%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n010.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 31 17:19:55 EDT 2022

% Result   : Theorem 2.12s 0.70s
% Output   : Refutation 2.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  565
% Syntax   : Number of formulae    :  570 (   7 unt; 563 typ;   0 def)
%            Number of atoms       :    7 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :  129 ( 127 usr;   1 ari)
%            Number of type conns  :  617 ( 374   >; 243   *;   0   +;   0  <<)
%            Number of predicates  :  127 ( 126 usr;   1 prp; 0-2 aty)
%            Number of functors    :  310 ( 310 usr;  62 con; 0-3 aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    'C_ell2_c_ell2_cblinfun_complex_fun$': $tType ).

tff(type_def_6,type,
    'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

tff(type_def_7,type,
    'Unit_ell2_unit_ell2_cblinfun$': $tType ).

tff(type_def_8,type,
    'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_9,type,
    'A_a_prod_ell2$': $tType ).

tff(type_def_10,type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_11,type,
    'A_ell2_a_ell2_cblinfun$': $tType ).

tff(type_def_12,type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

tff(type_def_13,type,
    'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_14,type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_15,type,
    'Complex_c_ell2_c_ell2_cblinfun_fun$': $tType ).

tff(type_def_16,type,
    'A_a_a_b_complement_domain_prod_prod_ell2_a_a_prod_a_b_complement_domain_prod_ell2_cblinfun$': $tType ).

tff(type_def_17,type,
    'B_ell2_b_ell2_cblinfun$': $tType ).

tff(type_def_18,type,
    'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$': $tType ).

tff(type_def_19,type,
    'A_a_b_complement_domain_prod_ell2_b_ell2_cblinfun$': $tType ).

tff(type_def_20,type,
    'B_a_a_b_complement_domain_prod_prod_ell2_b_a_a_b_complement_domain_prod_prod_ell2_cblinfun$': $tType ).

tff(type_def_21,type,
    'A_ell2_a_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_22,type,
    'Complex_complex_prod_complex_complex_prod_fun$': $tType ).

tff(type_def_23,type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_24,type,
    'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$': $tType ).

tff(type_def_25,type,
    'A_a_prod$': $tType ).

tff(type_def_26,type,
    'B_a_prod_a_b_complement_domain_prod_ell2_b_a_a_b_complement_domain_prod_prod_ell2_cblinfun$': $tType ).

tff(type_def_27,type,
    'B_a_a_b_complement_domain_prod_prod_ell2_b_a_prod_a_b_complement_domain_prod_ell2_cblinfun$': $tType ).

tff(type_def_28,type,
    'C_c_prod_ell2_c_c_prod_ell2_cblinfun_c_c_prod_ell2_c_c_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_29,type,
    'A_b_prod_ell2_b_b_prod_ell2_cblinfun$': $tType ).

tff(type_def_30,type,
    'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_31,type,
    'A_ell2_complex_cblinfun$': $tType ).

tff(type_def_32,type,
    'A_a_prod_ell2_a_a_prod_ell2_cblinfun$': $tType ).

tff(type_def_33,type,
    'A_ell2_a_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

tff(type_def_34,type,
    'A_ell2_a_ell2_cblinfun_complex_fun$': $tType ).

tff(type_def_35,type,
    'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_36,type,
    'C_ell2_c_ell2_cblinfun$': $tType ).

tff(type_def_37,type,
    'A_ell2_a_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$': $tType ).

tff(type_def_38,type,
    'Complex_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_39,type,
    'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun$': $tType ).

tff(type_def_40,type,
    'A_a_prod_ell2_a_b_prod_ell2_cblinfun$': $tType ).

tff(type_def_41,type,
    'B_ell2_complex_cblinfun$': $tType ).

tff(type_def_42,type,
    'B_a_prod_ell2$': $tType ).

tff(type_def_43,type,
    'Complex_a_ell2_cblinfun$': $tType ).

tff(type_def_44,type,
    'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_45,type,
    'A_a_prod_a_b_complement_domain_prod_ell2_a_a_prod_a_b_complement_domain_prod_ell2_cblinfun$': $tType ).

tff(type_def_46,type,
    'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

tff(type_def_47,type,
    'B$': $tType ).

tff(type_def_48,type,
    'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_49,type,
    'A_b_complement_domain_ell2$': $tType ).

tff(type_def_50,type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_51,type,
    'Complex_complex_cblinfun$': $tType ).

tff(type_def_52,type,
    'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_53,type,
    'A_a_a_b_complement_domain_prod_prod_ell2_a_a_a_b_complement_domain_prod_prod_ell2_cblinfun$': $tType ).

tff(type_def_54,type,
    'A_b_prod_ell2$': $tType ).

tff(type_def_55,type,
    'Complex$': $tType ).

tff(type_def_56,type,
    'B_ell2_b_ell2_cblinfun_complex_fun$': $tType ).

tff(type_def_57,type,
    'A_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_58,type,
    'B_b_prod_ell2$': $tType ).

tff(type_def_59,type,
    'A_a_prod_ell2_a_a_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_60,type,
    'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$': $tType ).

tff(type_def_61,type,
    'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_62,type,
    'B_b_prod_ell2_a_b_prod_ell2_cblinfun$': $tType ).

tff(type_def_63,type,
    'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

tff(type_def_64,type,
    'A_a_b_complement_domain_prod$': $tType ).

tff(type_def_65,type,
    'A_a_prod_ell2_b_b_prod_ell2_cblinfun$': $tType ).

tff(type_def_66,type,
    'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_67,type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_68,type,
    'Complex_complex_fun$': $tType ).

tff(type_def_69,type,
    'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$': $tType ).

tff(type_def_70,type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_71,type,
    'B_b_prod_ell2_a_a_prod_ell2_cblinfun$': $tType ).

tff(type_def_72,type,
    'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_73,type,
    'B_b_a_complement_domain_prod_ell2_b_b_a_complement_domain_prod_ell2_cblinfun$': $tType ).

tff(type_def_74,type,
    'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_75,type,
    'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_76,type,
    'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

tff(type_def_77,type,
    'A_a_prod_ell2_b_a_prod_ell2_cblinfun$': $tType ).

tff(type_def_78,type,
    tlbool: $tType ).

tff(type_def_79,type,
    'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

tff(type_def_80,type,
    'B_b_prod$': $tType ).

tff(type_def_81,type,
    'Complex_complex_complex_prod_complex_complex_prod_fun_fun$': $tType ).

tff(type_def_82,type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$': $tType ).

tff(type_def_83,type,
    'A_a_a_complement_domain_prod_ell2_a_a_a_complement_domain_prod_ell2_cblinfun$': $tType ).

tff(type_def_84,type,
    'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

tff(type_def_85,type,
    'Complex_complex_fun_complex_complex_fun_fun$': $tType ).

tff(type_def_86,type,
    'B_a_prod_ell2_b_a_prod_ell2_cblinfun$': $tType ).

tff(type_def_87,type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

tff(type_def_88,type,
    'A_b_prod$': $tType ).

tff(type_def_89,type,
    'Complex_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_90,type,
    'Unit_ell2_unit_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

tff(type_def_91,type,
    'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_92,type,
    'A_b_complement_domain$': $tType ).

tff(type_def_93,type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$': $tType ).

tff(type_def_94,type,
    'A_ell2$': $tType ).

tff(type_def_95,type,
    'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_96,type,
    'A_b_prod_ell2_b_a_prod_ell2_cblinfun$': $tType ).

tff(type_def_97,type,
    'A$': $tType ).

tff(type_def_98,type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_99,type,
    'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_100,type,
    'B_a_prod$': $tType ).

tff(type_def_101,type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_102,type,
    'B_a_prod_a_b_complement_domain_prod_ell2_b_a_prod_a_b_complement_domain_prod_ell2_cblinfun$': $tType ).

tff(type_def_103,type,
    'A_ell2_a_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_104,type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun$': $tType ).

tff(type_def_105,type,
    'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_106,type,
    'B_a_prod_ell2_a_b_prod_ell2_cblinfun$': $tType ).

tff(type_def_107,type,
    'A_b_prod_ell2_a_a_prod_ell2_cblinfun$': $tType ).

tff(type_def_108,type,
    'A_a_b_complement_domain_prod_ell2$': $tType ).

tff(type_def_109,type,
    'Complex_b_ell2_cblinfun$': $tType ).

tff(type_def_110,type,
    'B_a_prod_ell2_a_a_prod_ell2_cblinfun$': $tType ).

tff(type_def_111,type,
    'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_112,type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_113,type,
    'B_b_b_complement_domain_prod_ell2_b_b_b_complement_domain_prod_ell2_cblinfun$': $tType ).

tff(type_def_114,type,
    'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_115,type,
    'B_c_prod_ell2_b_c_prod_ell2_cblinfun_b_c_prod_ell2_b_c_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_116,type,
    'B_ell2_a_ell2_cblinfun$': $tType ).

tff(type_def_117,type,
    'Unit_ell2_unit_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_118,type,
    'A_a_prod_a_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_prod_ell2_cblinfun$': $tType ).

tff(type_def_119,type,
    'Complex_complex_prod$': $tType ).

tff(type_def_120,type,
    'Complex_complex_complex_fun_fun$': $tType ).

tff(type_def_121,type,
    'A_ell2_b_ell2_cblinfun$': $tType ).

tff(type_def_122,type,
    'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_123,type,
    'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$': $tType ).

tff(type_def_124,type,
    'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_125,type,
    'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

tff(type_def_126,type,
    'B_ell2$': $tType ).

tff(type_def_127,type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$': $tType ).

tff(type_def_128,type,
    'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

tff(type_def_129,type,
    'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

tff(type_def_130,type,
    'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

tff(type_def_131,type,
    'A_b_prod_ell2_a_b_prod_ell2_cblinfun$': $tType ).

tff(func_def_0,type,
    'fun_app$': ( 'Complex_complex_fun$' * 'Complex$' ) > 'Complex$' ).

tff(func_def_1,type,
    'comp$b': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_2,type,
    'comp$av': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_3,type,
    'comp$ac': ( 'C_ell2_c_ell2_cblinfun_complex_fun$' * 'Complex_c_ell2_c_ell2_cblinfun_fun$' ) > 'Complex_complex_fun$' ).

tff(func_def_4,type,
    'butterfly$s': ( 'A_a_prod_ell2$' * 'B_a_prod_ell2$' ) > 'B_a_prod_ell2_a_a_prod_ell2_cblinfun$' ).

tff(func_def_5,type,
    'register_pair$a': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_6,type,
    'tensor_op$q': ( 'A_ell2_a_ell2_cblinfun$' * 'B_ell2_a_ell2_cblinfun$' ) > 'A_b_prod_ell2_a_a_prod_ell2_cblinfun$' ).

tff(func_def_7,type,
    'tensor_op$j': ( 'B_ell2_a_ell2_cblinfun$' * 'A_ell2_b_ell2_cblinfun$' ) > 'B_a_prod_ell2_a_b_prod_ell2_cblinfun$' ).

tff(func_def_8,type,
    'butterfly$b': ( 'Complex$' * 'Complex$' ) > 'Complex_complex_cblinfun$' ).

tff(func_def_9,type,
    'register_pair$': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_10,type,
    'register_pair$c': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_11,type,
    'fun_app$x': ( 'A_ell2_a_ell2_cblinfun_complex_fun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'Complex$' ).

tff(func_def_12,type,
    'register_tensor$e': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'B_c_prod_ell2_b_c_prod_ell2_cblinfun_b_c_prod_ell2_b_c_prod_ell2_cblinfun_fun$' ).

tff(func_def_13,type,
    'butterfly$c': ( 'A_ell2$' * 'Complex$' ) > 'Complex_a_ell2_cblinfun$' ).

tff(func_def_14,type,
    'tensor_op$i': ( 'B_ell2_a_ell2_cblinfun$' * 'B_ell2_a_ell2_cblinfun$' ) > 'B_b_prod_ell2_a_a_prod_ell2_cblinfun$' ).

tff(func_def_15,type,
    'id$i': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

tff(func_def_16,type,
    'cblinfun_apply$f': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' * 'A_b_complement_domain_ell2$' ) > 'A_b_complement_domain_ell2$' ).

tff(func_def_17,type,
    'comp$ar': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_18,type,
    'id$b': 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ).

tff(func_def_19,type,
    'adj$e': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

tff(func_def_20,type,
    'scaleC$i': ( 'Complex$' * 'B_ell2$' ) > 'B_ell2$' ).

tff(func_def_21,type,
    'cblinfun_cinner_right$': 'Complex$' > 'Complex_complex_cblinfun$' ).

tff(func_def_22,type,
    'ket$f': 'A_a_b_complement_domain_prod$' > 'A_a_b_complement_domain_prod_ell2$' ).

tff(func_def_23,type,
    'pair$b': ( 'A$' * 'B$' ) > 'A_b_prod$' ).

tff(func_def_24,type,
    'id_cblinfun$d': 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_25,type,
    'tensor_op$g': ( 'B_ell2_b_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'B_a_prod_ell2_b_a_prod_ell2_cblinfun$' ).

tff(func_def_26,type,
    'empty_var$c': 'Unit_ell2_unit_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_27,type,
    'times$': 'Complex$' > 'Complex_complex_fun$' ).

tff(func_def_28,type,
    'comp$x': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_29,type,
    'tensor_op$r': ( 'A_ell2_a_ell2_cblinfun$' * 'A_ell2_b_ell2_cblinfun$' ) > 'A_a_prod_ell2_a_b_prod_ell2_cblinfun$' ).

tff(func_def_30,type,
    'butterfly$o': ( 'B_ell2$' * 'A_ell2$' ) > 'A_ell2_b_ell2_cblinfun$' ).

tff(func_def_31,type,
    'cblinfun_compose$a': 'A_ell2_a_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_32,type,
    'snd$': 'A_ell2_a_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_33,type,
    'cblinfun_mult_right$': 'Complex$' > 'Complex_complex_cblinfun$' ).

tff(func_def_34,type,
    'tensor_op$': ( 'A_ell2_a_ell2_cblinfun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_35,type,
    'register_tensor$f': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_36,type,
    'comp$o': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_37,type,
    'comp$au': ( 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_38,type,
    'fun_app$ai': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_39,type,
    'comp$q': 'Complex_complex_fun$' > 'Complex_complex_fun_complex_complex_fun_fun$' ).

tff(func_def_40,type,
    'id_cblinfun$b': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_41,type,
    'adj$a': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_42,type,
    'register_tensor$g': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_43,type,
    'of_complex$': 'Complex$' > 'Complex_complex_cblinfun$' ).

tff(func_def_44,type,
    'comp$a': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$' ).

tff(func_def_45,type,
    'complement$b': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_46,type,
    'cblinfun_apply$c': ( 'A_ell2_b_ell2_cblinfun$' * 'A_ell2$' ) > 'B_ell2$' ).

tff(func_def_47,type,
    'comp$af': ( 'Complex_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_complex_fun$' ) > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_48,type,
    'tensor_ell2$d': ( 'B_ell2$' * 'B_ell2$' ) > 'B_b_prod_ell2$' ).

tff(func_def_49,type,
    'comp$ad': ( 'Complex_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_complex_fun$' ) > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_50,type,
    'scaleC$a': 'Complex$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_51,type,
    'pair$a': ( 'B$' * 'B$' ) > 'B_b_prod$' ).

tff(func_def_52,type,
    'fun_app$ae': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun$' ).

tff(func_def_53,type,
    'tensor_ell2$b': ( 'A_ell2$' * 'B_ell2$' ) > 'A_b_prod_ell2$' ).

tff(func_def_54,type,
    'register_tensor$a': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_55,type,
    'norm$f': $real > $real ).

tff(func_def_56,type,
    'comp$e': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_57,type,
    'comp$an': ( 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' * 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ) > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_58,type,
    'cblinfun_compose$i': ( 'B_a_prod_a_b_complement_domain_prod_ell2_b_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' * 'B_a_prod_a_b_complement_domain_prod_ell2_b_a_prod_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'B_a_prod_a_b_complement_domain_prod_ell2_b_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' ).

tff(func_def_59,type,
    'id$f': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

tff(func_def_60,type,
    'sandwich$f': 'A_a_b_complement_domain_prod_ell2_b_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_61,type,
    'cblinfun_mult_left$': 'Complex$' > 'Complex_complex_cblinfun$' ).

tff(func_def_62,type,
    'norm$': 'Complex$' > $real ).

tff(func_def_63,type,
    'vector_to_cblinfun$': 'A_ell2$' > 'Complex_a_ell2_cblinfun$' ).

tff(func_def_64,type,
    'register_pair$d': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_65,type,
    'one_dim_iso$f': 'Complex$' > 'Unit_ell2_unit_ell2_cblinfun$' ).

tff(func_def_66,type,
    'pair$': ( 'A$' * 'A$' ) > 'A_a_prod$' ).

tff(func_def_67,type,
    'complement$d': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_68,type,
    'cblinfun_apply$e': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' * 'A_a_b_complement_domain_prod_ell2$' ) > 'A_a_b_complement_domain_prod_ell2$' ).

tff(func_def_69,type,
    'scaleC$e': 'Complex$' > 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ).

tff(func_def_70,type,
    'butterfly$v': ( 'B_b_prod_ell2$' * 'A_b_prod_ell2$' ) > 'A_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

tff(func_def_71,type,
    'f$': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_72,type,
    'one$a': 'Complex_complex_cblinfun$' ).

tff(func_def_73,type,
    'comp$at': ( 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_74,type,
    'cnj$': 'Complex_complex_fun$' ).

tff(func_def_75,type,
    'scaleC$g': 'Complex$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_76,type,
    'tensor_ell2$': ( 'A_ell2$' * 'A_b_complement_domain_ell2$' ) > 'A_a_b_complement_domain_prod_ell2$' ).

tff(func_def_77,type,
    'fst$': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_78,type,
    'complement$c': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_79,type,
    'tensor_op$k': ( 'A_ell2_b_ell2_cblinfun$' * 'B_ell2_a_ell2_cblinfun$' ) > 'A_b_prod_ell2_b_a_prod_ell2_cblinfun$' ).

tff(func_def_80,type,
    'fun_app$ad': ( 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' * 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_81,type,
    'fun_app$ag': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_82,type,
    'empty_var$': 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_83,type,
    'id$h': 'Complex_complex_fun_complex_complex_fun_fun$' ).

tff(func_def_84,type,
    'adj$c': 'Complex_b_ell2_cblinfun$' > 'B_ell2_complex_cblinfun$' ).

tff(func_def_85,type,
    'arcosh$': $real > $real ).

tff(func_def_86,type,
    'scale$': ( 'Complex_complex_complex_fun_fun$' * 'Complex_complex_complex_fun_fun$' ) > 'Complex_complex_complex_prod_complex_complex_prod_fun_fun$' ).

tff(func_def_87,type,
    'comp$aq': ( 'B_c_prod_ell2_b_c_prod_ell2_cblinfun_b_c_prod_ell2_b_c_prod_ell2_cblinfun_fun$' * 'B_c_prod_ell2_b_c_prod_ell2_cblinfun_b_c_prod_ell2_b_c_prod_ell2_cblinfun_fun$' ) > 'B_c_prod_ell2_b_c_prod_ell2_cblinfun_b_c_prod_ell2_b_c_prod_ell2_cblinfun_fun$' ).

tff(func_def_88,type,
    'comp$p': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_89,type,
    'tensor_op$f': ( 'A_ell2_a_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'A_b_prod_ell2_a_b_prod_ell2_cblinfun$' ).

tff(func_def_90,type,
    'scaleC$': 'Complex_complex_complex_fun_fun$' ).

tff(func_def_91,type,
    'fun_app$aa': ( 'Complex_complex_prod_complex_complex_prod_fun$' * 'Complex_complex_prod$' ) > 'Complex_complex_prod$' ).

tff(func_def_92,type,
    'fun_app$ac': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_93,type,
    'default$a': 'B$' ).

tff(func_def_94,type,
    'complement$a': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_95,type,
    'register_tensor$c': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_96,type,
    'cblinfun_compose$': 'B_ell2_b_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_97,type,
    'zero$e': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_98,type,
    'fun_app$d': ( 'Unit_ell2_unit_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

tff(func_def_99,type,
    'comp$j': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_100,type,
    'cblinfun_apply$d': ( 'B_ell2_a_ell2_cblinfun$' * 'B_ell2$' ) > 'A_ell2$' ).

tff(func_def_101,type,
    'register_pair$b': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_102,type,
    'tensor_op$s': ( 'A_ell2_a_ell2_cblinfun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_a_a_b_complement_domain_prod_prod_ell2_a_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' ).

tff(func_def_103,type,
    'assoc_ell2$b': 'B_a_prod_a_b_complement_domain_prod_ell2_b_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' ).

tff(func_def_104,type,
    'ket$d': 'A_b_prod$' > 'A_b_prod_ell2$' ).

tff(func_def_105,type,
    'butterfly$a': ( 'B_ell2$' * 'B_ell2$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_106,type,
    'sandwich$d': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

tff(func_def_107,type,
    'zero$f': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

tff(func_def_108,type,
    'comp$ai': ( 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' * 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ) > 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_109,type,
    'cblinfun_compose$g': ( 'A_a_prod_a_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' * 'A_a_prod_a_b_complement_domain_prod_ell2_a_a_prod_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_a_prod_a_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' ).

tff(func_def_110,type,
    'one_dim_iso$d': 'Complex_complex_fun$' ).

tff(func_def_111,type,
    'assoc_ell2$': 'A_a_prod_a_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' ).

tff(func_def_112,type,
    'swap$': 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

tff(func_def_113,type,
    'ket$': 'A$' > 'A_ell2$' ).

tff(func_def_114,type,
    'comp$ag': ( 'A_ell2_a_ell2_cblinfun_complex_fun$' * 'Complex_a_ell2_a_ell2_cblinfun_fun$' ) > 'Complex_complex_fun$' ).

tff(func_def_115,type,
    'butterfly$k': ( 'B_a_prod_ell2$' * 'B_a_prod_ell2$' ) > 'B_a_prod_ell2_b_a_prod_ell2_cblinfun$' ).

tff(func_def_116,type,
    'comp$i': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_117,type,
    'scaleC$d': 'Complex$' > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_118,type,
    'butterfly$i': ( 'A_a_prod_ell2$' * 'A_a_prod_ell2$' ) > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun$' ).

tff(func_def_119,type,
    'id$e': 'Complex_complex_fun$' ).

tff(func_def_120,type,
    'butterfly$m': ( 'A_ell2$' * 'B_ell2$' ) > 'B_ell2_a_ell2_cblinfun$' ).

tff(func_def_121,type,
    'fun_app$l': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_122,type,
    'one_dim_iso$a': 'Complex$' > 'Complex_complex_cblinfun$' ).

tff(func_def_123,type,
    'tensor_op$c': ( 'B_ell2_b_ell2_cblinfun$' * 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$' ) > 'B_b_a_complement_domain_prod_ell2_b_b_a_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_124,type,
    tltrue: tlbool ).

tff(func_def_125,type,
    'sandwich$': 'B_ell2_b_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_126,type,
    'ket$a': 'B$' > 'B_ell2$' ).

tff(func_def_127,type,
    'adj$f': 'Complex_complex_cblinfun$' > 'Complex_complex_cblinfun$' ).

tff(func_def_128,type,
    'ket$g': 'A_b_complement_domain$' > 'A_b_complement_domain_ell2$' ).

tff(func_def_129,type,
    'fun_app$ak': ( 'A_ell2_a_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun$' ).

tff(func_def_130,type,
    'butterfly$q': ( 'B_a_prod_ell2$' * 'A_b_prod_ell2$' ) > 'A_b_prod_ell2_b_a_prod_ell2_cblinfun$' ).

tff(func_def_131,type,
    'comp$as': ( 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_132,type,
    'ket$e': 'B_a_prod$' > 'B_a_prod_ell2$' ).

tff(func_def_133,type,
    'adj$b': 'Complex_a_ell2_cblinfun$' > 'A_ell2_complex_cblinfun$' ).

tff(func_def_134,type,
    'comp$w': ( 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ) > 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ).

tff(func_def_135,type,
    'empty_var$b': 'Unit_ell2_unit_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

tff(func_def_136,type,
    'pair$c': ( 'B$' * 'A$' ) > 'B_a_prod$' ).

tff(func_def_137,type,
    'fun_app$r': ( 'Complex_complex_fun_complex_complex_fun_fun$' * 'Complex_complex_fun$' ) > 'Complex_complex_fun$' ).

tff(func_def_138,type,
    'unit_register$c': 'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

tff(func_def_139,type,
    'comp$c': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_140,type,
    'tensor_op$v': ( 'B_a_prod_ell2_b_a_prod_ell2_cblinfun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ) > 'B_a_prod_a_b_complement_domain_prod_ell2_b_a_prod_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_141,type,
    'cinner$': ( 'A_ell2$' * 'A_ell2$' ) > 'Complex$' ).

tff(func_def_142,type,
    'fun_app$f': ( 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun$' ) > 'C_ell2_c_ell2_cblinfun$' ).

tff(func_def_143,type,
    'cblinfun_apply$b': ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2$' ) > 'B_ell2$' ).

tff(func_def_144,type,
    'times$a': ( $real * $real ) > $real ).

tff(func_def_145,type,
    'scaleC$h': 'Complex_complex_complex_prod_complex_complex_prod_fun_fun$' ).

tff(func_def_146,type,
    'tensor_op$o': ( 'B_ell2_a_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'B_b_prod_ell2_a_b_prod_ell2_cblinfun$' ).

tff(func_def_147,type,
    'fun_app$e': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

tff(func_def_148,type,
    'id$g': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$' ).

tff(func_def_149,type,
    'fun_app$v': ( 'B_ell2_b_ell2_cblinfun_complex_fun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'Complex$' ).

tff(func_def_150,type,
    'comp$g': ( 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ) > 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_151,type,
    'comp$t': ( 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_152,type,
    'ket$b': 'A_a_prod$' > 'A_a_prod_ell2$' ).

tff(func_def_153,type,
    'butterfly$t': ( 'B_a_prod_ell2$' * 'A_a_prod_ell2$' ) > 'A_a_prod_ell2_b_a_prod_ell2_cblinfun$' ).

tff(func_def_154,type,
    'cinner$b': 'Complex$' > 'Complex_complex_fun$' ).

tff(func_def_155,type,
    'butterfly$h': ( 'A_b_complement_domain_ell2$' * 'A_b_complement_domain_ell2$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

tff(func_def_156,type,
    'comp$aw': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_157,type,
    'id$d': 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_158,type,
    'default$b': 'A_a_prod$' ).

tff(func_def_159,type,
    'scaleC$j': ( 'Complex$' * 'A_ell2$' ) > 'A_ell2$' ).

tff(func_def_160,type,
    'register_tensor$d': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_161,type,
    'comp$n': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_162,type,
    'adj$h': 'A_ell2_b_ell2_cblinfun$' > 'B_ell2_a_ell2_cblinfun$' ).

tff(func_def_163,type,
    'fun_app$af': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_164,type,
    'minus$': 'Complex$' > 'Complex_complex_fun$' ).

tff(func_def_165,type,
    'butterfly$l': ( 'B_b_prod_ell2$' * 'B_b_prod_ell2$' ) > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

tff(func_def_166,type,
    'snd$a': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

tff(func_def_167,type,
    'register_tensor$': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_c_c_prod_ell2_c_c_prod_ell2_cblinfun_fun$' ).

tff(func_def_168,type,
    'comp$r': ( 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_169,type,
    'cblinfun_compose$d': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_170,type,
    'cblinfun_compose$f': ( 'A_a_prod_a_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' * 'A_a_a_b_complement_domain_prod_prod_ell2_a_a_prod_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_a_a_b_complement_domain_prod_prod_ell2_a_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' ).

tff(func_def_171,type,
    'norm$a': 'A_ell2$' > $real ).

tff(func_def_172,type,
    'fun_app$aj': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_173,type,
    'zero$b': 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_174,type,
    'one$': 'Complex$' ).

tff(func_def_175,type,
    'assoc_ell2$a': 'A_a_a_b_complement_domain_prod_prod_ell2_a_a_prod_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_176,type,
    'fst$a': 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

tff(func_def_177,type,
    'comp$am': ( 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' * 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ) > 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_178,type,
    'butterfly$g': ( 'A_a_b_complement_domain_prod_ell2$' * 'A_a_b_complement_domain_prod_ell2$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_179,type,
    'norm$d': 'B_ell2_b_ell2_cblinfun$' > $real ).

tff(func_def_180,type,
    'default$d': 'B_a_prod$' ).

tff(func_def_181,type,
    'register_pair$e': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_a_a_complement_domain_prod_ell2_a_a_a_complement_domain_prod_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_182,type,
    'comp$m': ( 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_183,type,
    'comp$k': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_184,type,
    'cblinfun_compose$e': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

tff(func_def_185,type,
    'zero$h': 'Complex_complex_cblinfun$' ).

tff(func_def_186,type,
    'unit_register$a': 'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_187,type,
    'fun_app$n': ( 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

tff(func_def_188,type,
    'tensor_op$n': ( 'A_ell2_b_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'A_a_prod_ell2_b_a_prod_ell2_cblinfun$' ).

tff(func_def_189,type,
    'default$': 'A$' ).

tff(func_def_190,type,
    'comp$ao': ( 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' * 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ) > 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_191,type,
    'butterfly$u': ( 'A_b_prod_ell2$' * 'B_b_prod_ell2$' ) > 'B_b_prod_ell2_a_b_prod_ell2_cblinfun$' ).

tff(func_def_192,type,
    'cinner$a': ( 'B_ell2$' * 'B_ell2$' ) > 'Complex$' ).

tff(func_def_193,type,
    'comp$l': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_194,type,
    'fun_app$s': ( 'Complex_c_ell2_c_ell2_cblinfun_fun$' * 'Complex$' ) > 'C_ell2_c_ell2_cblinfun$' ).

tff(func_def_195,type,
    'id_cblinfun$a': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

tff(func_def_196,type,
    'comp$al': ( 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' * 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ) > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_197,type,
    'comp$v': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_198,type,
    'fun_app$g': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun$' ) > 'C_ell2_c_ell2_cblinfun$' ).

tff(func_def_199,type,
    'norm$c': 'A_ell2_a_ell2_cblinfun$' > $real ).

tff(func_def_200,type,
    'fun_app$b': ( 'Unit_ell2_unit_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_201,type,
    'fun_app$p': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ) > 'C_ell2_c_ell2_cblinfun$' ).

tff(func_def_202,type,
    'tensor_ell2$c': ( 'B_ell2$' * 'A_ell2$' ) > 'B_a_prod_ell2$' ).

tff(func_def_203,type,
    'fun_app$m': ( 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'C_ell2_c_ell2_cblinfun$' ).

tff(func_def_204,type,
    'tensor_op$p': ( 'A_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'A_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

tff(func_def_205,type,
    'cblinfun_scaleC_right$': 'Complex$' > 'Complex_complex_cblinfun$' ).

tff(func_def_206,type,
    'comp$s': ( 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_207,type,
    'scaleC$c': ( 'Complex$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_208,type,
    'fun_app$c': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_209,type,
    'sandwich$b': 'A_ell2_a_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_210,type,
    'tensor_op$b': ( 'A_ell2_a_ell2_cblinfun$' * 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$' ) > 'A_a_a_complement_domain_prod_ell2_a_a_a_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_211,type,
    'comp$': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_212,type,
    'unit_register$': 'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_213,type,
    'cblinfun_compose$b': ( 'Complex_a_ell2_cblinfun$' * 'A_ell2_complex_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_214,type,
    'zero$a': 'A_ell2$' ).

tff(func_def_215,type,
    'comp$f': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_216,type,
    'id$a': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_217,type,
    'butterfly$': ( 'A_ell2$' * 'A_ell2$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_218,type,
    'norm$e': 'Complex_complex_cblinfun$' > $real ).

tff(func_def_219,type,
    'fun_app$q': ( 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun$' ) > 'Unit_ell2_unit_ell2_cblinfun$' ).

tff(func_def_220,type,
    'comp$ae': ( 'B_ell2_b_ell2_cblinfun_complex_fun$' * 'Complex_b_ell2_b_ell2_cblinfun_fun$' ) > 'Complex_complex_fun$' ).

tff(func_def_221,type,
    'one_dim_iso$b': 'Complex_complex_cblinfun$' > 'Complex$' ).

tff(func_def_222,type,
    'comp$aa': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_223,type,
    'tensor_op$t': ( 'A_a_prod_ell2_a_a_prod_ell2_cblinfun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ) > 'A_a_prod_a_b_complement_domain_prod_ell2_a_a_prod_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_224,type,
    'butterfly$e': ( 'B_ell2$' * 'Complex$' ) > 'Complex_b_ell2_cblinfun$' ).

tff(func_def_225,type,
    'zero$': 'Complex$' ).

tff(func_def_226,type,
    'comp$aj': ( 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' * 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ) > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_227,type,
    tlfalse: tlbool ).

tff(func_def_228,type,
    'zero$g': 'A_b_complement_domain_ell2$' ).

tff(func_def_229,type,
    'register_pair$g': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_b_b_complement_domain_prod_ell2_b_b_b_complement_domain_prod_ell2_cblinfun$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_230,type,
    'cblinfun_compose$h': ( 'B_a_prod_a_b_complement_domain_prod_ell2_b_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' * 'B_a_a_b_complement_domain_prod_prod_ell2_b_a_prod_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'B_a_a_b_complement_domain_prod_prod_ell2_b_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' ).

tff(func_def_231,type,
    'default$e': 'B_b_prod$' ).

tff(func_def_232,type,
    'norm$b': 'B_ell2$' > $real ).

tff(func_def_233,type,
    'zero$d': 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_234,type,
    'one_dim_iso$': 'Unit_ell2_unit_ell2_cblinfun$' > 'Complex$' ).

tff(func_def_235,type,
    'fun_app$o': ( 'A_ell2_a_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

tff(func_def_236,type,
    'pair$d': ( 'A$' * 'A_b_complement_domain$' ) > 'A_a_b_complement_domain_prod$' ).

tff(func_def_237,type,
    'comp$ap': ( 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' * 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ) > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_238,type,
    'fun_app$w': ( 'Complex_a_ell2_a_ell2_cblinfun_fun$' * 'Complex$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_239,type,
    'fun_app$j': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_240,type,
    'cblinfun_apply$': 'Complex_complex_cblinfun$' > 'Complex_complex_fun$' ).

tff(func_def_241,type,
    'scaleC$f': ( 'Complex$' * 'Complex_complex_cblinfun$' ) > 'Complex_complex_cblinfun$' ).

tff(func_def_242,type,
    'tensor_op$e': 'A_ell2_a_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_243,type,
    'of_complex$a': 'Complex_complex_fun$' ).

tff(func_def_244,type,
    'fun_app$y': ( 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'C_ell2_c_ell2_cblinfun$' ).

tff(func_def_245,type,
    'tensor_ell2$a': ( 'A_ell2$' * 'A_ell2$' ) > 'A_a_prod_ell2$' ).

tff(func_def_246,type,
    'id_cblinfun$c': 'C_ell2_c_ell2_cblinfun$' ).

tff(func_def_247,type,
    'tensor_op$d': ( 'B_ell2_b_ell2_cblinfun$' * 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$' ) > 'B_b_b_complement_domain_prod_ell2_b_b_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_248,type,
    'id$c': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_249,type,
    'butterfly$r': ( 'B_b_prod_ell2$' * 'A_a_prod_ell2$' ) > 'A_a_prod_ell2_b_b_prod_ell2_cblinfun$' ).

tff(func_def_250,type,
    'butterfly$x': ( 'A_b_prod_ell2$' * 'A_a_prod_ell2$' ) > 'A_a_prod_ell2_a_b_prod_ell2_cblinfun$' ).

tff(func_def_251,type,
    'register_pair$f': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_b_a_complement_domain_prod_ell2_b_b_a_complement_domain_prod_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_252,type,
    'sandwich$c': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

tff(func_def_253,type,
    'scaleC$b': 'Complex$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

tff(func_def_254,type,
    'comp$h': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_255,type,
    'comp$ak': ( 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' * 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ) > 'C_b_prod_ell2_c_b_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_256,type,
    'butterfly$j': ( 'A_b_prod_ell2$' * 'A_b_prod_ell2$' ) > 'A_b_prod_ell2_a_b_prod_ell2_cblinfun$' ).

tff(func_def_257,type,
    'unit_register$b': 'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_258,type,
    'zero$c': 'B_ell2$' ).

tff(func_def_259,type,
    'tensor_op$u': ( 'B_ell2_b_ell2_cblinfun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'B_a_a_b_complement_domain_prod_prod_ell2_b_a_a_b_complement_domain_prod_prod_ell2_cblinfun$' ).

tff(func_def_260,type,
    'sandwich$e': 'A_ell2_b_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_261,type,
    'butterfly$f': ( 'Complex$' * 'B_ell2$' ) > 'B_ell2_complex_cblinfun$' ).

tff(func_def_262,type,
    'register_tensor$b': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_c_b_prod_ell2_c_b_prod_ell2_cblinfun_fun$' ).

tff(func_def_263,type,
    'butterfly$d': ( 'Complex$' * 'A_ell2$' ) > 'A_ell2_complex_cblinfun$' ).

tff(func_def_264,type,
    'default$c': 'A_b_prod$' ).

tff(func_def_265,type,
    'butterfly$p': ( 'A_b_prod_ell2$' * 'B_a_prod_ell2$' ) > 'B_a_prod_ell2_a_b_prod_ell2_cblinfun$' ).

tff(func_def_266,type,
    'ket$c': 'B_b_prod$' > 'B_b_prod_ell2$' ).

tff(func_def_267,type,
    'tensor_op$a': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun$' ).

tff(func_def_268,type,
    'uu$': 'Complex$' > 'Complex_complex_fun$' ).

tff(func_def_269,type,
    'comp$ab': ( 'Complex_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_complex_fun$' ) > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_270,type,
    'empty_var$a': 'Unit_ell2_unit_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_271,type,
    'comp$u': ( 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_272,type,
    'comp$z': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_273,type,
    'adj$d': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_274,type,
    'cblinfun_apply$a': ( 'A_ell2_a_ell2_cblinfun$' * 'A_ell2$' ) > 'A_ell2$' ).

tff(func_def_275,type,
    'tensor_op$m': ( 'B_ell2_a_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'B_a_prod_ell2_a_a_prod_ell2_cblinfun$' ).

tff(func_def_276,type,
    'cblinfun_compose$c': ( 'Complex_b_ell2_cblinfun$' * 'B_ell2_complex_cblinfun$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_277,type,
    'pair$e': ( 'Complex$' * 'Complex$' ) > 'Complex_complex_prod$' ).

tff(func_def_278,type,
    'register_tensor$h': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

tff(func_def_279,type,
    'butterfly$n': ( 'A_a_prod_ell2$' * 'B_b_prod_ell2$' ) > 'B_b_prod_ell2_a_a_prod_ell2_cblinfun$' ).

tff(func_def_280,type,
    'fun_app$a': ( 'Complex_complex_complex_fun_fun$' * 'Complex$' ) > 'Complex_complex_fun$' ).

tff(func_def_281,type,
    'fun_app$i': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_282,type,
    'adj$g': 'B_ell2_a_ell2_cblinfun$' > 'A_ell2_b_ell2_cblinfun$' ).

tff(func_def_283,type,
    'vector_to_cblinfun$a': 'B_ell2$' > 'Complex_b_ell2_cblinfun$' ).

tff(func_def_284,type,
    'fun_app$h': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_a_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_285,type,
    'comp$ah': ( 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_c_c_prod_ell2_c_c_prod_ell2_cblinfun_fun$' * 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_c_c_prod_ell2_c_c_prod_ell2_cblinfun_fun$' ) > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_c_c_prod_ell2_c_c_prod_ell2_cblinfun_fun$' ).

tff(func_def_286,type,
    'comp$y': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_287,type,
    'id_cblinfun$': 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_288,type,
    'id$': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_289,type,
    'complement$': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_290,type,
    'a$': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

tff(func_def_291,type,
    'butterfly$w': ( 'A_a_prod_ell2$' * 'A_b_prod_ell2$' ) > 'A_b_prod_ell2_a_a_prod_ell2_cblinfun$' ).

tff(func_def_292,type,
    'assoc_ell2$c': 'B_a_a_b_complement_domain_prod_prod_ell2_b_a_prod_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_293,type,
    'one_dim_iso$e': 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ).

tff(func_def_294,type,
    'fun_app$t': ( 'C_ell2_c_ell2_cblinfun_complex_fun$' * 'C_ell2_c_ell2_cblinfun$' ) > 'Complex$' ).

tff(func_def_295,type,
    'fun_app$u': ( 'Complex_b_ell2_b_ell2_cblinfun_fun$' * 'Complex$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_296,type,
    'ln$': $real > $real ).

tff(func_def_297,type,
    'register_pair$h': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_298,type,
    'adj$': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

tff(func_def_299,type,
    'comp$d': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

tff(func_def_300,type,
    'tensor_op$l': ( 'A_ell2_b_ell2_cblinfun$' * 'A_ell2_b_ell2_cblinfun$' ) > 'A_a_prod_ell2_b_b_prod_ell2_cblinfun$' ).

tff(func_def_301,type,
    'sandwich$a': 'C_ell2_c_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

tff(func_def_302,type,
    'fun_app$ah': ( 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

tff(func_def_303,type,
    'fun_app$z': ( 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun$' ) > 'B_ell2_b_ell2_cblinfun$' ).

tff(func_def_304,type,
    'one_dim_iso$c': 'Complex_complex_cblinfun$' > 'Complex_complex_cblinfun$' ).

tff(func_def_305,type,
    'fun_app$k': ( 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).

tff(func_def_306,type,
    'tensor_op$h': ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

tff(func_def_307,type,
    'swap$a': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$' ).

tff(func_def_308,type,
    'fun_app$ab': ( 'Complex_complex_complex_prod_complex_complex_prod_fun_fun$' * 'Complex$' ) > 'Complex_complex_prod_complex_complex_prod_fun$' ).

tff(func_def_309,type,
    'cblinfun_scaleC_left$': 'Complex$' > 'Complex_complex_cblinfun$' ).

tff(pred_def_1,type,
    'register$a': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_2,type,
    'compatible$c': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_3,type,
    'is_unit_register$j': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_4,type,
    'is_Proj$': 'A_ell2_a_ell2_cblinfun$' > $o ).

tff(pred_def_5,type,
    'equivalent_registers$i': ( 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' * 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_6,type,
    'equivalent_registers$j': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_7,type,
    'register$n': 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' > $o ).

tff(pred_def_8,type,
    'register$e': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_9,type,
    'iso_register$s': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_10,type,
    'register$c': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_11,type,
    'equivalent_registers$h': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_12,type,
    'equivalent_registers$l': ( 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_13,type,
    'equivalent_registers$': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_14,type,
    'regular_register$b': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_15,type,
    'iso_register$h': 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' > $o ).

tff(pred_def_16,type,
    'iso_register$k': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

tff(pred_def_17,type,
    'iso_register$b': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' > $o ).

tff(pred_def_18,type,
    'regular_register$g': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_19,type,
    'compatible$b': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_20,type,
    'antilinear_axioms$': 'Complex_complex_fun$' > $o ).

tff(pred_def_21,type,
    'complements$u': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' * 'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_22,type,
    'register$': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_23,type,
    'complements$v': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_24,type,
    'complements$p': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_25,type,
    'equivalent_registers$a': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_26,type,
    'register$d': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_27,type,
    'equivalent_registers$c': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_28,type,
    'regular_register$h': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_29,type,
    'complements$l': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_30,type,
    'complements$h': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_31,type,
    'iso_register$d': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_32,type,
    'complements$d': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_33,type,
    'iso_register$r': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_34,type,
    'register$p': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_35,type,
    'equivalent_registers$x': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_36,type,
    'complements$a': ( 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' * 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_37,type,
    'equivalent_registers$f': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_38,type,
    'is_unit_register$f': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_39,type,
    'is_unit_register$d': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_40,type,
    'equivalent_registers$u': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_41,type,
    'complements$c': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_42,type,
    'equivalent_registers$p': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_43,type,
    'register$o': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

tff(pred_def_44,type,
    'equivalent_registers$m': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_45,type,
    'register$j': 'A_ell2_a_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

tff(pred_def_46,type,
    'iso_register$t': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_47,type,
    'register$b': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_48,type,
    'iso_register$m': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_49,type,
    'complements$g': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_50,type,
    'register$m': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_51,type,
    'complements$k': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_52,type,
    'unitary$b': 'A_ell2_b_ell2_cblinfun$' > $o ).

tff(pred_def_53,type,
    'complements$': ( 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_54,type,
    'compatible$': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_55,type,
    'complements$b': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_56,type,
    'compatible$a': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_57,type,
    'iso_register$a': 'Unit_ell2_unit_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_58,type,
    'is_unit_register$e': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_59,type,
    'register$h': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_60,type,
    'is_unit_register$h': 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

tff(pred_def_61,type,
    'is_unit_register$b': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_62,type,
    'compatible$d': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_63,type,
    'iso_register$o': 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_64,type,
    'is_unit_register$': 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_65,type,
    'unitary$c': 'A_a_b_complement_domain_prod_ell2_b_ell2_cblinfun$' > $o ).

tff(pred_def_66,type,
    'less_eq$a': ( 'Complex_complex_cblinfun$' * 'Complex_complex_cblinfun$' ) > $o ).

tff(pred_def_67,type,
    'equivalent_registers$v': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_68,type,
    'equivalent_registers$o': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_69,type,
    'unitary$a': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' > $o ).

tff(pred_def_70,type,
    'register$r': 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_71,type,
    'iso_register$c': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

tff(pred_def_72,type,
    'equivalent_registers$w': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_73,type,
    'equivalent_registers$r': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_74,type,
    'iso_register$l': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_75,type,
    'equivalent_registers$n': ( 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_76,type,
    'complements$m': ( 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' * 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_77,type,
    'equivalent_registers$y': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_78,type,
    'iso_register$n': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_79,type,
    'is_unit_register$g': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_80,type,
    'register$i': 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

tff(pred_def_81,type,
    'complements$n': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_82,type,
    'register$f': 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_83,type,
    'regular_register$a': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_84,type,
    'iso_register$g': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_85,type,
    'complements$q': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_86,type,
    'regular_register$e': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_87,type,
    'register$k': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_88,type,
    'equivalent_registers$s': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_89,type,
    'iso_register$u': 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

tff(pred_def_90,type,
    'complements$r': ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_91,type,
    'equivalent_registers$g': ( 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_92,type,
    'equivalent_registers$q': ( 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' * 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_93,type,
    'iso_register$i': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_94,type,
    'iso_register$q': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_95,type,
    'regular_register$d': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_96,type,
    'iso_register$e': 'A_ell2_a_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' > $o ).

tff(pred_def_97,type,
    'complements$o': ( 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_98,type,
    'less_eq$': ( 'Complex$' * 'Complex$' ) > $o ).

tff(pred_def_99,type,
    'regular_register$': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_100,type,
    'iso_register$p': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_101,type,
    'complements$j': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_102,type,
    'equivalent_registers$b': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_103,type,
    'is_Proj$a': 'B_ell2_b_ell2_cblinfun$' > $o ).

tff(pred_def_104,type,
    'equivalent_registers$d': ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_105,type,
    'register$g': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_106,type,
    'complements$f': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_107,type,
    'equivalent_registers$e': ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_108,type,
    'iso_register$j': 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_109,type,
    'register$q': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

tff(pred_def_110,type,
    'equivalent_registers$k': ( 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_111,type,
    'is_unit_register$a': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_112,type,
    'register$l': 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

tff(pred_def_113,type,
    'complements$t': ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_114,type,
    'is_unit_register$c': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_115,type,
    'regular_register$c': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

tff(pred_def_116,type,
    'iso_register$f': 'A_ell2_a_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

tff(pred_def_117,type,
    'complements$s': ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'Unit_unit_complement_domain_ell2_unit_unit_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_118,type,
    'less$': ( 'Complex$' * 'Complex$' ) > $o ).

tff(pred_def_119,type,
    'clinear$': 'Complex_complex_fun$' > $o ).

tff(pred_def_120,type,
    'unitary$': 'A_ell2_a_ell2_cblinfun$' > $o ).

tff(pred_def_121,type,
    'equivalent_registers$t': ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_122,type,
    'is_unit_register$i': 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

tff(pred_def_123,type,
    'regular_register$f': 'A_ell2_a_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$' > $o ).

tff(pred_def_124,type,
    'complements$i': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_125,type,
    'complements$e': ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > $o ).

tff(pred_def_126,type,
    'iso_register$': 'Unit_ell2_unit_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

tff(f688,plain,
    $false,
    inference(subsumption_resolution,[],[f685,f686]) ).

tff(f686,plain,
    'is_unit_register$'('empty_var$'),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    'is_unit_register$'('empty_var$'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).

tff(f685,plain,
    ~ 'is_unit_register$'('empty_var$'),
    inference(cnf_transformation,[],[f684]) ).

tff(f684,plain,
    ~ 'is_unit_register$'('empty_var$'),
    inference(flattening,[],[f3]) ).

tff(f3,negated_conjecture,
    ~ 'is_unit_register$'('empty_var$'),
    inference(negated_conjecture,[],[f2]) ).

tff(f2,conjecture,
    'is_unit_register$'('empty_var$'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 00:13:14 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.18/0.53  % (9621)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.53  % (9613)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.53  % (9602)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.18/0.53  % (9613)Instruction limit reached!
% 0.18/0.53  % (9613)------------------------------
% 0.18/0.53  % (9613)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.53  % (9613)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.53  % (9613)Termination reason: Unknown
% 0.18/0.53  % (9613)Termination phase: shuffling
% 0.18/0.53  
% 0.18/0.53  % (9613)Memory used [KB]: 1791
% 0.18/0.53  % (9613)Time elapsed: 0.004 s
% 0.18/0.53  % (9613)Instructions burned: 2 (million)
% 0.18/0.53  % (9613)------------------------------
% 0.18/0.53  % (9613)------------------------------
% 0.18/0.54  % (9607)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.54  % (9607)Instruction limit reached!
% 0.18/0.54  % (9607)------------------------------
% 0.18/0.54  % (9607)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.54  % (9607)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.54  % (9607)Termination reason: Unknown
% 0.18/0.54  % (9607)Termination phase: shuffling
% 0.18/0.54  
% 0.18/0.54  % (9607)Memory used [KB]: 1791
% 0.18/0.54  % (9607)Time elapsed: 0.005 s
% 0.18/0.54  % (9607)Instructions burned: 2 (million)
% 0.18/0.54  % (9607)------------------------------
% 0.18/0.54  % (9607)------------------------------
% 0.18/0.57  % (9619)dis+10_1:64_nwc=1.4:rp=on:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.18/0.58  % (9611)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.18/0.58  % (9621)Instruction limit reached!
% 0.18/0.58  % (9621)------------------------------
% 0.18/0.58  % (9621)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.58  % (9621)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.58  % (9621)Termination reason: Unknown
% 0.18/0.58  % (9621)Termination phase: Property scanning
% 0.18/0.58  
% 0.18/0.58  % (9621)Memory used [KB]: 2942
% 0.18/0.58  % (9621)Time elapsed: 0.058 s
% 0.18/0.58  % (9621)Instructions burned: 50 (million)
% 0.18/0.58  % (9621)------------------------------
% 0.18/0.58  % (9621)------------------------------
% 0.18/0.58  % (9627)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=41:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/41Mi)
% 0.18/0.59  % (9601)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.59  % (9601)Instruction limit reached!
% 0.18/0.59  % (9601)------------------------------
% 0.18/0.59  % (9601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.59  % (9601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.59  % (9601)Termination reason: Unknown
% 0.18/0.59  % (9601)Termination phase: shuffling
% 0.18/0.59  
% 0.18/0.59  % (9601)Memory used [KB]: 1791
% 0.18/0.59  % (9601)Time elapsed: 0.003 s
% 0.18/0.59  % (9601)Instructions burned: 2 (million)
% 0.18/0.59  % (9601)------------------------------
% 0.18/0.59  % (9601)------------------------------
% 0.18/0.60  % (9598)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59848Mi)
% 0.18/0.60  % (9603)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.18/0.60  % (9599)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.18/0.60  % (9600)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.18/0.62  % (9604)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 0.18/0.62  % (9602)Instruction limit reached!
% 0.18/0.62  % (9602)------------------------------
% 0.18/0.62  % (9602)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.62  % (9602)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.62  % (9602)Termination reason: Unknown
% 0.18/0.62  % (9602)Termination phase: Preprocessing 3
% 0.18/0.62  
% 0.18/0.62  % (9602)Memory used [KB]: 2558
% 0.18/0.62  % (9602)Time elapsed: 0.029 s
% 0.18/0.62  % (9602)Instructions burned: 37 (million)
% 0.18/0.62  % (9602)------------------------------
% 0.18/0.62  % (9602)------------------------------
% 1.69/0.62  % (9626)dis+1011_1:1_bd=off:canc=force:ev=cautious:nwc=5.0:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 1.69/0.62  % (9623)lrs+1002_1:1_br=off:canc=force:drc=off:s2a=on:sos=on:sp=reverse_frequency:urr=on:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/42Mi)
% 1.69/0.62  % (9622)lrs+1_1:10_av=off:drc=off:nwc=2.0:sp=reverse_frequency:thsq=on:thsqc=64:thsql=off:i=47:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/47Mi)
% 1.69/0.62  % (9624)lrs+1_3:1_ep=RSTC:sos=on:urr=on:i=43:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/43Mi)
% 1.69/0.62  % (9619)Instruction limit reached!
% 1.69/0.62  % (9619)------------------------------
% 1.69/0.62  % (9619)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.69/0.62  % (9619)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.69/0.62  % (9619)Termination reason: Unknown
% 1.69/0.62  % (9619)Termination phase: Preprocessing 3
% 1.69/0.62  
% 1.69/0.62  % (9619)Memory used [KB]: 2430
% 1.69/0.62  % (9619)Time elapsed: 0.017 s
% 1.69/0.62  % (9619)Instructions burned: 22 (million)
% 1.69/0.62  % (9619)------------------------------
% 1.69/0.62  % (9619)------------------------------
% 1.69/0.62  % (9618)dis+1002_1:5_av=off:nwc=2.0:sos=all:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.69/0.62  % (9611)Instruction limit reached!
% 1.69/0.62  % (9611)------------------------------
% 1.69/0.62  % (9611)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.69/0.63  % (9611)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.69/0.63  % (9611)Termination reason: Unknown
% 1.69/0.63  % (9611)Termination phase: Naming
% 1.69/0.63  
% 1.69/0.63  % (9611)Memory used [KB]: 2302
% 1.69/0.63  % (9611)Time elapsed: 0.016 s
% 1.69/0.63  % (9611)Instructions burned: 21 (million)
% 1.69/0.63  % (9611)------------------------------
% 1.69/0.63  % (9611)------------------------------
% 1.69/0.63  % (9614)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.69/0.63  % (9614)Instruction limit reached!
% 1.69/0.63  % (9614)------------------------------
% 1.69/0.63  % (9614)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.69/0.63  % (9614)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.69/0.63  % (9614)Termination reason: Unknown
% 1.69/0.63  % (9614)Termination phase: shuffling
% 1.69/0.63  
% 1.69/0.63  % (9614)Memory used [KB]: 1791
% 1.69/0.63  % (9614)Time elapsed: 0.003 s
% 1.69/0.63  % (9614)Instructions burned: 2 (million)
% 1.69/0.63  % (9614)------------------------------
% 1.69/0.63  % (9614)------------------------------
% 1.69/0.63  % (9610)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.69/0.63  % (9603)Instruction limit reached!
% 1.69/0.63  % (9603)------------------------------
% 1.69/0.63  % (9603)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.69/0.63  % (9603)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.69/0.63  % (9603)Termination reason: Unknown
% 1.69/0.63  % (9603)Termination phase: Property scanning
% 1.69/0.63  
% 1.69/0.63  % (9603)Memory used [KB]: 1791
% 1.69/0.63  % (9603)Time elapsed: 0.012 s
% 1.69/0.63  % (9603)Instructions burned: 15 (million)
% 1.69/0.63  % (9603)------------------------------
% 1.69/0.63  % (9603)------------------------------
% 1.69/0.63  % (9615)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.69/0.63  % (9610)Instruction limit reached!
% 1.69/0.63  % (9610)------------------------------
% 1.69/0.63  % (9610)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.69/0.63  % (9610)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.69/0.63  % (9610)Termination reason: Unknown
% 1.69/0.63  % (9610)Termination phase: shuffling
% 1.69/0.63  
% 1.69/0.63  % (9610)Memory used [KB]: 1791
% 1.69/0.63  % (9610)Time elapsed: 0.003 s
% 1.69/0.63  % (9610)Instructions burned: 2 (million)
% 1.69/0.63  % (9610)------------------------------
% 1.69/0.63  % (9610)------------------------------
% 1.69/0.63  % (9600)Instruction limit reached!
% 1.69/0.63  % (9600)------------------------------
% 1.69/0.63  % (9600)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.69/0.63  % (9600)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.69/0.63  % (9600)Termination reason: Unknown
% 1.69/0.63  % (9600)Termination phase: Property scanning
% 1.69/0.63  
% 1.69/0.63  % (9600)Memory used [KB]: 1791
% 1.69/0.63  % (9600)Time elapsed: 0.008 s
% 1.69/0.63  % (9600)Instructions burned: 9 (million)
% 1.69/0.63  % (9600)------------------------------
% 1.69/0.63  % (9600)------------------------------
% 1.69/0.63  % (9616)lrs+10_1:1_ss=axioms:st=5.0:tha=off:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.69/0.63  % (9605)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 1.69/0.64  % (9608)lrs+10_1:1_canc=force:tha=some:to=lpo:i=35:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/35Mi)
% 2.02/0.64  % (9606)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 2.02/0.64  % (9609)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 2.02/0.65  % (9617)lrs+10_1:1_sd=10:sos=all:ss=axioms:st=5.0:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 2.02/0.65  % (9617)Instruction limit reached!
% 2.02/0.65  % (9617)------------------------------
% 2.02/0.65  % (9617)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.02/0.65  % (9617)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.02/0.65  % (9617)Termination reason: Unknown
% 2.02/0.65  % (9617)Termination phase: shuffling
% 2.02/0.65  
% 2.02/0.65  % (9617)Memory used [KB]: 1791
% 2.02/0.65  % (9617)Time elapsed: 0.004 s
% 2.02/0.65  % (9617)Instructions burned: 2 (million)
% 2.02/0.65  % (9617)------------------------------
% 2.02/0.65  % (9617)------------------------------
% 2.02/0.65  % (9625)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 2.02/0.65  % (9612)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 2.02/0.65  % (9618)Instruction limit reached!
% 2.02/0.65  % (9618)------------------------------
% 2.02/0.65  % (9618)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.02/0.65  % (9618)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.02/0.65  % (9618)Termination reason: Unknown
% 2.02/0.65  % (9618)Termination phase: Property scanning
% 2.02/0.65  
% 2.02/0.65  % (9618)Memory used [KB]: 1791
% 2.02/0.65  % (9618)Time elapsed: 0.011 s
% 2.02/0.65  % (9618)Instructions burned: 15 (million)
% 2.02/0.65  % (9618)------------------------------
% 2.02/0.65  % (9618)------------------------------
% 2.12/0.66  % (9620)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 2.12/0.66  % (9616)Instruction limit reached!
% 2.12/0.66  % (9616)------------------------------
% 2.12/0.66  % (9616)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.12/0.66  % (9616)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.12/0.66  % (9616)Termination reason: Unknown
% 2.12/0.66  % (9616)Termination phase: SInE selection
% 2.12/0.66  
% 2.12/0.66  % (9616)Memory used [KB]: 1791
% 2.12/0.66  % (9616)Time elapsed: 0.012 s
% 2.12/0.66  % (9616)Instructions burned: 15 (million)
% 2.12/0.66  % (9616)------------------------------
% 2.12/0.66  % (9616)------------------------------
% 2.12/0.67  % (9609)Instruction limit reached!
% 2.12/0.67  % (9609)------------------------------
% 2.12/0.67  % (9609)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.12/0.67  % (9609)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.12/0.67  % (9609)Termination reason: Unknown
% 2.12/0.67  % (9609)Termination phase: Property scanning
% 2.12/0.67  
% 2.12/0.67  % (9609)Memory used [KB]: 1791
% 2.12/0.67  % (9609)Time elapsed: 0.005 s
% 2.12/0.67  % (9609)Instructions burned: 5 (million)
% 2.12/0.67  % (9609)------------------------------
% 2.12/0.67  % (9609)------------------------------
% 2.12/0.67  % (9626)Instruction limit reached!
% 2.12/0.67  % (9626)------------------------------
% 2.12/0.67  % (9626)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.12/0.67  % (9626)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.12/0.67  % (9626)Termination reason: Unknown
% 2.12/0.67  % (9626)Termination phase: Including theory axioms
% 2.12/0.67  
% 2.12/0.67  % (9626)Memory used [KB]: 1791
% 2.12/0.67  % (9626)Time elapsed: 0.016 s
% 2.12/0.67  % (9626)Instructions burned: 21 (million)
% 2.12/0.67  % (9626)------------------------------
% 2.12/0.67  % (9626)------------------------------
% 2.12/0.67  % (9661)lrs+1_1:1_aac=none:acc=on:add=large:bd=off:bs=unit_only:bsr=on:cond=on:nm=0:sac=on:sd=3:sos=on:ss=axioms:st=2.0:i=47:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/47Mi)
% 2.12/0.67  % (9604)First to succeed.
% 2.12/0.68  % (9627)Instruction limit reached!
% 2.12/0.68  % (9627)------------------------------
% 2.12/0.68  % (9627)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.12/0.68  % (9627)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.12/0.68  % (9627)Termination reason: Unknown
% 2.12/0.68  % (9627)Termination phase: Preprocessing 3
% 2.12/0.68  
% 2.12/0.68  % (9627)Memory used [KB]: 2814
% 2.12/0.68  % (9627)Time elapsed: 0.031 s
% 2.12/0.68  % (9627)Instructions burned: 41 (million)
% 2.12/0.68  % (9627)------------------------------
% 2.12/0.68  % (9627)------------------------------
% 2.12/0.68  % (9625)Instruction limit reached!
% 2.12/0.68  % (9625)------------------------------
% 2.12/0.68  % (9625)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.12/0.68  % (9625)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.12/0.68  % (9625)Termination reason: Unknown
% 2.12/0.68  % (9625)Termination phase: Preprocessing 3
% 2.12/0.68  
% 2.12/0.68  % (9625)Memory used [KB]: 2430
% 2.12/0.68  % (9625)Time elapsed: 0.018 s
% 2.12/0.68  % (9625)Instructions burned: 22 (million)
% 2.12/0.68  % (9625)------------------------------
% 2.12/0.68  % (9625)------------------------------
% 2.12/0.69  % (9599)Instruction limit reached!
% 2.12/0.69  % (9599)------------------------------
% 2.12/0.69  % (9599)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.12/0.69  % (9599)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.12/0.69  % (9599)Termination reason: Unknown
% 2.12/0.69  % (9599)Termination phase: Preprocessing 3
% 2.12/0.69  
% 2.12/0.69  % (9599)Memory used [KB]: 2686
% 2.12/0.69  % (9599)Time elapsed: 0.025 s
% 2.12/0.69  % (9599)Instructions burned: 34 (million)
% 2.12/0.69  % (9599)------------------------------
% 2.12/0.69  % (9599)------------------------------
% 2.12/0.69  % (9606)Instruction limit reached!
% 2.12/0.69  % (9606)------------------------------
% 2.12/0.69  % (9606)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.12/0.69  % (9606)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.12/0.69  % (9606)Termination reason: Unknown
% 2.12/0.69  % (9606)Termination phase: Preprocessing 1
% 2.12/0.69  
% 2.12/0.69  % (9606)Memory used [KB]: 1791
% 2.12/0.69  % (9606)Time elapsed: 0.018 s
% 2.12/0.69  % (9606)Instructions burned: 27 (million)
% 2.12/0.69  % (9606)------------------------------
% 2.12/0.69  % (9606)------------------------------
% 2.12/0.70  % (9604)Refutation found. Thanks to Tanya!
% 2.12/0.70  % SZS status Theorem for theBenchmark
% 2.12/0.70  % SZS output start Proof for theBenchmark
% See solution above
% 2.12/0.70  % (9604)------------------------------
% 2.12/0.70  % (9604)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.12/0.70  % (9604)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.12/0.70  % (9604)Termination reason: Refutation
% 2.12/0.70  
% 2.12/0.70  % (9604)Memory used [KB]: 6396
% 2.12/0.70  % (9604)Time elapsed: 0.021 s
% 2.12/0.70  % (9604)Instructions burned: 24 (million)
% 2.12/0.70  % (9604)------------------------------
% 2.12/0.70  % (9604)------------------------------
% 2.12/0.70  % (9597)Success in time 0.344 s
%------------------------------------------------------------------------------