%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP400_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:33:48 AM UTC 2026
% Result : Theorem 4.12s 1.84s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 11 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 0 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 129 ( 127 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 128 ( 127 usr; 2 prp; 0-2 aty)
% Number of functors : 399 ( 399 usr; 68 con; 0-5 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(func_def_316,type,
sK0: ( 'Complex_complex_cblinfun$' * 'Complex_complex_cblinfun$' ) > 'Complex$' ).
tff(func_def_317,type,
sK1: ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(func_def_318,type,
sK2: ( '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_ell2_a_b_complement_domain_ell2_cblinfun$' ).
tff(func_def_319,type,
sK3: ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(func_def_320,type,
sK4: ( 'A_ell2_b_ell2_cblinfun$' * 'B_ell2_a_ell2_cblinfun$' ) > 'B$' ).
tff(func_def_321,type,
sK5: ( 'A_ell2_b_ell2_cblinfun$' * 'B_ell2_a_ell2_cblinfun$' ) > 'A$' ).
tff(func_def_322,type,
sK6: ( 'A_ell2$' * 'A_ell2$' ) > 'Complex$' ).
tff(func_def_323,type,
sK7: 'Complex_complex_fun$' > 'Complex$' ).
tff(func_def_324,type,
sK8: 'Complex_complex_fun$' > 'Complex$' ).
tff(func_def_325,type,
sK9: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_b_ell2_cblinfun$' ).
tff(func_def_326,type,
sK10: 'Complex_complex_fun$' > 'Complex$' ).
tff(func_def_327,type,
sK11: ( 'B_ell2_a_ell2_cblinfun$' * 'A_ell2_b_ell2_cblinfun$' ) > 'A$' ).
tff(func_def_328,type,
sK12: ( 'B_ell2_a_ell2_cblinfun$' * 'A_ell2_b_ell2_cblinfun$' ) > 'B$' ).
tff(func_def_329,type,
sK13: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).
tff(func_def_330,type,
sK14: ( 'B_ell2_b_ell2_cblinfun_complex_fun$' * 'Complex_b_ell2_b_ell2_cblinfun_fun$' ) > 'Complex$' ).
tff(func_def_331,type,
sK15: ( 'B_ell2_b_ell2_cblinfun_complex_fun$' * 'Complex_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(func_def_332,type,
sK16: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).
tff(func_def_333,type,
sK17: ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(func_def_334,type,
sK18: ( '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_ell2_a_b_complement_domain_ell2_cblinfun$' ).
tff(func_def_335,type,
sK19: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$' ).
tff(func_def_336,type,
sK20: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(func_def_337,type,
sK21: 'A_ell2_a_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).
tff(func_def_338,type,
sK22: ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(func_def_339,type,
sK23: ( 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * '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_340,type,
sK24: ( 'A_ell2_a_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'A$' ).
tff(func_def_341,type,
sK25: ( 'A_ell2_a_ell2_cblinfun$' * 'A_ell2_a_ell2_cblinfun$' ) > 'A$' ).
tff(func_def_342,type,
sK26: ( '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$' ).
tff(func_def_343,type,
sK27: ( 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun$' ).
tff(func_def_344,type,
sK28: ( 'A_ell2$' * 'A_ell2$' * 'A_b_complement_domain_ell2$' * 'A_b_complement_domain_ell2$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(func_def_345,type,
sK29: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$' ).
tff(func_def_346,type,
sK30: ( 'Complex_complex_fun$' * 'Complex_complex_fun$' ) > 'Complex$' ).
tff(func_def_347,type,
sK31: ( 'Complex_complex_fun$' * 'Complex_complex_fun$' ) > 'Complex$' ).
tff(func_def_348,type,
sK32: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$' ).
tff(func_def_349,type,
sK33: 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ).
tff(func_def_350,type,
sK34: ( 'B_ell2_b_ell2_cblinfun_complex_fun$' * 'Complex_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun$' ).
tff(func_def_351,type,
sK35: ( 'B_ell2_b_ell2_cblinfun_complex_fun$' * 'Complex_b_ell2_b_ell2_cblinfun_fun$' ) > 'Complex$' ).
tff(func_def_352,type,
sK36: ( 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * '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_353,type,
sK37: ( 'Complex_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_complex_fun$' ) > 'Complex$' ).
tff(func_def_354,type,
sK38: ( 'Complex_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_complex_fun$' ) > 'C_ell2_c_ell2_cblinfun$' ).
tff(func_def_355,type,
sK39: ( 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'Unit_ell2_unit_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ).
tff(func_def_356,type,
sK40: ( 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * '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_357,type,
sK41: ( 'Complex$' * 'Complex$' ) > 'Complex$' ).
tff(func_def_358,type,
sK42: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).
tff(func_def_359,type,
sK43: ( $real * $real ) > $real ).
tff(func_def_360,type,
sK44: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(func_def_361,type,
sK45: ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(func_def_362,type,
sK46: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(func_def_363,type,
sK47: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(func_def_364,type,
sK48: ( 'Complex_complex_cblinfun$' * 'Complex$' ) > 'Complex$' ).
tff(func_def_365,type,
sK49: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(func_def_366,type,
sK50: ( 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ) > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(func_def_367,type,
sK51: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).
tff(func_def_368,type,
sK52: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(func_def_369,type,
sK53: ( '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$' ).
tff(func_def_370,type,
sK54: ( 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(func_def_371,type,
sK55: 'Complex_complex_fun$' > 'Complex$' ).
tff(func_def_372,type,
sK56: ( 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' * 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ) > 'Complex$' ).
tff(func_def_373,type,
sK57: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(func_def_374,type,
sK58: 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' > 'Unit_ell2_unit_ell2_cblinfun_unit_ell2_unit_ell2_cblinfun_fun$' ).
tff(func_def_375,type,
sK59: 'Complex_complex_cblinfun$' > 'Complex$' ).
tff(func_def_376,type,
sK60: ( 'Complex_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_complex_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(func_def_377,type,
sK61: ( 'Complex_a_ell2_a_ell2_cblinfun_fun$' * 'A_ell2_a_ell2_cblinfun_complex_fun$' ) > 'Complex$' ).
tff(func_def_378,type,
sK62: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(func_def_379,type,
sK63: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).
tff(func_def_380,type,
sK64: ( 'A_ell2_a_ell2_cblinfun_complex_fun$' * 'Complex_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(func_def_381,type,
sK65: ( 'A_ell2_a_ell2_cblinfun_complex_fun$' * 'Complex_a_ell2_a_ell2_cblinfun_fun$' ) > 'Complex$' ).
tff(func_def_382,type,
sK66: ( 'Complex_complex_cblinfun$' * 'Complex_complex_cblinfun$' ) > 'Complex$' ).
tff(func_def_383,type,
sK67: ( 'Complex_complex_cblinfun$' * 'Complex_complex_cblinfun$' ) > 'Complex$' ).
tff(func_def_384,type,
sK68: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).
tff(func_def_385,type,
sK69: ( 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ) > 'C_ell2_c_ell2_cblinfun$' ).
tff(func_def_386,type,
sK70: ( '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$' ).
tff(func_def_387,type,
sK71: ( 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' * 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ) > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).
tff(func_def_388,type,
sK72: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_b_ell2_cblinfun$' ).
tff(func_def_389,type,
sK73: 'Complex_complex_cblinfun$' > 'Complex$' ).
tff(func_def_390,type,
sK74: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).
tff(func_def_391,type,
sK75: ( 'A_b_complement_domain_ell2$' * 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' * 'B_ell2$' * 'A_b_complement_domain_ell2$' * 'B_ell2$' ) > 'A_ell2_a_ell2_cblinfun$' ).
tff(func_def_392,type,
sK76: ( 'Complex_complex_cblinfun$' * 'Complex$' ) > 'Complex$' ).
tff(func_def_393,type,
sK77: ( 'Complex$' * 'Complex_complex_cblinfun$' ) > 'Complex$' ).
tff(func_def_394,type,
sK78: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).
tff(func_def_395,type,
sK79: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun$' ).
tff(func_def_396,type,
sK80: 'Complex_complex_fun$' > 'Complex$' ).
tff(func_def_397,type,
sK81: ( 'B_ell2$' * 'B_ell2$' ) > 'Complex$' ).
tff(func_def_398,type,
sK82: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun$' ).
tff(func_def_399,type,
sK83: ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'B$' ).
tff(func_def_400,type,
sK84: ( 'B_ell2_b_ell2_cblinfun$' * 'B_ell2_b_ell2_cblinfun$' ) > 'B$' ).
tff(func_def_401,type,
sK85: ( 'Complex_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_complex_fun$' ) > 'C_ell2_c_ell2_cblinfun$' ).
tff(func_def_402,type,
sK86: ( 'Complex_c_ell2_c_ell2_cblinfun_fun$' * 'C_ell2_c_ell2_cblinfun_complex_fun$' ) > 'Complex$' ).
tff(func_def_403,type,
sK87: ( '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$' ).
tff(func_def_404,type,
sK88: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_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$' > $o ).
tff(f2,conjecture,
'is_unit_register$'('empty_var$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture1) ).
tff(f3,negated_conjecture,
~ 'is_unit_register$'('empty_var$'),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,axiom,
'is_unit_register$'('empty_var$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
tff(f786,plain,
~ 'is_unit_register$'('empty_var$'),
inference(flattening,[],[f3]) ).
tff(f2057,plain,
~ 'is_unit_register$'('empty_var$'),
inference(cnf_transformation,[],[f786]) ).
tff(f2709,plain,
'is_unit_register$'('empty_var$'),
inference(cnf_transformation,[],[f4]) ).
tff(f2977,definition,
( spl89_3
<=> 'is_unit_register$'('empty_var$') ),
introduced(definition,[new_symbols(definition,[spl89_3])],[avatar_definition]) ).
tff(f2980,plain,
~ spl89_3,
inference(avatar_split_clause,[],[f2057,f2977]) ).
tff(f2986,plain,
spl89_3,
inference(avatar_split_clause,[],[f2709,f2977]) ).
tff(f3232,plain,
$false,
inference(avatar_smt_refutation,[],[f2986,f2980]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP400_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 % Computer : n019.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 27 12:57:18 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.12/1.84 % (3072852)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.12/1.84 % (3072865)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3599062041:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.12/1.84 % (3072865)Instruction limit reached!
% 4.12/1.84 % (3072865)------------------------------
% 4.12/1.84 % (3072865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072865)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072865)Termination reason: Instruction limit
% 4.12/1.84 % (3072865)Termination phase: Property scanning
% 4.12/1.84 % (3072865)Time elapsed: 0.018 s
% 4.12/1.84 % (3072865)Peak memory usage: 87 MB
% 4.12/1.84 % (3072865)Instructions burned: 34 (million)
% 4.12/1.84 % (3072859)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1887537469:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.12/1.84 % (3072862)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1042813702:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.12/1.84 % (3072861)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1918740351:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.12/1.84 % (3072860)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2437210404:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.12/1.84 % (3072862)Instruction limit reached!
% 4.12/1.84 % (3072862)------------------------------
% 4.12/1.84 % (3072862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072862)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072862)Termination reason: Instruction limit
% 4.12/1.84 % (3072862)Termination phase: Property scanning
% 4.12/1.84 % (3072862)Time elapsed: 0.008 s
% 4.12/1.84 % (3072862)Peak memory usage: 86 MB
% 4.12/1.84 % (3072862)Instructions burned: 7 (million)
% 4.12/1.84 % (3072859)Instruction limit reached!
% 4.12/1.84 % (3072859)------------------------------
% 4.12/1.84 % (3072859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072859)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072859)Termination reason: Instruction limit
% 4.12/1.84 % (3072859)Termination phase: Property scanning
% 4.12/1.84 % (3072859)Time elapsed: 0.012 s
% 4.12/1.84 % (3072859)Peak memory usage: 86 MB
% 4.12/1.84 % (3072859)Instructions burned: 12 (million)
% 4.12/1.84 % (3072863)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3767995470:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.12/1.84 % (3072864)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4270242272:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.12/1.84 % (3072863)Instruction limit reached!
% 4.12/1.84 % (3072863)------------------------------
% 4.12/1.84 % (3072863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072863)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072863)Termination reason: Instruction limit
% 4.12/1.84 % (3072863)Termination phase: Property scanning
% 4.12/1.84 % (3072863)Time elapsed: 0.005 s
% 4.12/1.84 % (3072863)Peak memory usage: 86 MB
% 4.12/1.84 % (3072863)Instructions burned: 5 (million)
% 4.12/1.84 % (3072864)Instruction limit reached!
% 4.12/1.84 % (3072864)------------------------------
% 4.12/1.84 % (3072864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072864)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072864)Termination reason: Instruction limit
% 4.12/1.84 % (3072864)Termination phase: Saturation
% 4.12/1.84 % (3072864)Time elapsed: 0.071 s
% 4.12/1.84 % (3072864)Peak memory usage: 111 MB
% 4.12/1.84 % (3072864)Instructions burned: 46 (million)
% 4.12/1.84 % (3072860)First to succeed.
% 4.12/1.84 % (3072860)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3072852"
% 4.12/1.84 % (3072867)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=296784940:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 4.12/1.84 % (3072867)Instruction limit reached!
% 4.12/1.84 % (3072867)------------------------------
% 4.12/1.84 % (3072867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072867)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072867)Termination reason: Instruction limit
% 4.12/1.84 % (3072867)Termination phase: Preprocessing 1
% 4.12/1.84 % (3072867)Time elapsed: 0.015 s
% 4.12/1.84 % (3072867)Peak memory usage: 86 MB
% 4.12/1.84 % (3072867)Instructions burned: 14 (million)
% 4.12/1.84 % (3072873)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1360608703:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.12/1.84 % (3072873)Instruction limit reached!
% 4.12/1.84 % (3072873)------------------------------
% 4.12/1.84 % (3072873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072873)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072873)Termination reason: Instruction limit
% 4.12/1.84 % (3072873)Termination phase: Preprocessing 3
% 4.12/1.84 % (3072873)Time elapsed: 0.010 s
% 4.12/1.84 % (3072873)Peak memory usage: 87 MB
% 4.12/1.84 % (3072873)Instructions burned: 17 (million)
% 4.12/1.84 % (3072861)Instruction limit reached!
% 4.12/1.84 % (3072861)------------------------------
% 4.12/1.84 % (3072861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072861)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072861)Termination reason: Instruction limit
% 4.12/1.84 % (3072861)Termination phase: Saturation
% 4.12/1.84 % (3072861)Time elapsed: 0.242 s
% 4.12/1.84 % (3072861)Peak memory usage: 116 MB
% 4.12/1.84 % (3072861)Instructions burned: 202 (million)
% 4.12/1.84 % (3072872)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=3171559868:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 4.12/1.84 % (3072872)Instruction limit reached!
% 4.12/1.84 % (3072872)------------------------------
% 4.12/1.84 % (3072872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072872)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072872)Termination reason: Instruction limit
% 4.12/1.84 % (3072872)Termination phase: Property scanning
% 4.12/1.84 % (3072872)Time elapsed: 0.029 s
% 4.12/1.84 % (3072872)Peak memory usage: 88 MB
% 4.12/1.84 % (3072872)Instructions burned: 29 (million)
% 4.12/1.84 % (3072876)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=731503293:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 4.12/1.84 % (3072876)Instruction limit reached!
% 4.12/1.84 % (3072876)------------------------------
% 4.12/1.84 % (3072876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072876)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072876)Termination reason: Instruction limit
% 4.12/1.84 % (3072876)Termination phase: Preprocessing 3
% 4.12/1.84 % (3072876)Time elapsed: 0.025 s
% 4.12/1.84 % (3072876)Peak memory usage: 88 MB
% 4.12/1.84 % (3072876)Instructions burned: 24 (million)
% 4.12/1.84 % (3072877)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=3182522769:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 4.12/1.84 % (3072877)Instruction limit reached!
% 4.12/1.84 % (3072877)------------------------------
% 4.12/1.84 % (3072877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072877)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072877)Termination reason: Instruction limit
% 4.12/1.84 % (3072877)Termination phase: Preprocessing 3
% 4.12/1.84 % (3072877)Time elapsed: 0.029 s
% 4.12/1.84 % (3072877)Peak memory usage: 88 MB
% 4.12/1.84 % (3072877)Instructions burned: 27 (million)
% 4.12/1.84 % (3072881)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=897830926:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2994 on theBenchmark for (2994ds/2Mi)
% 4.12/1.84 % (3072881)Instruction limit reached!
% 4.12/1.84 % (3072881)------------------------------
% 4.12/1.84 % (3072881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.84 % (3072881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.84 % (3072881)CaDiCaL version: 2.1.3
% 4.12/1.84 % (3072881)Termination reason: Instruction limit
% 4.12/1.84 % (3072881)Termination phase: Property scanning
% 4.12/1.84 % (3072881)Time elapsed: 0.002 s
% 4.12/1.84 % (3072881)Peak memory usage: 86 MB
% 4.12/1.84 % (3072881)Instructions burned: 3 (million)
% 4.12/1.84 % (3072879)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=3971596519:i=85:gtgl=4:rtra=on:gtg=exists_sym_2995 on theBenchmark for (2995ds/85Mi)
% 4.12/1.84 % (3072882)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=2822770086:i=181:rtra=on:ss=axioms:ev=cautious_2994 on theBenchmark for (2994ds/181Mi)
% 4.12/1.84 % (3072879)Also succeeded, but the first one will report.
% 4.12/1.84 % (3072882)Also succeeded, but the first one will report.
% 4.12/1.84 % (3072885)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=1328297076:i=4:ep=RST:ins=2:rtra=on_2994 on theBenchmark for (2994ds/4Mi)
% 4.12/1.84 % (3072860)Refutation found. Thanks to Tanya!
% 4.12/1.84 % SZS status Theorem for theBenchmark
% 4.12/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 6.29/2.07 % (3072860)------------------------------
% 6.29/2.07 % (3072860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.29/2.07 % (3072860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.29/2.07 % (3072860)CaDiCaL version: 2.1.3
% 6.29/2.07 % (3072860)Termination reason: Refutation
% 6.29/2.07 % (3072860)Time elapsed: 0.106 s
% 6.29/2.07 % (3072860)Peak memory usage: 118 MB
% 6.29/2.07 % (3072860)Instructions burned: 71 (million)
% 6.29/2.07 % (3072860)------------------------------
% 6.29/2.07 % (3072860)------------------------------
% 6.29/2.07 % (3072852)Success in time 0.804 s
% 6.29/2.07 % Vampire exiting
%------------------------------------------------------------------------------