) _let_7)) _let_3)))) _let_6) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.in) _let_7)) _let_6))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.independent) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s _let_6 B0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (= _let_3 _let_2))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.in) _let_3)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.span) (tptp.s _let_5 B0)))))) (=> (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) F0) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.vec) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.independent) _let_2))) (exists ((G0 $$unsorted)) (and (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) G0))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_8 _let_8) tptp.span) (tptp.s _let_8 B0))))) (let ((_let_10 (tptp.fun _let_8 tptp.bool))) (let ((_let_11 (tptp.s (tptp.fun _let_1 _let_10) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_5)) _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_2)) _let_9)))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.vectoru_add) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.vectoru_add) (tptp.s _let_3 (tptp.i _let_4 _let_5)))) (tptp.s _let_3 (tptp.i _let_4 _let_2)))))))))))))))))) (forall ((X $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) G0))) (let ((_let_5 (tptp.s tptp.real C0))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.in) _let_2)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_8 _let_8) tptp.span) (tptp.s _let_8 B0)))))) (= (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) _let_5)) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_5)) (tptp.s _let_3 (tptp.i _let_4 _let_2)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) _let_2)) (tptp.s _let_5 B0)))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 G0) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 F0) _let_2))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.independent) (tptp.s _let_1 B0)))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 G0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) _let_2)) (tptp.s _let_5 B0)))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 G0) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 F0) _let_2))))))))))))))))) (forall ((Q128666 $$unsorted) (Q128687 $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (GENR_PVARR_321 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128666))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real Q128687)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_321)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128666))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.cart tptp.real Q128687))) (and (= (tptp.p _let_3) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) F0) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_321))) _let_3)) _let_2)))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128666))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real Q128687)))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.subspace) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_0) _let_3))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 B0)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.span) (tptp.s _let_4 B0)))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))))) (forall ((Q128763 $$unsorted) (Q128793 $$unsorted) (F0 $$unsorted) (B0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128763))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 (tptp.cart tptp.real Q128793)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) (tptp.s _let_4 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.subset) (tptp.s _let_2 S0))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 B0)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128793))) (let ((_let_2 (tptp.cart tptp.real Q128763))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 B0)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128793))) (let ((_let_2 (tptp.cart tptp.real Q128763))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 S0)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))))) (forall ((Q128822 $$unsorted) (Q128829 $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (B0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128829))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_1 (tptp.cart tptp.real Q128822)))) (let ((_let_5 (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_4 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_5 (tptp.s _let_4 G0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.subset) (tptp.s _let_2 S0))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 B0)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128829))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q128822))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) _let_2)) (tptp.s _let_5 B0)))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 F0) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 G0) _let_2)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q128829))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real Q128822))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) _let_2)) (tptp.s _let_5 S0)))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_4 F0) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 G0) _let_2)))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s _let_1 F0))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1)))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.fun M tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_5 F0) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 G0) _let_3))))))))))))))) (= _let_3 _let_2))))))) (forall ((P $$unsorted) (M $$unsorted) (N $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun _let_4 (tptp.fun _let_1 (tptp.cart tptp.real P))))) (let ((_let_8 (tptp.s (tptp.fun _let_7 tptp.bool) tptp.bilinear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_7 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_7 G0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.subset) (tptp.s _let_5 S0))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.span) (tptp.s _let_5 B0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.subset) (tptp.s _let_2 tptp.t0))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 C0)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real P))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.in) _let_4)) (tptp.s _let_10 B0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.in) _let_2)) (tptp.s _let_8 C0))))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 F0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 G0) _let_4)) _let_2))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart tptp.real P))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun _let_3 tptp.bool))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_3 _let_11) tptp.in) _let_4)) (tptp.s _let_10 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.in) _let_2)) (tptp.s _let_8 tptp.t0))))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 F0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 G0) _let_4)) _let_2)))))))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (P $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.fun (tptp.cart tptp.real N) (tptp.cart tptp.real P))))) (let ((_let_2 (tptp.s _let_1 G0))) (let ((_let_3 (tptp.s _let_1 F0))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.bilinear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2))) (forall ((I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1)))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.basis) _let_4)))) (let ((_let_7 (tptp.cart tptp.real P))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun _let_5 _let_8))) (let ((_let_10 (tptp.fun N tptp.bool))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (let ((_let_12 (tptp.s (tptp.fun tptp.num _let_11) tptp.l_a_))) (let ((_let_13 (tptp.fun tptp.num tptp.num))) (let ((_let_14 (tptp.s _let_11 (tptp.i _let_12 (tptp.s tptp.num (tptp.i (tptp.s _let_13 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_13 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_15 (tptp.fun M tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_15 tptp.num) tptp.dimindex) (tptp.s _let_15 tptp.univ)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_14 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_10 tptp.num) tptp.dimindex) (tptp.s _let_10 tptp.univ))))))) (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 F0) _let_6)) _let_3)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s _let_9 G0) _let_6)) _let_3))))))))))))))))))))) (= _let_3 _let_2))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.cart _let_2 N))) (let ((_let_6 (tptp.fun _let_5 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrixu_mul) (tptp.s _let_4 B0))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.transp) (tptp.s _let_4 A5))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.cart _let_2 N))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 A5))) (tptp.s _let_4 B0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.cart _let_2 M))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.transp) (tptp.s _let_4 A5))))) (tptp.s _let_4 B0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.cart _let_2 M))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 B0))) (tptp.s _let_4 A5))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2))))))))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun _let_4 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.o) _let_6)) (tptp.s _let_4 F0))) (tptp.s _let_2 tptp.i1)))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) (tptp.s _let_2 X))) (tptp.s _let_1 Y))))))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_4 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.o) (tptp.s _let_6 F0))) _let_5)) (tptp.s _let_2 tptp.i1)))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.cart _let_2 M))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 B0))) (tptp.s _let_4 A5))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart _let_1 M))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrixu_vectoru_mul) (tptp.s _let_4 A5))))) (=> (= (tptp.s _let_5 (tptp.i _let_7 _let_3)) (tptp.s _let_5 (tptp.i _let_7 _let_2))) (= _let_3 _let_2)))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.cart _let_2 M))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 B0))) (tptp.s _let_4 A5))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.cart _let_2 M))) (let ((_let_6 (tptp.fun _let_2 _let_4))) (=> (= (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_vectoru_mul) (tptp.s _let_5 A5))) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.vec) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.cart _let_2 N))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 A5))) (tptp.s _let_4 B0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.matrixu_vectoru_mul) (tptp.s _let_3 A5))) (tptp.s _let_2 X))) (tptp.s _let_1 Y)))))))))) (forall ((M $$unsorted) (N $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 C0))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun tptp.num _let_4))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (= (tptp.s _let_4 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_2)) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) (tptp.s tptp.real (tptp.i _let_7 _let_3)))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.column) _let_3)) _let_2)))))))))))))))) (forall ((A5 $$unsorted)) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.cart _let_2 M))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 B0))) (tptp.s _let_4 A5))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((C0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun _let_6 _let_5))) (let ((_let_9 (tptp.fun N tptp.bool))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_4))) (=> (= (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.vsum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dimindex) (tptp.s _let_9 tptp.univ))))))) (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) U_0) (tptp.s _let_7 C0))) (tptp.s _let_6 A5))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1))))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.num I0))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 C0) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (A5 $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart _let_1 M))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.s tptp.num I0))) (let ((_let_5 (tptp.fun _let_2 _let_1))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (let ((_let_7 (tptp.s _let_6 C0))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (let ((_let_9 (tptp.fun tptp.num _let_1))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) U_0) _let_7)) _let_3)) _let_4)) (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.r_) (tptp.s tptp.real (tptp.i _let_7 _let_4)))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.row) _let_4)) _let_3)))))))))))))))) (forall ((A5 $$unsorted)) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.cart _let_2 N))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 A5))) (tptp.s _let_4 B0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((C0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.cart _let_4 M))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.fun _let_6 _let_5))) (let ((_let_9 (tptp.fun M tptp.bool))) (let ((_let_10 (tptp.fun tptp.num tptp.bool))) (let ((_let_11 (tptp.fun tptp.num _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_4))) (=> (= (tptp.s _let_4 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_10 _let_12) tptp.vsum) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.o_o_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dimindex) (tptp.s _let_9 tptp.univ))))))) (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) U_0) (tptp.s _let_7 C0))) (tptp.s _let_6 A5))))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.vec) (tptp.s tptp.num (tptp.i _let_3 _let_1))))) (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num tptp.u_0))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.s _let_2 tptp.numeral))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.s tptp.num I0))) (let ((_let_6 (tptp.fun M tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) _let_1)))))) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 C0) _let_5)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i _let_3 _let_1))))))))))))))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) tptp.bool))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real N) M))) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.cart _let_2 N))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 A5))) (tptp.s _let_4 B0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) tptp.columns) (tptp.s _let_2 A5))))) (tptp.s _let_1 tptp.univ)))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.cart _let_1 M))) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.cart _let_2 M))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_6 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_mul) (tptp.s _let_5 B0))) (tptp.s _let_4 A5))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_3 _let_2) tptp.rows) (tptp.s _let_3 A5))))) (tptp.s _let_2 tptp.univ))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2)))))))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) F0) (tptp.s _let_1 X))) (tptp.s _let_1 Y))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) F0) (tptp.s _let_1 X))) (tptp.s _let_1 Y)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (= (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) F0) (tptp.s _let_1 X))) (tptp.s _let_1 Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2)))))))))))) (forall ((A $$unsorted) (F0 $$unsorted) (G0 $$unsorted) (H0 $$unsorted)) (let ((_let_1 (tptp.fun A A))) (let ((_let_2 (tptp.s _let_1 H0))) (let ((_let_3 (tptp.s _let_1 F0))) (let ((_let_4 (tptp.s _let_1 tptp.i1))) (let ((_let_5 (tptp.s _let_1 G0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.o))) (=> (and (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_5)) _let_4) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)) _let_4)) (= _let_3 _let_2)))))))))) (forall ((Q130465 $$unsorted) (Q130466 $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.fun Q130466 Q130466))) (let ((_let_2 (tptp.fun Q130466 Q130465))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.fun Q130465 Q130466))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun _let_2 _let_1))) (let ((_let_7 (tptp.fun Q130465 Q130465))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (= (and (= (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.o) _let_3)) _let_5)) (tptp.s _let_7 tptp.i1)) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.o) _let_5)) _let_3)) (tptp.s _let_1 tptp.i1))) (and (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q130465 X))) (= (tptp.s Q130465 (tptp.i (tptp.s (tptp.fun Q130466 Q130465) F0) (tptp.s Q130466 (tptp.i (tptp.s (tptp.fun Q130465 Q130466) G0) _let_1)))) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.s Q130466 X))) (= (tptp.s Q130466 (tptp.i (tptp.s (tptp.fun Q130465 Q130466) G0) (tptp.s Q130465 (tptp.i (tptp.s (tptp.fun Q130466 Q130465) F0) _let_1)))) _let_1)))))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2)))))))) (exists ((FI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 FI_)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 FI_) (tptp.s _let_1 (tptp.i (tptp.s _let_3 F0) _let_2)))) _let_2))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 F0) (tptp.s _let_1 (tptp.i (tptp.s _let_3 FI_) _let_2)))) _let_2))))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) F0) (tptp.s _let_1 X))) (tptp.s _let_1 Y)))))) (exists ((FI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 FI_)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 FI_) (tptp.s _let_1 (tptp.i (tptp.s _let_3 F0) _let_2)))) _let_2))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_3 F0) (tptp.s _let_1 (tptp.i (tptp.s _let_3 FI_) _let_2)))) _let_2))))))))))))) (forall ((N $$unsorted) (F0 $$unsorted) (FI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 tptp.i1))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.s _let_2 FI_))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_6) tptp.o))) (let ((_let_8 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_5)))) (= (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_5)) _let_3) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_4)) _let_3)))))))))))) (forall ((N $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear))) (let ((_let_5 (tptp.s _let_2 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.o) _let_3)) _let_5)) (tptp.s _let_2 tptp.i1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_3))))))))))) (forall ((N $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear))) (let ((_let_5 (tptp.s _let_2 F0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.o) _let_5)) _let_3)) (tptp.s _let_2 tptp.i1))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_3))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.s _let_3 G0))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_1 _let_2))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun _let_3 _let_5))) (let ((_let_9 (tptp.fun _let_1 _let_1))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.linear) _let_7))) (= (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_3 _let_10) tptp.o) _let_4)) _let_7)) (tptp.s _let_9 tptp.i1)) (= (tptp.s _let_5 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.o) _let_7)) _let_4)) (tptp.s _let_5 tptp.i1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) _let_4))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2)))))))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) (tptp.s _let_2 X))) (tptp.s _let_1 Y))))))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) (tptp.cart tptp.real M)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 G0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) G0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))) _let_2))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) F0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) G0) _let_2)))) _let_2))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (AI_ $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real N) N))) (let ((_let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_4 (tptp.s _let_2 A5))) (let ((_let_5 (tptp.s _let_2 AI_))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_6) tptp.matrixu_mul))) (= (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_5)) _let_3) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_4)) _let_3)))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 M))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (let ((_let_6 (tptp.cart _let_2 N))) (let ((_let_7 (tptp.cart _let_4 M))) (let ((_let_8 (tptp.fun _let_6 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) tptp.matrixu_mul) (tptp.s _let_7 B0))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrix) (tptp.s _let_5 F0))))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun _let_4 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.o) _let_6)) (tptp.s _let_4 F0))) (tptp.s _let_2 tptp.i1))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (= (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.cart _let_2 M))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun _let_5 _let_2))) (let ((_let_7 (tptp.cart _let_5 N))) (let ((_let_8 (tptp.fun _let_4 _let_3))) (= (tptp.s _let_3 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) tptp.matrixu_mul) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.matrix) (tptp.s _let_6 F0))))) (tptp.s _let_4 B0))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 G0))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.fun _let_4 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.o) (tptp.s _let_6 F0))) _let_5)) (tptp.s _let_2 tptp.i1))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) N))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.invertible) (tptp.s _let_1 A5)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real N) N))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.matrixu_mul) (tptp.s _let_2 B0))) (tptp.s _let_2 A5))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) N))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.invertible) (tptp.s _let_1 A5)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real N) N))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.matrixu_mul) (tptp.s _let_2 A5))) (tptp.s _let_2 B0))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mat) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 F0))) (let ((_let_4 (tptp.cart _let_1 N))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.invertible) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.matrix) _let_3))))) (exists ((G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 tptp.i1))) (let ((_let_4 (tptp.s _let_2 F0))) (let ((_let_5 (tptp.s _let_2 G0))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_6) tptp.o))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) _let_5))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_5)) _let_3) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_4)) _let_3))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.s _let_6 G0))) (let ((_let_8 (tptp.fun _let_4 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.linear) _let_7))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.o) _let_7)) _let_5)) (tptp.s _let_2 tptp.i1))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real B0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))))))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_3 _let_1))) (let ((_let_7 (tptp.s _let_6 G0))) (let ((_let_8 (tptp.fun _let_4 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.linear) _let_7))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.o) _let_7)) _let_5)) (tptp.s _let_2 tptp.i1))) (exists ((B0 $$unsorted)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) (tptp.s tptp.real B0))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2))))))))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.real _let_1) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real B0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))) (tptp.s tptp.real B0))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2))))))))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dim) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) _let_3))))))))))))) (forall ((N $$unsorted) (U_1 $$unsorted)) (=> (forall ((V $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num J0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 V))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun _let_2 _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 U_1) _let_3)) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 tptp.d_) _let_3)) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((V $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.fun tptp.num _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2)) (tptp.s tptp.num I0))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_1) _let_2)))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.fun tptp.num _let_1))) (let ((_let_4 (tptp.cart _let_1 tptp.n10))) (= (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.rowvector) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.lambda) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2)))))))))))))) (forall ((N $$unsorted) (U_1 $$unsorted)) (=> (forall ((V $$unsorted) (I0 $$unsorted) (J0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 V))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_1) _let_3)) _let_1)) (tptp.s tptp.num J0))) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.d_) _let_3)) _let_1))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((V $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 V))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.num _let_4))) (let ((_let_6 (tptp.cart tptp.real tptp.n10))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (= (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) U_0) _let_3)) _let_1)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_1) _let_3)) _let_1))))))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.cart _let_3 N))) (= (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.columnvector) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.lambda) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) U_0) _let_2))))))))))))))) (forall ((Q131708 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q131708))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.cart _let_1 tptp.n10))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real tptp.n10) Q131708))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.transp) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.columnvector) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.rowvector) _let_2)))))))) (forall ((Q131723 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q131723))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real tptp.n10) Q131723))) (let ((_let_4 (tptp.cart _let_1 tptp.n10))) (= (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.transp) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.rowvector) _let_2)))) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.columnvector) _let_2)))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 V))) (let ((_let_3 (tptp.cart tptp.real tptp.n10))) (let ((_let_4 (tptp.cart _let_3 N))) (let ((_let_5 (tptp.cart _let_1 M))) (let ((_let_6 (tptp.s _let_5 A5))) (let ((_let_7 (tptp.cart _let_3 M))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.cart tptp.real M))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (= (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_9 _let_7) tptp.columnvector) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_5 _let_10) tptp.matrixu_vectoru_mul) _let_6)) _let_2)))) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.matrixu_mul) _let_6)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.columnvector) _let_2)))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.cart tptp.real tptp.n10))) (let ((_let_6 (tptp.cart _let_5 N))) (let ((_let_7 (tptp.s _let_3 X))) (let ((_let_8 (tptp.cart _let_3 tptp.n10))) (let ((_let_9 (tptp.cart _let_5 tptp.n10))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (let ((_let_11 (tptp.fun tptp.num _let_5))) (let ((_let_12 (tptp.fun tptp.num tptp.real))) (let ((_let_13 (tptp.fun _let_3 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_3 _let_13) tptp.dot) _let_7)) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_5 _let_12) tptp.d_) (tptp.s _let_5 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.d_) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_8 _let_10) tptp.matrixu_mul) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_3 _let_8) tptp.rowvector) _let_7)))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.columnvector) _let_4)))))) _let_2)))) _let_2))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.s _let_3 Y))) (let ((_let_5 (tptp.cart tptp.real tptp.n10))) (let ((_let_6 (tptp.cart _let_5 N))) (let ((_let_7 (tptp.cart _let_3 N))) (let ((_let_8 (tptp.s _let_7 B0))) (let ((_let_9 (tptp.s _let_7 A5))) (let ((_let_10 (tptp.fun _let_7 _let_7))) (let ((_let_11 (tptp.fun _let_6 _let_6))) (let ((_let_12 (tptp.s _let_3 X))) (let ((_let_13 (tptp.cart _let_3 tptp.n10))) (let ((_let_14 (tptp.cart _let_5 tptp.n10))) (let ((_let_15 (tptp.fun _let_6 _let_14))) (let ((_let_16 (tptp.fun tptp.num _let_5))) (let ((_let_17 (tptp.fun tptp.num tptp.real))) (let ((_let_18 (tptp.fun _let_3 _let_3))) (let ((_let_19 (tptp.s (tptp.fun _let_7 _let_18) tptp.matrixu_vectoru_mul))) (let ((_let_20 (tptp.fun _let_3 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_20 (tptp.i (tptp.s (tptp.fun _let_3 _let_20) tptp.dot) (tptp.s _let_3 (tptp.i (tptp.s _let_18 (tptp.i _let_19 _let_9)) _let_12)))) (tptp.s _let_3 (tptp.i (tptp.s _let_18 (tptp.i _let_19 _let_8)) _let_4)))) (tptp.s tptp.real (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_5 _let_17) tptp.d_) (tptp.s _let_5 (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun _let_14 _let_16) tptp.d_) (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i (tptp.s (tptp.fun _let_13 _let_15) tptp.matrixu_mul) (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_3 _let_13) tptp.rowvector) _let_12)))) (tptp.s _let_6 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_7 _let_11) tptp.matrixu_mul) (tptp.s _let_7 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_7 _let_10) tptp.matrixu_mul) (tptp.s _let_7 (tptp.i (tptp.s _let_10 tptp.transp) _let_9)))) _let_8)))) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) tptp.columnvector) _let_4)))))))) _let_2)))) _let_2)))))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_4))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.in) (tptp.s _let_4 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.matrixu_vectoru_mul) _let_3)) (tptp.s _let_1 X))))) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.span) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.columns) _let_3))))))))))))))) (forall ((Q131992 $$unsorted) (U_0 $$unsorted)) (=> (forall ((X $$unsorted) (GENR_PVARR_327 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q131992))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 X))) (tptp.s _let_1 GENR_PVARR_327)))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q131992))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_327))) (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))) _let_2)))) _let_2)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q131992))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.subspace) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 X))))))))))))) (forall ((Q132023 $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_328 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132023))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_328)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132023))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132023))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) _let_2)) (tptp.s _let_1 Y))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_328))) _let_2)) (tptp.s _let_1 Y)))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q132023) tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 (tptp.i (tptp.s _let_2 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_2 U_0) (tptp.s _let_1 S0))))))))))))) (forall ((Q132081 $$unsorted) (S0 $$unsorted) (X $$unsorted)) (=> (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132081))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))) _let_2))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132081))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))) _let_2))))))))))) (forall ((Q132106 $$unsorted) (S0 $$unsorted) (X $$unsorted)) (= (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132106))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))) _let_2))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132106))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))) _let_2))))))))))) (forall ((Q132154 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132154))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_4 _let_4) tptp.span))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_4 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_4 T0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal) _let_3)) _let_2)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q132154))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_4 T0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal) _let_3)) _let_2))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.cart _let_1 N))) (let ((_let_6 (tptp.s _let_5 A5))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.cart tptp.real N))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (=> (and (= (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_5 _let_9) tptp.matrixu_vectoru_mul) _let_6)) _let_3)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.in) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.span) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.rows) _let_6)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal) _let_3)) _let_2)))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.cart _let_2 N))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.cart tptp.real N))) (let ((_let_9 (tptp.fun _let_2 _let_8))) (= (and (= (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.matrixu_vectoru_mul) _let_5)) _let_3)) (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.num _let_8) tptp.vec) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.in) _let_3)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.span) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.rows) _let_5)))))))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart _let_1 N))) (let ((_let_5 (tptp.s _let_4 A5))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.matrixu_vectoru_mul) _let_5)))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_9 _let_9) tptp.span) (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_4 _let_9) tptp.rows) _let_5)))))) (let ((_let_11 (tptp.fun _let_9 tptp.bool))) (let ((_let_12 (tptp.s (tptp.fun _let_1 _let_11) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_3)) _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_2)) _let_10))) (= (tptp.s _let_6 (tptp.i _let_8 _let_3)) (tptp.s _let_6 (tptp.i _let_8 _let_2)))) (= _let_3 _let_2))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dim) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.rows) _let_3)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dim) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.columns) _let_3)))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.rank) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dim) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.columns) _let_2))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dim) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.rows) _let_3)))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.cart (tptp.cart tptp.real N) M))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.rank) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.transp) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.rank) _let_2))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (K0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.s tptp.num K0))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_1 _let_5))) (let ((_let_8 (tptp.fun M tptp.bool))) (let ((_let_9 (tptp.fun tptp.num tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.l_a_))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_11 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i _let_10 _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_8 tptp.num) tptp.dimindex) (tptp.s _let_8 tptp.univ))))))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.matrixu_vectoru_mul) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.basis) _let_4)))) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.column) _let_4)) _let_3)))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_1 $$unsorted)) (=> (forall ((GENR_PVARR_331 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) U_1) (tptp.s _let_1 GENR_PVARR_331)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun M tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.setspec) (tptp.s _let_2 GENR_PVARR_331))) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.basis) _let_1))))))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.matrixu_vectoru_mul) _let_4)) _let_2))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_3 _let_7) tptp.columns) _let_4)) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 U_1))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (= (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 U_0) _let_4)) _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 tptp.matrixu_vectoru_mul) _let_4)) _let_2))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.cart _let_1 N))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.rank) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dim) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.image) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_3 _let_6) U_0) _let_4)))) (tptp.s _let_2 tptp.univ))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.subset) _let_4)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_5 _let_2)))) (tptp.s tptp.num (tptp.i _let_5 _let_4)))))) (= (tptp.s _let_1 (tptp.i _let_3 _let_4)) (tptp.s _let_1 (tptp.i _let_3 _let_2)))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun N tptp.bool))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dimindex) (tptp.s _let_3 tptp.univ)))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) _let_2)) (tptp.s _let_1 tptp.univ))))))) (forall ((Q132744 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q132744) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.psubset) (tptp.s _let_1 (tptp.i _let_6 _let_4)))) (tptp.s _let_1 (tptp.i _let_6 _let_2))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun M tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.rank) (tptp.s _let_4 A5))))) (tptp.s tptp.num (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.min) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun M tptp.bool))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real M) N))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) (tptp.s _let_2 A5))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart _let_1 N))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrixu_vectoru_mul) (tptp.s _let_4 A5))))) (=> (= (tptp.s _let_5 (tptp.i _let_7 _let_3)) (tptp.s _let_5 (tptp.i _let_7 _let_2))) (= _let_3 _let_2)))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real M) N))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) (tptp.s _let_2 A5))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.matrixu_vectoru_mul) (tptp.s _let_3 A5))) (tptp.s _let_2 X))) (tptp.s _let_1 Y)))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real M) N))) (=> (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) (tptp.s _let_2 A5))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.matrixu_vectoru_mul) (tptp.s _let_3 A5))) (tptp.s _let_2 X))) (tptp.s _let_1 B0))))))))))) (forall ((N $$unsorted) (M $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun M tptp.bool))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real M) N))) (= (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart _let_3 N))) (let ((_let_6 (tptp.fun _let_3 _let_2))) (and (not (= _let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_vectoru_mul) (tptp.s _let_5 A5))) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))))) (not (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) (tptp.s _let_2 A5))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun M tptp.bool))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real M) N))) (=> (not (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) (tptp.s _let_2 A5))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart _let_3 N))) (let ((_let_6 (tptp.fun _let_3 _let_2))) (and (not (= _let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_vectoru_mul) (tptp.s _let_5 A5))) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun M tptp.bool))) (let ((_let_2 (tptp.fun N tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.s _let_3 X))) (let ((_let_5 (tptp.cart _let_3 N))) (let ((_let_6 (tptp.fun _let_3 _let_2))) (and (not (= _let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.vec) _let_1)))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.matrixu_vectoru_mul) (tptp.s _let_5 A5))) _let_4)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_3 (tptp.s _let_2 A5))) (= (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) _let_3)) _let_1) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mat) _let_1)))))))) (forall ((Q133117 $$unsorted) (Q133118 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart (tptp.cart tptp.real Q133117) Q133118))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.mat) _let_1)))) _let_1)))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real P))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.cart _let_1 M))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.rank) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrixu_mul) (tptp.s _let_4 A5))) _let_3)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) _let_3))))))))))))) (forall ((P $$unsorted) (N $$unsorted) (M $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.cart tptp.real P))) (let ((_let_4 (tptp.cart _let_3 N))) (let ((_let_5 (tptp.cart _let_3 M))) (let ((_let_6 (tptp.fun _let_4 _let_5))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.rank) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.matrixu_mul) _let_2)) (tptp.s _let_4 B0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.rank) _let_2))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.fun _let_4 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_4))) (let ((_let_7 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.adjoint) (tptp.s _let_5 F0))))) (=> (= (tptp.s _let_4 (tptp.i _let_7 _let_3)) (tptp.s _let_4 (tptp.i _let_7 _let_2))) (= _let_3 _let_2)))))))))) (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.cart tptp.real M))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_2 _let_1) F0) (tptp.s _let_2 X))) (tptp.s _let_1 Y)))))))))) (forall ((N $$unsorted) (M $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (= (forall ((Y $$unsorted)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.adjoint) (tptp.s _let_3 F0))) (tptp.s _let_2 X))) (tptp.s _let_1 Y)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2)))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (= (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.adjoint) (tptp.s _let_4 F0))))) (=> (= (tptp.s _let_1 (tptp.i _let_5 _let_3)) (tptp.s _let_1 (tptp.i _let_5 _let_2))) (= _let_3 _let_2)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2)))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (= (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (=> (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.adjoint) (tptp.s _let_4 F0))) _let_3)) _let_2) (= _let_3 _let_2))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s _let_1 X))) (=> (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) F0) _let_3)) _let_2) (= _let_3 _let_2))))))))))) (forall ((N $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (= (not (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2)))))))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (and (not (= (tptp.s _let_1 A5) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.dot) (tptp.s _let_1 A5))) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) F0) (tptp.s _let_1 X))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_332 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 A5))) (tptp.s _let_1 GENR_PVARR_332)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (and (= (tptp.p _let_3) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.dot) (tptp.s _let_1 A5))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_332))) _let_3)) _let_2))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) (tptp.s _let_2 F0)))) (not (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_1) F0))) (=> (= (tptp.s _let_1 (tptp.i _let_4 _let_3)) (tptp.s _let_1 (tptp.i _let_4 _let_2))) (= _let_3 _let_2))))))))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (and (not (= (tptp.s _let_1 A5) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.subset) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.image) (tptp.s _let_4 F0))) (tptp.s _let_2 S0))))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 A5))))))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dim) (tptp.s _let_5 S0))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))) (exists ((T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (and (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2)) (tptp.s tptp.num N0)) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 S0))))) (tptp.s _let_1 (tptp.i _let_3 _let_2)))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (N0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.s tptp.num N0))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_))) (let ((_let_5 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dim) (tptp.s _let_5 S0))))) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i _let_4 _let_2)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.hasu_size) _let_2)) (tptp.s tptp.num N0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.subset) (tptp.s _let_1 (tptp.i _let_3 (tptp.s _let_1 S0))))) (tptp.s _let_1 (tptp.i _let_3 _let_2))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 _let_2) tptp.span))) (let ((_let_5 (tptp.fun _let_1 _let_2))) (= (tptp.s _let_2 (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.delete) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s _let_2 (tptp.i _let_4 _let_3))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((C0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 C0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.r_) (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_2))))))))) (forall ((C0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s _let_4 tptp.span))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.finite) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (not (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) C0) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))))))))) (= (tptp.s _let_2 (tptp.i _let_5 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_7 _let_4) tptp.image) (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) U_0) (tptp.s _let_6 C0))))) _let_3)))) (tptp.s _let_2 (tptp.i _let_5 _let_3)))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_2))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.pairwise) (tptp.s _let_5 tptp.orthogonal))) _let_3))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.independent) _let_3)))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_2))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_5 _let_4) tptp.pairwise) (tptp.s _let_5 tptp.orthogonal))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.finite) _let_3)))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) _let_2)))) (let ((_let_5 (tptp.s _let_1 A5))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) U_0) _let_5)) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_div) (tptp.s tptp.real (tptp.i _let_4 _let_5)))) (tptp.s tptp.real (tptp.i _let_4 _let_2)))))) _let_2))))))))))) (forall ((S0 $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.s _let_5 S0))) (let ((_let_7 (tptp.fun _let_3 _let_1))) (let ((_let_8 (tptp.s _let_1 X))) (let ((_let_9 (tptp.fun _let_1 _let_5))) (let ((_let_10 (tptp.s _let_9 tptp.orthogonal))) (let ((_let_11 (tptp.fun _let_5 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.pairwise) _let_10)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.in) _let_8)) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.span) _let_6)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_10 _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.vectoru_sub) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.vsum) _let_6)) (tptp.s _let_3 (tptp.i (tptp.s _let_4 U_0) _let_2)))))))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.pairwise) (tptp.s _let_3 tptp.orthogonal))) (tptp.s _let_2 S0)))) (exists ((U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.union) (tptp.s _let_2 S0))))) (let ((_let_5 (tptp.s _let_3 tptp.span))) (let ((_let_6 (tptp.s _let_2 (tptp.i _let_4 (tptp.s _let_2 U))))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (let ((_let_8 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) tptp.pairwise) (tptp.s _let_7 tptp.orthogonal))) _let_6))) (= (tptp.s _let_2 (tptp.i _let_5 _let_6)) (tptp.s _let_2 (tptp.i _let_5 (tptp.s _let_2 (tptp.i _let_4 (tptp.s _let_2 T0)))))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.pairwise) (tptp.s _let_3 tptp.orthogonal))) (tptp.s _let_2 S0)))) (exists ((U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.union) _let_3)))) (let ((_let_6 (tptp.s _let_4 tptp.span))) (let ((_let_7 (tptp.s _let_2 U))) (let ((_let_8 (tptp.s _let_2 (tptp.i _let_5 _let_7)))) (let ((_let_9 (tptp.fun _let_1 _let_2))) (let ((_let_10 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) tptp.disjoint) _let_7)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.insert) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_9 _let_10) tptp.pairwise) (tptp.s _let_9 tptp.orthogonal))) _let_8))) (= (tptp.s _let_2 (tptp.i _let_6 _let_8)) (tptp.s _let_2 (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 (tptp.s _let_2 T0)))))))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) tptp.pairwise) (tptp.s _let_3 tptp.orthogonal))) (tptp.s _let_2 S0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 S0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))))))))))) (exists ((U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.union) _let_3)))) (let ((_let_6 (tptp.s _let_4 tptp.span))) (let ((_let_7 (tptp.s _let_2 U))) (let ((_let_8 (tptp.s _let_2 (tptp.i _let_5 _let_7)))) (let ((_let_9 (tptp.fun _let_1 _let_2))) (let ((_let_10 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_2 _let_10) tptp.disjoint) _let_7)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_9 _let_10) tptp.pairwise) (tptp.s _let_9 tptp.orthogonal))) _let_8))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 U)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (= (tptp.s _let_2 (tptp.i _let_6 _let_8)) (tptp.s _let_2 (tptp.i _let_6 (tptp.s _let_2 (tptp.i _let_5 (tptp.s _let_2 T0)))))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted)) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) (tptp.s _let_1 A5))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_4 _let_5) tptp.pairwise) (tptp.s _let_4 tptp.orthogonal))) _let_3))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)) (tptp.s _let_2 tptp.univ)))))))))) (forall ((N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (=> (not (= (tptp.s _let_1 A5) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_6) tptp.in))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_1 A5))) _let_3))) (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.pairwise) (tptp.s _let_7 tptp.orthogonal))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.hasu_size) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ)))))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)) (tptp.s _let_2 tptp.univ))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (=> (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) (tptp.s _let_2 A5))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0)))))))) (exists ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) (tptp.s _let_1 A5))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.pairwise) (tptp.s _let_7 tptp.orthogonal))) _let_3))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 S0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.independent) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.hasu_size) _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ)))))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_3)) (tptp.s _let_2 tptp.univ))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 S0)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_2 B0))) (let ((_let_5 (tptp.fun _let_1 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.subset) _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_5 _let_6) tptp.pairwise) (tptp.s _let_5 tptp.orthogonal))) _let_4))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_4)) _let_3)))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 S0)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_2 B0))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_2))) (and (not (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_4)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.subset) _let_4)) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.pairwise) (tptp.s _let_7 tptp.orthogonal))) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.independent) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.hasu_size) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) _let_3))))) (= (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) _let_4)) _let_3))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 S0)))) (exists ((B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s _let_2 B0))) (let ((_let_5 (tptp.s (tptp.fun _let_2 _let_2) tptp.span))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_2 _let_7) tptp.subset) _let_4)) (tptp.s _let_2 (tptp.i _let_5 _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_8 _let_7) tptp.pairwise) (tptp.s _let_8 tptp.orthogonal))) _let_4))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) tptp.in) _let_3)) (tptp.s _let_4 B0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.vectoru_norm) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 tptp.independent) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.hasu_size) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) _let_3))))) (= (tptp.s _let_2 (tptp.i _let_5 _let_4)) _let_3)))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s (tptp.fun _let_1 _let_1) tptp.span))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.psubset) (tptp.s _let_1 (tptp.i _let_2 (tptp.s _let_1 S0))))) (tptp.s _let_1 (tptp.i _let_2 (tptp.s _let_1 T0)))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (and (not (= _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_3)) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.span) (tptp.s _let_2 T0)))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))) _let_2)))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) (tptp.s _let_2 S0))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))) (exists ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (and (not (= (tptp.s _let_1 X) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))) _let_2))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (and (not (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 X))) _let_2))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (not (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.univ))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (and (not (= (tptp.s _let_1 A5) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.span) (tptp.s _let_4 S0)))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.dot) (tptp.s _let_1 A5))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_335 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 A5))) (tptp.s _let_1 GENR_PVARR_335)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (and (= (tptp.p _let_3) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.dot) (tptp.s _let_1 A5))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_335))) _let_3)) _let_2))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (=> (not (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.span) (tptp.s _let_1 S0))) (tptp.s _let_1 tptp.univ))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (not (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.subset) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.span) (tptp.s _let_3 S0))))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_336 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 A5))) (tptp.s _let_1 GENR_PVARR_336)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (and (= (tptp.p _let_3) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.dot) (tptp.s _let_1 A5))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_336))) _let_3)) _let_2))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim) (tptp.s _let_2 S0))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))) (exists ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (and (not (= _let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) tptp.subset) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.span) (tptp.s _let_3 S0))))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.gspec) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) U_0) _let_2))))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted) (X $$unsorted) (Y $$unsorted) (XI_ $$unsorted) (YI_ $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 YI_))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.s _let_1 XI_))) (let ((_let_5 (tptp.s _let_1 X))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_8 _let_8) tptp.span))) (let ((_let_10 (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_8 T0))))) (let ((_let_11 (tptp.fun _let_8 tptp.bool))) (let ((_let_12 (tptp.s (tptp.fun _let_1 _let_11) tptp.in))) (let ((_let_13 (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_8 S0))))) (=> (and (forall ((A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) (tptp.s _let_4 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_4 T0))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.orthogonal) _let_3)) _let_2))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_5)) _let_13))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_4)) _let_13))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_3)) _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_2)) _let_10))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) _let_2)))) (and (= _let_5 _let_4) (= _let_3 _let_2))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (X $$unsorted)) (exists ((Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.span) (tptp.s _let_4 S0)))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 W))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 Z0))) _let_2))))))))) (= (tptp.s _let_1 X) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.vectoru_add) _let_2)) (tptp.s _let_1 Z0)))))))))))) (forall ((N $$unsorted) (U_1 $$unsorted)) (=> (forall ((S0 $$unsorted) (GENR_PVARR_338 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) U_1) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_338)))) (exists ((Z0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s tptp.bool V))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool _let_3))) (and (= (tptp.p _let_2) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_3 _let_3) tptp.span) (tptp.s _let_3 S0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) (tptp.s _let_1 Z0))) _let_2)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.setspec) (tptp.s _let_1 GENR_PVARR_338))) _let_2)) (tptp.s _let_1 Z0)))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (X $$unsorted) (F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun (tptp.prod _let_1 _let_1) tptp.bool))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) (tptp.s _let_3 S0))) (tptp.s _let_1 X))) (tptp.s _let_2 F0)))) (forall ((Y $$unsorted) (Z0 $$unsorted)) (exists ((V $$unsorted)) (let ((_let_1 (tptp.s tptp.bool V))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.s _let_2 Z0))) (let ((_let_4 (tptp.s _let_2 Y))) (let ((_let_5 (tptp.prod _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.fun _let_2 tptp.bool))) (let ((_let_10 (tptp.s _let_9 S0))) (let ((_let_11 (tptp.fun _let_9 _let_9))) (let ((_let_12 (tptp.fun _let_9 tptp.bool))) (let ((_let_13 (tptp.s (tptp.fun _let_2 _let_12) tptp.in))) (and (= (tptp.p _let_1) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_4)) (tptp.s _let_9 (tptp.i (tptp.s _let_11 tptp.span) _let_10))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_3)) (tptp.s _let_9 (tptp.i (tptp.s _let_11 tptp.gspec) (tptp.s _let_9 (tptp.i (tptp.s _let_11 U_1) _let_10))))))) (= (tptp.s _let_2 X) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) tptp.vectoru_add) _let_4)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.bool _let_7) tptp.geq) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) F0) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_2 _let_6) tptp.c_) _let_4)) _let_3)))))) _let_1)))))))))))))))))))))))))) (forall ((S0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun (tptp.prod _let_1 _let_1) tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 tptp.q_) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_4 _let_3) tptp.gabs) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_2 _let_5) U_0) (tptp.s _let_2 S0))) (tptp.s _let_1 X)))))))) (forall ((X0 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.prod _let_1 _let_1))) (let ((_let_3 (tptp.s _let_2 Y))) (let ((_let_4 (tptp.s _let_2 X0))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_7 _let_6) tptp.gabs) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) U_0) (tptp.s _let_5 S0))) (tptp.s _let_1 X))))))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_3)))) (= _let_4 _let_3))))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun (tptp.cart tptp.real M) tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.subspace) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dim) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) _let_6)) (tptp.s _let_4 S0))) (tptp.s _let_2 T0)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun M tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dimindex) (tptp.s _let_3 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) _let_6)) (tptp.s _let_4 tptp.univ))) (tptp.s _let_2 S0)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun M tptp.bool))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))))) (let ((_let_4 (tptp.fun tptp.num tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun tptp.num _let_4) tptp.l_a_))) (let ((_let_6 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.subspace) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dim) _let_7)))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.cart tptp.real N))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_6 _let_8) tptp.subset) (tptp.s _let_6 S0))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_4 _let_7) tptp.image) _let_5)) (tptp.s _let_2 tptp.univ)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2)))))))))))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun M tptp.bool))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.num _let_3) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.fun (tptp.cart tptp.real M) tptp.bool))) (let ((_let_4 (tptp.s _let_3 S0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.subspace) _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) _let_2))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dim) _let_4)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim) _let_2)))) (exists ((F0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (= (tptp.s _let_2 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) _let_6)) (tptp.s _let_4 S0))) (tptp.s _let_2 T0)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.s _let_6 S0))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) _let_7))) (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2)))) (= _let_3 _let_2))))))))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun M tptp.bool))) (=> (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))) (exists ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_2))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) (tptp.s _let_4 F0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_3 tptp.bool) tptp.linear) (tptp.s _let_3 G0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_3 tptp.real) tptp.vectoru_norm) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) G0) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm) _let_2))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.cart tptp.real N))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) G0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) F0) _let_2)))) _let_2))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.cart tptp.real M))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) F0) (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) G0) _let_2)))) _let_2))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_340 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 A5))) (tptp.s _let_1 GENR_PVARR_340)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun _let_1 tptp.real))) (and (= (tptp.p _let_3) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.dot) (tptp.s _let_1 A5))) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_340))) _let_3)) _let_2))))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.subspace) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) U_0) (tptp.s _let_1 A5))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((K0 $$unsorted) (GENR_PVARR_341 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) (tptp.s tptp.num K0))) (tptp.s _let_1 GENR_PVARR_341)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (and (= (tptp.p _let_3) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.d_) _let_2)) (tptp.s tptp.num K0))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_341))) _let_3)) _let_2))))))))))))))) (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) U_0) (tptp.s tptp.num K0)))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((K0 $$unsorted) (GENR_PVARR_342 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) (tptp.s tptp.num K0))) (tptp.s _let_1 GENR_PVARR_342)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (and (= (tptp.p _let_3) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.d_) _let_2)) (tptp.s tptp.num K0))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_342))) _let_3)) _let_2))))))))))))))) (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num K0))) (let ((_let_2 (tptp.fun N tptp.bool))) (let ((_let_3 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.dimindex) (tptp.s _let_2 tptp.univ))))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_6 (tptp.fun tptp.num tptp.bool))) (let ((_let_7 (tptp.fun tptp.num _let_6))) (let ((_let_8 (tptp.cart tptp.real N))) (let ((_let_9 (tptp.fun tptp.num _let_8))) (let ((_let_10 (tptp.fun _let_8 tptp.bool))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (let ((_let_12 (tptp.fun _let_10 _let_10))) (let ((_let_13 (tptp.s _let_7 tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_13 _let_5)) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_13 _let_1)) _let_3)))) (= (tptp.s _let_10 (tptp.i (tptp.s _let_12 tptp.gspec) (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.num _let_10) U_0) _let_1)))) (tptp.s _let_10 (tptp.i (tptp.s _let_12 tptp.span) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.image) (tptp.s _let_9 tptp.basis))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_6 _let_7) tptp.delete) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.o_o_) _let_5)) _let_3)))) _let_1)))))))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((K0 $$unsorted) (GENR_PVARR_344 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) U_0) (tptp.s tptp.num K0))) (tptp.s _let_1 GENR_PVARR_344)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun tptp.num tptp.real))) (and (= (tptp.p _let_3) (= (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.d_) _let_2)) (tptp.s tptp.num K0))) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_344))) _let_3)) _let_2))))))))))))))) (forall ((K0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.fun N tptp.bool))) (let ((_let_4 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.dimindex) (tptp.s _let_3 tptp.univ))))) (let ((_let_5 (tptp.s tptp.num K0))) (let ((_let_6 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_2)) _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_5)) _let_4)))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dim) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) U_0) _let_5)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.m_) _let_4)) _let_2))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_353 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real N)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_2 _let_3))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_3 _let_4) U_0) (tptp.s _let_3 S0))) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_353)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.in) _let_2)) (tptp.s _let_4 S0)))) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) F0) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_353))) _let_3)) _let_2)))))))))))))))))) (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.s (tptp.fun _let_2 tptp.num) tptp.dim))) (let ((_let_5 (tptp.cart tptp.real N))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun _let_6 _let_2))) (let ((_let_9 (tptp.fun _let_5 tptp.bool))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.linear) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.subspace) _let_3)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_9 tptp.num) tptp.dim) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.image) _let_7)) _let_3)))))) (tptp.s tptp.num (tptp.i _let_4 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_2 _let_2) tptp.gspec) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_2 _let_8) U_0) _let_3)) _let_7)))))))) (tptp.s tptp.num (tptp.i _let_4 _let_3)))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((F0 $$unsorted) (GENR_PVARR_354 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real N)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_354)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.cart tptp.real N))) (and (= (tptp.p _let_3) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) F0) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_354))) _let_3)) _let_2)))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun M tptp.bool))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.cart tptp.real M))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.s _let_4 F0))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (let ((_let_8 (tptp.fun _let_6 _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.linear) _let_5))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.num _let_9) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dim) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_4 _let_8) tptp.image) _let_5)) (tptp.s _let_6 tptp.univ))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dim) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) _let_5)))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((S0 $$unsorted) (T0 $$unsorted) (GENR_PVARR_357 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 S0))) (tptp.s _let_2 T0))) (tptp.s _let_1 GENR_PVARR_357)))) (exists ((X $$unsorted) (Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s tptp.bool V))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool _let_6))) (let ((_let_8 (tptp.fun _let_6 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.in))) (and (= (tptp.p _let_5) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) (tptp.s _let_6 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) (tptp.s _let_6 T0)))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.setspec) (tptp.s _let_1 GENR_PVARR_357))) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) _let_3)) _let_2))))))))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.s (tptp.fun tptp.num _let_5) tptp.p_))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.s (tptp.fun _let_1 tptp.bool) tptp.subspace))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_7 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 U_0) _let_4)) _let_2)))))))) (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s _let_8 tptp.inter) _let_4)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2)))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (P $$unsorted) (U_2 $$unsorted)) (=> (forall ((G0 $$unsorted) (GENR_PVARR_366 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real P)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_2) (tptp.s _let_2 G0))) (tptp.s _let_1 GENR_PVARR_366)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.cart tptp.real P))) (and (= (tptp.p _let_3) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) G0) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_366))) _let_3)) _let_2)))))))))))))))) (forall ((U_1 $$unsorted)) (=> (forall ((F0 $$unsorted) (GENR_PVARR_365 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real N)))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_1) (tptp.s _let_2 F0))) (tptp.s _let_1 GENR_PVARR_365)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.cart tptp.real N))) (and (= (tptp.p _let_3) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) F0) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_365))) _let_3)) _let_2)))))))))))))))) (forall ((U_0 $$unsorted)) (=> (forall ((G0 $$unsorted) (F0 $$unsorted) (GENR_PVARR_364 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_2 (tptp.cart tptp.real P)))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) U_0) (tptp.s _let_4 G0))) (tptp.s _let_3 F0))) (tptp.s _let_1 GENR_PVARR_364)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.cart tptp.real P))) (let ((_let_7 (tptp.cart tptp.real N))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (let ((_let_9 (tptp.fun _let_7 _let_6))) (let ((_let_10 (tptp.fun _let_1 _let_6))) (let ((_let_11 (tptp.fun _let_8 _let_10))) (and (= (tptp.p _let_3) (= (tptp.s _let_6 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_9 _let_11) tptp.o) (tptp.s _let_9 G0))) (tptp.s _let_8 F0))) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_364))) _let_3)) _let_2)))))))))))))))))))))))) (forall ((F0 $$unsorted) (G0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 (tptp.cart tptp.real P)))) (let ((_let_3 (tptp.s _let_2 G0))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.cart tptp.real M))) (let ((_let_6 (tptp.fun _let_5 _let_1))) (let ((_let_7 (tptp.s _let_6 F0))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.fun _let_6 _let_8))) (let ((_let_10 (tptp.s (tptp.fun _let_8 _let_8) tptp.gspec))) (let ((_let_11 (tptp.s (tptp.fun _let_8 tptp.num) tptp.dim))) (let ((_let_12 (tptp.fun tptp.num tptp.num))) (let ((_let_13 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) tptp.linear) _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.linear) _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.num _let_13) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_11 (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_2 _let_9) U_0) _let_3)) _let_7)))))))) (tptp.s tptp.num (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun tptp.num _let_12) tptp.p_) (tptp.s tptp.num (tptp.i _let_11 (tptp.s _let_8 (tptp.i _let_10 (tptp.s _let_8 (tptp.i (tptp.s _let_9 U_1) _let_7)))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dim) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_4 _let_4) tptp.gspec) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) U_2) _let_3)))))))))))))))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s _let_5 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s _let_5 T0))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.dot) _let_3)) _let_2)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))))))))) (= (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.union) _let_4)) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (=> (forall ((T0 $$unsorted) (S0 $$unsorted) (GENR_PVARR_367 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 T0))) (tptp.s _let_2 S0))) (tptp.s _let_1 GENR_PVARR_367)))) (exists ((Y $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (and (= (tptp.p _let_3) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) _let_2)) (tptp.s _let_4 T0)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.in) _let_2)) (tptp.s _let_3 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.orthogonal) _let_2)) (tptp.s _let_1 Y)))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_367))) _let_3)) _let_2)))))))))))))))) (forall ((S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real N) tptp.bool))) (let ((_let_2 (tptp.s _let_1 T0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.dim))) (let ((_let_4 (tptp.s _let_1 S0))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.s _let_7 tptp.subspace))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_4))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.subset) _let_4)) _let_2)))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.p_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_5 tptp.gspec) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) U_0) _let_2)) _let_4)))))))) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (U_0 $$unsorted)) (=> (forall ((A5 $$unsorted) (GENR_PVARR_368 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) U_0) (tptp.s _let_2 A5))) (tptp.s _let_1 GENR_PVARR_368)))) (exists ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.bool V))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool _let_4))) (let ((_let_6 (tptp.cart tptp.real N))) (let ((_let_7 (tptp.cart _let_1 N))) (let ((_let_8 (tptp.fun _let_1 _let_6))) (and (= (tptp.p _let_3) (= (tptp.s _let_6 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_7 _let_8) tptp.matrixu_vectoru_mul) (tptp.s _let_7 A5))) _let_2)) (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.setspec) (tptp.s _let_1 GENR_PVARR_368))) _let_3)) _let_2)))))))))))))))))) (forall ((A5 $$unsorted)) (let ((_let_1 (tptp.fun M tptp.bool))) (let ((_let_2 (tptp.cart tptp.real M))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.s _let_3 A5))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (tptp.fun tptp.num tptp.num))) (= (tptp.s tptp.num (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.num _let_6) tptp.p_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.rank) _let_4)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.dim) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_5 _let_5) tptp.gspec) (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_3 _let_5) U_0) _let_4)))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))))) (forall ((M $$unsorted) (P $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.cart tptp.real P))) (let ((_let_3 (tptp.cart _let_2 N))) (let ((_let_4 (tptp.s _let_3 B0))) (let ((_let_5 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_6 (tptp.s _let_5 A5))) (let ((_let_7 (tptp.cart _let_2 M))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (let ((_let_10 (tptp.s (tptp.fun tptp.num _let_9) tptp.p_))) (let ((_let_11 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.num _let_11) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.rank) _let_6)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_3 tptp.num) tptp.rank) _let_4)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_9 (tptp.i _let_10 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.rank) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.matrixu_mul) _let_6)) _let_4)))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ)))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.cart _let_1 N))) (let ((_let_3 (tptp.s _let_2 A5))) (let ((_let_4 (tptp.cart (tptp.cart tptp.real N) M))) (let ((_let_5 (tptp.cart _let_1 M))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (= (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_5 tptp.num) tptp.rank) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_4 _let_6) tptp.matrixu_mul) (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_2 _let_4) tptp.transp) _let_3)))) _let_3)))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_2 tptp.num) tptp.rank) _let_3)))))))))) (forall ((M $$unsorted) (N $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart (tptp.cart tptp.real M) N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.num) tptp.rank))) (let ((_let_4 (tptp.s _let_1 A5))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_) (tptp.s tptp.num (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.matrixu_add) _let_4)) _let_2)))))) (tptp.s tptp.num (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.p_) (tptp.s tptp.num (tptp.i _let_3 _let_4)))) (tptp.s tptp.num (tptp.i _let_3 _let_2))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.cart tptp.real N))) (=> (forall ((GENR_PVARR_374 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) U_0) (tptp.s tptp.real GENR_PVARR_374)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun N tptp.bool))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_4) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dimindex) (tptp.s _let_7 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.setspec) (tptp.s tptp.real GENR_PVARR_374))) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 tptp.x))) _let_1))))))))))))))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.infnorm) (tptp.s _let_2 tptp.x))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.sup) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 U_0)))))))))) (forall ((N $$unsorted)) (exists ((I0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun _let_3 tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.in) (tptp.s tptp.num I0))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))))))) (forall ((Q138882 $$unsorted) (N $$unsorted) (U_1 $$unsorted)) (=> (forall ((I0 $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real Q138882))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_3 U_1) _let_1)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 tptp.x))) _let_1))))))))) (forall ((U_0 $$unsorted)) (let ((_let_1 (tptp.fun N tptp.bool))) (let ((_let_2 (tptp.fun tptp.num tptp.num))) (let ((_let_3 (tptp.fun tptp.num tptp.bool))) (let ((_let_4 (tptp.fun tptp.num _let_3))) (let ((_let_5 (tptp.fun tptp.num tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (let ((_let_7 (tptp.fun _let_3 _let_6))) (=> (forall ((GENR_PVARR_375 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) U_0) (tptp.s tptp.real GENR_PVARR_375)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real Q138882))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun N tptp.bool))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_4) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dimindex) (tptp.s _let_7 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.setspec) (tptp.s tptp.real GENR_PVARR_375))) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 tptp.x))) _let_1))))))))))))))))))))) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_6 _let_6) tptp.gspec) (tptp.s _let_6 U_0))) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) (tptp.s _let_5 U_1))) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.num _let_4) tptp.o_o_) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_2 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.dimindex) (tptp.s _let_1 tptp.univ))))))))))))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (forall ((GENR_PVARR_376 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) U_0) (tptp.s tptp.real GENR_PVARR_376)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun N tptp.bool))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_4) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dimindex) (tptp.s _let_7 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.setspec) (tptp.s tptp.real GENR_PVARR_376))) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 tptp.x))) _let_1))))))))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.finite) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 U_0))))))))) (forall ((N $$unsorted) (U_0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (forall ((GENR_PVARR_377 $$unsorted)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun tptp.real tptp.bool) U_0) (tptp.s tptp.real GENR_PVARR_377)))) (exists ((I0 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.s tptp.num I0))) (let ((_let_2 (tptp.cart tptp.real N))) (let ((_let_3 (tptp.fun tptp.num tptp.real))) (let ((_let_4 (tptp.s tptp.bool V))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.bool _let_5))) (let ((_let_7 (tptp.fun N tptp.bool))) (let ((_let_8 (tptp.fun tptp.num tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun tptp.num _let_8) tptp.l_a_))) (let ((_let_10 (tptp.fun tptp.num tptp.num))) (and (= (tptp.p _let_4) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_10 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_1))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_1)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_7 tptp.num) tptp.dimindex) (tptp.s _let_7 tptp.univ)))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.setspec) (tptp.s tptp.real GENR_PVARR_377))) _let_4)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_2 _let_3) tptp.d_) (tptp.s _let_2 tptp.x))) _let_1))))))))))))))))))))) (not (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.gspec) (tptp.s _let_1 U_0))) (tptp.s _let_1 tptp.empty)))))) (forall ((Q138980 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q138980))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm) (tptp.s _let_1 X))))))))) (forall ((Q139038 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q139038))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_4)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_3 _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2))))))))))))))) (forall ((Q139075 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q139075))) (let ((_let_3 (tptp.s _let_2 X))) (= (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.infnorm) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1))) (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))) (forall ((Q139083 $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q139083))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.infnorm) (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))))) (forall ((Q139102 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q139102))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_1 _let_1) tptp.vectoru_neg) _let_2)))) (tptp.s tptp.real (tptp.i _let_3 _let_2))))))) (forall ((Q139133 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q139133))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub))) (let ((_let_6 (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm))) (= (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_3)))) (tptp.s tptp.real (tptp.i _let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))))))))))) (forall ((Q139185 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q139185))) (let ((_let_2 (tptp.s _let_1 tptp.y))) (let ((_let_3 (tptp.s _let_1 tptp.x))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_6 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_sub) (tptp.s tptp.real (tptp.i _let_5 _let_3)))) (tptp.s tptp.real (tptp.i _let_5 _let_2)))))))) (tptp.s tptp.real (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub) _let_3)) _let_2))))))))))))))) (forall ((Q139200 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q139200))) (let ((_let_2 (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm) (tptp.s _let_1 X))))) (= (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) _let_2)) _let_2)))) (forall ((N $$unsorted) (X $$unsorted) (I0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s tptp.num I0))) (let ((_let_4 (tptp.fun tptp.num tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun N tptp.bool))) (let ((_let_7 (tptp.fun tptp.num tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun tptp.num _let_7) tptp.l_a_))) (let ((_let_9 (tptp.fun tptp.num tptp.num))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_9 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_3)) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_6 tptp.num) tptp.dimindex) (tptp.s _let_6 tptp.univ))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.d_) _let_2)) _let_3)))))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm) _let_2)))))))))))))))) (forall ((Q139282 $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q139282))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm))) (let ((_let_4 (tptp.s tptp.real A5))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_le) (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_4)) _let_2)))))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_abs) _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s (tptp.fun _let_1 tptp.real) tptp.infnorm))) (let ((_let_4 (tptp.s tptp.real A5))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (= (tptp.s tptp.real (tptp.i _let_3 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.r_) _let_4)) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.realu_abs) _let_4)))) (tptp.s tptp.real (tptp.i _let_3 _let_2)))))))))))) (forall ((Q139356 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))) (let ((_let_2 (tptp.cart tptp.real Q139356))) (let ((_let_3 (tptp.s _let_2 X))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) _let_1)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun _let_2 tptp.real) tptp.infnorm) _let_3))))) (not (= _let_3 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.num _let_2) tptp.vec) _let_1)))))))))) (forall ((Q139366 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q139366))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.infnorm) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2)))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.fun _let_1 tptp.real))) (let ((_let_4 (tptp.fun N tptp.bool))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.vectoru_norm) _let_2)))) (tptp.s tptp.real (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.real _let_5) tptp.realu_mul) (tptp.s tptp.real (tptp.i (tptp.s _let_5 tptp.sqrt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_4 tptp.num) tptp.dimindex) (tptp.s _let_4 tptp.univ))))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_3 tptp.infnorm) _let_2)))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.vectoru_norm))) (let ((_let_6 (tptp.s tptp.real (tptp.i _let_5 _let_3)))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.s (tptp.fun tptp.real _let_7) tptp.r_))) (let ((_let_9 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (let ((_let_10 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.dot) _let_2)) _let_3)) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun tptp.real _let_10) tptp.realu_mul) _let_9)) _let_6))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_9)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_6)) _let_2))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.s _let_4 tptp.vectoru_norm))) (let ((_let_6 (tptp.s tptp.real (tptp.i _let_5 _let_3)))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun _let_1 _let_1))) (let ((_let_9 (tptp.s (tptp.fun tptp.real _let_8) tptp.r_))) (let ((_let_10 (tptp.s tptp.real (tptp.i _let_5 _let_2)))) (let ((_let_11 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_10)) _let_3)))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.dot) _let_2)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun tptp.real _let_7) tptp.realu_mul) _let_10)) _let_6))) (or (= _let_11 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_6)) _let_2))) (= _let_11 (tptp.s _let_1 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s tptp.real (tptp.i (tptp.s _let_7 tptp.realu_neg) _let_6)))) _let_2))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_5 (tptp.s tptp.real (tptp.i _let_4 _let_3)))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun tptp.real _let_6) tptp.r_))) (let ((_let_8 (tptp.s tptp.real (tptp.i _let_4 _let_2)))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i _let_4 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_add) _let_2)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) _let_8)) _let_5))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_8)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_2)))))))))))))) (forall ((Q139869 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q139869))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub))) (let ((_let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) (let ((_let_7 (tptp.s _let_1 Z0))) (let ((_let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_7)))) (let ((_let_9 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_4) tptp.r_))) (let ((_let_11 (tptp.prod _let_1 _let_1))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.s (tptp.fun _let_1 _let_12) tptp.c_))) (let ((_let_14 (tptp.s (tptp.fun _let_11 tptp.real) tptp.distance))) (let ((_let_15 (tptp.s _let_12 (tptp.i _let_13 _let_3)))) (let ((_let_16 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i _let_14 (tptp.s _let_11 (tptp.i _let_15 _let_7)))) (tptp.s tptp.real (tptp.i (tptp.s _let_16 (tptp.i (tptp.s (tptp.fun tptp.real _let_16) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_14 (tptp.s _let_11 (tptp.i _let_15 _let_2)))))) (tptp.s tptp.real (tptp.i _let_14 (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i _let_13 _let_2)) _let_7))))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_6)))) _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_8)))) _let_6))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.r_))) (let ((_let_7 (tptp.s tptp.real B0))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun tptp.real _let_8) tptp.realu_lt) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))))) (let ((_let_10 (tptp.s tptp.real A5))) (=> (and (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_10)) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_7)))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_4 _let_2)))) _let_3)) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i _let_4 _let_3)))) _let_2))))))))))))))) (forall ((Q140000 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q140000) tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.collinear) (tptp.s _let_1 S0)))) (exists ((U $$unsorted)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q140000))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.in))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 X))) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 Y))) _let_3)))) (exists ((C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q140000))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.vectoru_sub) (tptp.s _let_1 X))) (tptp.s _let_1 Y))) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.r_) (tptp.s tptp.real C0))) (tptp.s _let_1 U)))))))))))))))))) (forall ((Q140023 $$unsorted) (S0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q140023) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.s _let_3 tptp.collinear))) (let ((_let_5 (tptp.s _let_1 T0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_5))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.subset) _let_2)) _let_5)))) (tptp.p (tptp.s tptp.bool (tptp.i _let_4 _let_2)))))))))) (forall ((Q140026 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q140026) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.collinear) (tptp.s _let_1 tptp.empty)))))) (forall ((Q140034 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q140034))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun _let_1 _let_3) tptp.insert) (tptp.s _let_1 X))) (tptp.s _let_2 tptp.empty)))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.s (tptp.fun _let_1 _let_3) tptp.insert))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 X))) (tptp.s _let_2 (tptp.i (tptp.s _let_3 (tptp.i _let_4 (tptp.s _let_1 Y))) (tptp.s _let_2 tptp.empty))))))))))))) (forall ((Q140117 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real Q140117) tptp.bool))) (let ((_let_2 (tptp.s _let_1 S0))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun tptp.num tptp.num))) (let ((_let_5 (tptp.fun tptp.num tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.finite) _let_2))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun tptp.num _let_5) tptp.l_a_) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun _let_1 tptp.num) tptp.card) _let_2)))) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_4 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_3 tptp.collinear) _let_2)))))))))) (forall ((Q140276 $$unsorted) (X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q140276))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.empty))) (let ((_let_4 (tptp.s _let_1 Y))) (let ((_let_5 (tptp.s _let_1 Z0))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.vectoru_sub))) (let ((_let_8 (tptp.fun _let_2 _let_2))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.insert))) (let ((_let_10 (tptp.s _let_1 X))) (let ((_let_11 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear))) (= (tptp.s tptp.bool (tptp.i _let_11 (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_10)) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_4)) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_5)) _let_3)))))))) (tptp.s tptp.bool (tptp.i _let_11 (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_10)) _let_4)))) (tptp.s _let_2 (tptp.i (tptp.s _let_8 (tptp.i _let_9 (tptp.s _let_1 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_5)) _let_4)))) _let_3))))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.s _let_1 X))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_5 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.insert))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.collinear) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_4)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) (tptp.s _let_5 tptp.empty)))))))))) (or (= _let_4 _let_2) (= _let_3 _let_2) (exists ((C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 Y) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.r_) (tptp.s tptp.real C0))) (tptp.s _let_1 X))))))))))))))))) (forall ((Q140433 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q140433))) (let ((_let_2 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.insert))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.collinear) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 Y))) (tptp.s _let_4 tptp.empty)))))))))) (or (= _let_3 _let_2) (exists ((C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q140433))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.s _let_1 Y) (tptp.s _let_1 (tptp.i (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun tptp.real _let_2) tptp.r_) (tptp.s tptp.real C0))) (tptp.s _let_1 X)))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_1 X))) (let ((_let_7 (tptp.fun _let_1 tptp.real))) (let ((_let_8 (tptp.s _let_7 tptp.vectoru_norm))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_9 tptp.realu_abs) (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.dot) _let_6)) _let_3)))) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_8 _let_6)))) (tptp.s tptp.real (tptp.i _let_8 _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_2 tptp.empty))))))))))))))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 Y))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_1 X))) (let ((_let_7 (tptp.s tptp.num tptp.u_0))) (let ((_let_8 (tptp.fun tptp.num tptp.num))) (let ((_let_9 (tptp.s _let_8 tptp.numeral))) (let ((_let_10 (tptp.fun _let_1 tptp.real))) (let ((_let_11 (tptp.s (tptp.fun _let_1 _let_10) tptp.dot))) (let ((_let_12 (tptp.s _let_10 (tptp.i _let_11 _let_6)))) (let ((_let_13 (tptp.fun tptp.real tptp.real))) (let ((_let_14 (tptp.fun tptp.num tptp.real))) (= (= (tptp.s tptp.real (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun tptp.real _let_14) tptp.realu_pow) (tptp.s tptp.real (tptp.i _let_12 _let_3)))) (tptp.s tptp.num (tptp.i _let_9 (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_8 tptp.bit1) _let_7)))))))) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun tptp.real _let_13) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_12 _let_6)))) (tptp.s tptp.real (tptp.i (tptp.s _let_10 (tptp.i _let_11 _let_3)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i _let_9 _let_7)))))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_2 tptp.empty)))))))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.insert))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_4 tptp.bool) tptp.collinear) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 B0))) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_4 tptp.empty)))))))))) (or (= _let_3 _let_2) (exists ((U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s tptp.real U))) (let ((_let_3 (tptp.fun tptp.num tptp.num))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.s (tptp.fun tptp.real _let_5) tptp.r_))) (= (tptp.s _let_1 B0) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.vectoru_add) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) (tptp.s _let_1 A5))))) (tptp.s _let_1 (tptp.i (tptp.s _let_5 (tptp.i _let_6 (tptp.s tptp.real (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.realu_sub) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_3 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))) _let_2)))) (tptp.s _let_1 C0)))))))))))))))))))))) (forall ((N $$unsorted) (S0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_1 A5))) (=> (not (= _let_6 _let_3)) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_2 S0)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.in) _let_3)) (tptp.s _let_2 S0)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 A5))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 B0))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_2 tptp.empty))))))))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.empty))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 D0))) _let_3)))) (let ((_let_7 (tptp.s _let_1 B0))) (let ((_let_8 (tptp.s _let_4 (tptp.i _let_5 _let_7)))) (let ((_let_9 (tptp.s _let_1 A5))) (let ((_let_10 (tptp.s _let_4 (tptp.i _let_5 _let_9)))) (let ((_let_11 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear))) (let ((_let_12 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 C0))))) (=> (not (= _let_9 _let_7)) (= (tptp.p (tptp.s tptp.bool (tptp.i _let_11 (tptp.s _let_2 (tptp.i _let_10 (tptp.s _let_2 (tptp.i _let_8 (tptp.s _let_2 (tptp.i _let_12 _let_6))))))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_11 (tptp.s _let_2 (tptp.i _let_10 (tptp.s _let_2 (tptp.i _let_8 (tptp.s _let_2 (tptp.i _let_12 _let_3))))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_11 (tptp.s _let_2 (tptp.i _let_10 (tptp.s _let_2 (tptp.i _let_8 _let_6))))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 tptp.empty))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 D0))) _let_3)))) (let ((_let_7 (tptp.s _let_1 B0))) (let ((_let_8 (tptp.s _let_4 (tptp.i _let_5 _let_7)))) (let ((_let_9 (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 A5))))) (let ((_let_10 (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear))) (let ((_let_11 (tptp.s _let_1 C0))) (let ((_let_12 (tptp.s _let_4 (tptp.i _let_5 _let_11)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 (tptp.s _let_2 (tptp.i _let_9 (tptp.s _let_2 (tptp.i _let_8 (tptp.s _let_2 (tptp.i _let_12 _let_3))))))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 (tptp.s _let_2 (tptp.i _let_8 (tptp.s _let_2 (tptp.i _let_12 _let_6))))))) (not (= _let_7 _let_11))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 (tptp.s _let_2 (tptp.i _let_9 (tptp.s _let_2 (tptp.i _let_8 _let_6))))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real tptp.n20))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 Z0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_1 Y))) (let ((_let_7 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun tptp.num _let_1) tptp.vec) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) (let ((_let_8 (tptp.s _let_1 X))) (let ((_let_9 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_1 _let_2) tptp.orthogonal) _let_8)))) (=> (and (not (= _let_8 _let_7)) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_3)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_2 tptp.empty))))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))) (let ((_let_3 (tptp.s _let_1 tptp.numeral))) (let ((_let_4 (tptp.s tptp.num (tptp.i _let_3 (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) _let_2)))))) (let ((_let_5 (tptp.cart tptp.real tptp.n20))) (let ((_let_6 (tptp.s _let_5 X))) (let ((_let_7 (tptp.fun tptp.num tptp.real))) (let ((_let_8 (tptp.s (tptp.fun _let_5 _let_7) tptp.d_))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 _let_6)))) (let ((_let_10 (tptp.s tptp.real (tptp.i _let_9 _let_4)))) (let ((_let_11 (tptp.s _let_5 Z0))) (let ((_let_12 (tptp.s _let_7 (tptp.i _let_8 _let_11)))) (let ((_let_13 (tptp.fun tptp.real tptp.real))) (let ((_let_14 (tptp.fun tptp.real _let_13))) (let ((_let_15 (tptp.s _let_14 tptp.realu_sub))) (let ((_let_16 (tptp.s tptp.num (tptp.i _let_3 _let_2)))) (let ((_let_17 (tptp.s tptp.real (tptp.i _let_9 _let_16)))) (let ((_let_18 (tptp.s _let_5 Y))) (let ((_let_19 (tptp.s _let_7 (tptp.i _let_8 _let_18)))) (let ((_let_20 (tptp.s _let_14 tptp.realu_mul))) (let ((_let_21 (tptp.fun _let_5 tptp.bool))) (let ((_let_22 (tptp.fun _let_21 _let_21))) (let ((_let_23 (tptp.s (tptp.fun _let_5 _let_22) tptp.insert))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_21 tptp.bool) tptp.collinear) (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i _let_23 _let_6)) (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i _let_23 _let_18)) (tptp.s _let_21 (tptp.i (tptp.s _let_22 (tptp.i _let_23 _let_11)) (tptp.s _let_21 tptp.empty)))))))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i _let_20 (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i _let_15 (tptp.s tptp.real (tptp.i _let_12 _let_16)))) _let_17)))) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i _let_15 (tptp.s tptp.real (tptp.i _let_19 _let_4)))) _let_10)))) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i _let_20 (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i _let_15 (tptp.s tptp.real (tptp.i _let_19 _let_16)))) _let_17)))) (tptp.s tptp.real (tptp.i (tptp.s _let_13 (tptp.i _let_15 (tptp.s tptp.real (tptp.i _let_12 _let_4)))) _let_10)))))))))))))))))))))))))))))) (forall ((Q141274 $$unsorted) (A5 $$unsorted) (X $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q141274))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_8 (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 A5))))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.s _let_4 (tptp.i _let_8 _let_2)))) (let ((_let_11 (tptp.fun _let_4 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun _let_1 _let_11) tptp.between) _let_3)) _let_10))) (= (tptp.s tptp.real (tptp.i _let_7 _let_10)) (tptp.s tptp.real (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun tptp.real _let_9) tptp.realu_add) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i _let_8 _let_3)))))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))))))))))))))))))) (forall ((Q141313 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q141313))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.c_) _let_2)))) (let ((_let_6 (tptp.fun _let_3 tptp.bool))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.between))) (let ((_let_8 (tptp.s _let_6 (tptp.i _let_7 _let_2)))) (let ((_let_9 (tptp.s _let_1 B0))) (let ((_let_10 (tptp.s _let_3 (tptp.i _let_5 _let_9)))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_8 _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_9)) _let_10))) (tptp.p (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_3 (tptp.i _let_5 _let_2))))))))))))))))) (forall ((Q141347 $$unsorted) (A5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q141347))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.between) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_2)) _let_2))))) (= _let_3 _let_2))))))))) (forall ((Q141372 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q141372))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.between) (tptp.s _let_1 X))))) (= (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_3)))) (tptp.s tptp.bool (tptp.i _let_8 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))))))))))))) (forall ((Q141403 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q141403))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.s _let_1 C0))) (let ((_let_5 (tptp.prod _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_1 _let_6) tptp.c_))) (let ((_let_8 (tptp.fun _let_5 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.between))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_2)) _let_4))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_4)))))) (= _let_3 _let_2)))))))))))) (forall ((Q141441 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q141441))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.c_))) (let ((_let_6 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 B0))) _let_2)))) (let ((_let_7 (tptp.fun _let_3 tptp.bool))) (let ((_let_8 (tptp.s (tptp.fun _let_1 _let_7) tptp.between))) (let ((_let_9 (tptp.s _let_7 (tptp.i _let_8 (tptp.s _let_1 D0))))) (let ((_let_10 (tptp.s _let_1 A5))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_7 (tptp.i _let_8 _let_10)) _let_6))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_10)) _let_2)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_6))))))))))))))) (forall ((Q141483 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted) (D0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q141483))) (let ((_let_2 (tptp.s _let_1 D0))) (let ((_let_3 (tptp.s _let_1 C0))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s _let_1 A5))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.between))) (let ((_let_10 (tptp.s _let_8 (tptp.i _let_9 _let_7)))) (let ((_let_11 (tptp.s _let_1 B0))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i _let_10 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_11)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_11)))))) (tptp.p (tptp.s tptp.bool (tptp.i _let_10 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub))) (let ((_let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) (let ((_let_7 (tptp.s _let_1 B0))) (let ((_let_8 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) _let_3)))) (let ((_let_9 (tptp.s (tptp.fun _let_1 tptp.real) tptp.vectoru_norm))) (let ((_let_10 (tptp.s (tptp.fun tptp.real _let_4) tptp.r_))) (let ((_let_11 (tptp.prod _let_1 _let_1))) (let ((_let_12 (tptp.fun _let_1 _let_11))) (let ((_let_13 (tptp.fun _let_11 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_1 _let_13) tptp.between) _let_3)) (tptp.s _let_11 (tptp.i (tptp.s _let_12 (tptp.i (tptp.s (tptp.fun _let_1 _let_12) tptp.c_) _let_2)) _let_7))))) (= (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_6)))) _let_8)) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_10 (tptp.s tptp.real (tptp.i _let_9 _let_8)))) _let_6)))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_sub))) (let ((_let_6 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) _let_2)))) (let ((_let_7 (tptp.fun _let_1 tptp.real))) (let ((_let_8 (tptp.s _let_7 tptp.vectoru_norm))) (let ((_let_9 (tptp.s _let_1 A5))) (let ((_let_10 (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_2)) _let_9)))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.prod _let_1 _let_1))) (let ((_let_13 (tptp.fun _let_1 _let_12))) (let ((_let_14 (tptp.fun _let_12 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_14 (tptp.i (tptp.s (tptp.fun _let_1 _let_14) tptp.between) _let_2)) (tptp.s _let_12 (tptp.i (tptp.s _let_13 (tptp.i (tptp.s (tptp.fun _let_1 _let_13) tptp.c_) _let_9)) _let_3))))) (= (tptp.s tptp.real (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.dot) _let_10)) _let_6)) (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_mul) (tptp.s tptp.real (tptp.i _let_8 _let_10)))) (tptp.s tptp.real (tptp.i _let_8 _let_6))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.between) _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_2)) (tptp.s _let_1 X)))))) (not (= _let_3 _let_2))) (exists ((D0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (let ((_let_5 (tptp.s tptp.real D0))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun tptp.real _let_6) tptp.realu_le) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s (tptp.fun tptp.num tptp.num) tptp.numeral) (tptp.s tptp.num tptp.u_0))))))) _let_5))) (= (tptp.s _let_1 X) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.vectoru_add) _let_2)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s (tptp.fun tptp.real _let_3) tptp.r_) _let_5)) (tptp.s _let_1 (tptp.i (tptp.s _let_3 (tptp.i (tptp.s _let_4 tptp.vectoru_sub) _let_2)) (tptp.s _let_1 A5)))))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_1 X))) (let ((_let_7 (tptp.s _let_1 A5))) (let ((_let_8 (tptp.prod _let_1 _let_1))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.fun _let_8 tptp.bool))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_1 _let_10) tptp.between) _let_6)) (tptp.s _let_8 (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.c_) _let_7)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_7)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_2 tptp.empty)))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s _let_1 C0))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (let ((_let_9 (tptp.s (tptp.fun _let_1 _let_8) tptp.between))) (let ((_let_10 (tptp.fun _let_1 tptp.bool))) (let ((_let_11 (tptp.fun _let_10 _let_10))) (let ((_let_12 (tptp.s (tptp.fun _let_1 _let_11) tptp.insert))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_10 tptp.bool) tptp.collinear) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_3)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_2)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_7)) (tptp.s _let_10 tptp.empty)))))))))) (or (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_3)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_7))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_2)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_7)) _let_3))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_8 (tptp.i _let_9 _let_7)) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))))))))))))))))))) (forall ((Q142205 $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q142205))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))) (let ((_let_8 (tptp.s _let_1 X))) (let ((_let_9 (tptp.fun _let_4 tptp.bool))) (let ((_let_10 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_11 (tptp.s tptp.real (tptp.i _let_10 _let_7)))) (let ((_let_12 (tptp.s _let_5 (tptp.i _let_6 _let_8)))) (let ((_let_13 (tptp.fun tptp.real tptp.bool))) (let ((_let_14 (tptp.s (tptp.fun tptp.real _let_13) tptp.realu_le))) (let ((_let_15 (tptp.fun _let_1 tptp.bool))) (let ((_let_16 (tptp.fun _let_15 _let_15))) (let ((_let_17 (tptp.s (tptp.fun _let_1 _let_16) tptp.insert))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_15 tptp.bool) tptp.collinear) (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i _let_17 _let_8)) (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i _let_17 _let_3)) (tptp.s _let_15 (tptp.i (tptp.s _let_16 (tptp.i _let_17 _let_2)) (tptp.s _let_15 tptp.empty)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.real (tptp.i _let_10 (tptp.s _let_4 (tptp.i _let_12 _let_3)))))) _let_11))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_13 (tptp.i _let_14 (tptp.s tptp.real (tptp.i _let_10 (tptp.s _let_4 (tptp.i _let_12 _let_2)))))) _let_11)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_9 (tptp.i (tptp.s (tptp.fun _let_1 _let_9) tptp.between) _let_8)) _let_7)))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))) (let ((_let_8 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_9 (tptp.s tptp.real (tptp.i _let_8 _let_7)))) (let ((_let_10 (tptp.s _let_1 X))) (let ((_let_11 (tptp.s _let_5 (tptp.i _let_6 _let_10)))) (let ((_let_12 (tptp.fun tptp.real tptp.bool))) (let ((_let_13 (tptp.s (tptp.fun tptp.real _let_12) tptp.realu_le))) (let ((_let_14 (tptp.fun _let_1 tptp.bool))) (let ((_let_15 (tptp.fun _let_14 _let_14))) (let ((_let_16 (tptp.s (tptp.fun _let_1 _let_15) tptp.insert))) (let ((_let_17 (tptp.fun _let_4 tptp.bool))) (= (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_17 (tptp.i (tptp.s (tptp.fun _let_1 _let_17) tptp.between) _let_10)) _let_7))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_14 tptp.bool) tptp.collinear) (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_16 _let_3)) (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_16 _let_10)) (tptp.s _let_14 (tptp.i (tptp.s _let_15 (tptp.i _let_16 _let_2)) (tptp.s _let_14 tptp.empty)))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i _let_11 _let_3)))))) _let_9))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_12 (tptp.i _let_13 (tptp.s tptp.real (tptp.i _let_8 (tptp.s _let_4 (tptp.i _let_11 _let_2)))))) _let_9))))))))))))))))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real tptp.n10) tptp.bool))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.collinear) (tptp.s _let_1 S0)))))) (forall ((Q142377 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q142377))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun tptp.num tptp.num))) (let ((_let_6 (tptp.prod _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_6 _let_1) tptp.midpoint) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_1 _let_7) tptp.c_) _let_3)) _let_2)))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun tptp.real _let_4) tptp.r_) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.real tptp.real) tptp.realu_inv) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_5 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (tptp.s _let_1 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.vectoru_add) _let_3)) _let_2))))))))))))) (forall ((Q142390 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q142390))) (let ((_let_2 (tptp.s _let_1 X))) (let ((_let_3 (tptp.prod _let_1 _let_1))) (let ((_let_4 (tptp.fun _let_1 _let_3))) (= (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_3 _let_1) tptp.midpoint) (tptp.s _let_3 (tptp.i (tptp.s _let_4 (tptp.i (tptp.s (tptp.fun _let_1 _let_4) tptp.c_) _let_2)) _let_2)))) _let_2)))))) (forall ((Q142414 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q142414))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 _let_1) tptp.midpoint))) (= (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_3)))) (tptp.s _let_1 (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))))))))))))) (forall ((Q142467 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.num tptp.num))) (let ((_let_2 (tptp.cart tptp.real Q142467))) (let ((_let_3 (tptp.s _let_2 B0))) (let ((_let_4 (tptp.s _let_2 A5))) (let ((_let_5 (tptp.prod _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.s (tptp.fun _let_2 _let_6) tptp.c_))) (let ((_let_8 (tptp.s _let_6 (tptp.i _let_7 _let_4)))) (let ((_let_9 (tptp.s _let_5 (tptp.i _let_8 _let_3)))) (let ((_let_10 (tptp.s (tptp.fun _let_5 tptp.real) tptp.distance))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.s tptp.real (tptp.i (tptp.s _let_11 (tptp.i (tptp.s (tptp.fun tptp.real _let_11) tptp.realu_div) (tptp.s tptp.real (tptp.i _let_10 _let_9)))) (tptp.s tptp.real (tptp.i (tptp.s (tptp.fun tptp.num tptp.real) tptp.realu_ofu_num) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.numeral) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit0) (tptp.s tptp.num (tptp.i (tptp.s _let_1 tptp.bit1) (tptp.s tptp.num tptp.u_0))))))))))))) (let ((_let_13 (tptp.s _let_2 (tptp.i (tptp.s (tptp.fun _let_5 _let_2) tptp.midpoint) _let_9)))) (let ((_let_14 (tptp.s _let_6 (tptp.i _let_7 _let_13)))) (and (= (tptp.s tptp.real (tptp.i _let_10 (tptp.s _let_5 (tptp.i _let_8 _let_13)))) _let_12) (= (tptp.s tptp.real (tptp.i _let_10 (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i _let_7 _let_3)) _let_13)))) _let_12) (= (tptp.s tptp.real (tptp.i _let_10 (tptp.s _let_5 (tptp.i _let_14 _let_4)))) _let_12) (= (tptp.s tptp.real (tptp.i _let_10 (tptp.s _let_5 (tptp.i _let_14 _let_3)))) _let_12))))))))))))))))) (forall ((Q142613 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q142613))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (= _let_3 _let_2))) (let ((_let_5 (tptp.prod _let_1 _let_1))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_5 _let_1) tptp.midpoint) (tptp.s _let_5 (tptp.i (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_1 _let_6) tptp.c_) _let_3)) _let_2)))))) (and (= (= _let_7 _let_3) _let_4) (= (= _let_7 _let_2) _let_4) (= (= _let_3 _let_7) _let_4) (= (= _let_2 _let_7) _let_4)))))))))) (forall ((Q142636 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q142636))) (let ((_let_2 (tptp.s _let_1 A5))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_2)) _let_3)))) (let ((_let_8 (tptp.fun _let_4 tptp.bool))) (let ((_let_9 (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.between) (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.midpoint) _let_7)))))) (and (tptp.p (tptp.s tptp.bool (tptp.i _let_9 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i _let_9 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))))))))))))))) (forall ((Q142675 $$unsorted) (Q142689 $$unsorted) (F0 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q142689))) (let ((_let_2 (tptp.s _let_1 B0))) (let ((_let_3 (tptp.s _let_1 A5))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.cart tptp.real Q142675))) (let ((_let_7 (tptp.fun _let_1 _let_6))) (let ((_let_8 (tptp.s _let_7 F0))) (let ((_let_9 (tptp.prod _let_6 _let_6))) (let ((_let_10 (tptp.fun _let_6 _let_9))) (=> (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) tptp.linear) _let_8))) (= (tptp.s _let_6 (tptp.i (tptp.s (tptp.fun _let_9 _let_6) tptp.midpoint) (tptp.s _let_9 (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_6 _let_10) tptp.c_) (tptp.s _let_6 (tptp.i _let_8 _let_3)))) (tptp.s _let_6 (tptp.i _let_8 _let_2)))))) (tptp.s _let_6 (tptp.i _let_8 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.midpoint) (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i (tptp.s (tptp.fun _let_1 _let_5) tptp.c_) _let_3)) _let_2))))))))))))))))))) (forall ((Q142719 $$unsorted) (A5 $$unsorted) (B0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q142719))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) tptp.insert))) (let ((_let_6 (tptp.s _let_1 A5))) (let ((_let_7 (tptp.prod _let_1 _let_1))) (let ((_let_8 (tptp.fun _let_1 _let_7))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) tptp.collinear) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_6)) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_7 _let_1) tptp.midpoint) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_1 _let_8) tptp.c_) _let_6)) _let_3)))))) (tptp.s _let_2 (tptp.i (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_2 tptp.empty))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_8 (tptp.s _let_1 A5))) (let ((_let_9 (tptp.s _let_5 (tptp.i _let_6 _let_8)))) (let ((_let_10 (tptp.fun _let_1 tptp.bool))) (let ((_let_11 (tptp.fun _let_10 _let_10))) (let ((_let_12 (tptp.s (tptp.fun _let_1 _let_11) tptp.insert))) (=> (not (= _let_8 _let_2)) (= (= _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.midpoint) (tptp.s _let_4 (tptp.i _let_9 _let_2))))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_10 tptp.bool) tptp.collinear) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_8)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_3)) (tptp.s _let_10 (tptp.i (tptp.s _let_11 (tptp.i _let_12 _let_2)) (tptp.s _let_10 tptp.empty)))))))))) (= (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i _let_9 _let_3)))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2))))))))))))))))))))) (forall ((N $$unsorted) (A5 $$unsorted) (B0 $$unsorted) (C0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.s _let_1 C0))) (let ((_let_3 (tptp.s _let_1 B0))) (let ((_let_4 (tptp.prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s (tptp.fun _let_1 _let_5) tptp.c_))) (let ((_let_7 (tptp.s (tptp.fun _let_4 tptp.real) tptp.distance))) (let ((_let_8 (tptp.s _let_5 (tptp.i _let_6 (tptp.s _let_1 A5))))) (let ((_let_9 (tptp.s _let_4 (tptp.i _let_8 _let_2)))) (let ((_let_10 (tptp.fun _let_4 tptp.bool))) (= (= _let_3 (tptp.s _let_1 (tptp.i (tptp.s (tptp.fun _let_4 _let_1) tptp.midpoint) _let_9))) (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s _let_10 (tptp.i (tptp.s (tptp.fun _let_1 _let_10) tptp.between) _let_3)) _let_9))) (= (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i _let_8 _let_3)))) (tptp.s tptp.real (tptp.i _let_7 (tptp.s _let_4 (tptp.i (tptp.s _let_5 (tptp.i _let_6 _let_3)) _let_2)))))))))))))))))) (forall ((N $$unsorted) (M $$unsorted) (P0 $$unsorted) (Q0 $$unsorted)) (=> (and (forall ((F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) P0) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) Q0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))))))))))))) (forall ((G0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real N))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.cart tptp.real M))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) Q0) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) P0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3)))))))))))))))) (forall ((F0 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.cart tptp.real M) (tptp.cart tptp.real N)))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_1 tptp.bool) tptp.linear) (tptp.s _let_1 F0)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2))))))))) (forall ((S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real M))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real N))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_6 tptp.bool) Q0) (tptp.s _let_6 (tptp.i (tptp.s _let_7 (tptp.i (tptp.s (tptp.fun _let_5 _let_7) tptp.image) (tptp.s _let_5 F0))) _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) P0) _let_3)))))))))))))))) (forall ((Q143197 $$unsorted) (Q143187 $$unsorted) (P0 $$unsorted) (Q0 $$unsorted) (F0 $$unsorted) (S0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143187))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 S0))) (let ((_let_4 (tptp.cart tptp.real Q143197))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 F0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (forall ((H0 $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143187))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 U))) (let ((_let_4 (tptp.cart tptp.real Q143197))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 H0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) P0) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) Q0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))))))))))))) (forall ((G0 $$unsorted) (T0 $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143197))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.s _let_2 T0))) (let ((_let_4 (tptp.cart tptp.real Q143187))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.s _let_5 G0))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (=> (and (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) Q0) _let_3))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6)))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) P0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3))))))))))))))) (tptp.p (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_5 tptp.bool) tptp.linear) _let_6))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.cart tptp.real Q143187))) (let ((_let_2 (tptp.s _let_1 Y))) (let ((_let_3 (tptp.s _let_1 X))) (let ((_let_4 (tptp.cart tptp.real Q143197))) (let ((_let_5 (tptp.s (tptp.fun _let_1 _let_4) F0))) (=> (= (tptp.s _let_4 (tptp.i _let_5 _let_3)) (tptp.s _let_4 (tptp.i _let_5 _let_2))) (= _let_3 _let_2))))))))) (= (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_7 tptp.bool) Q0) (tptp.s _let_7 (tptp.i (tptp.s _let_8 (tptp.i (tptp.s (tptp.fun _let_5 _let_8) tptp.image) _let_6)) _let_3)))) (tptp.s tptp.bool (tptp.i (tptp.s (tptp.fun _let_2 tptp.bool) P0) _let_3))))))))))))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 8.13/8.36  )
% 8.13/8.36  % SZS output end Proof for GEO479+1
% 8.13/8.36  % cvc5---1.0.5 exiting
% 8.13/8.36  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------