SET007 Axioms: SET007+50.ax


%------------------------------------------------------------------------------
% File     : SET007+50 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Binary Operations on Numbers
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : binop_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  146 (  10 unit)
%            Number of atoms       :  535 ( 105 equality)
%            Maximal formula depth :   11 (   5 average)
%            Number of connectives :  389 (   0 ~  ;   0  |; 222  &)
%                                         (  24 <=>; 143 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   12 (   0 propositional; 1-3 arity)
%            Number of functors    :   70 (  34 constant; 0-6 arity)
%            Number of variables   :  185 (   0 singleton; 185 !;   0 ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_numbers)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v1_rat_1(A) ) ) )).

fof(fc1_binop_2,axiom,
    ( v1_funct_1(k27_binop_2)
    & v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
    & v1_binop_1(k27_binop_2,k2_numbers)
    & v2_binop_1(k27_binop_2,k2_numbers) )).

fof(fc2_binop_2,axiom,
    ( v1_funct_1(k29_binop_2)
    & v1_funct_2(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
    & v1_binop_1(k29_binop_2,k2_numbers)
    & v2_binop_1(k29_binop_2,k2_numbers) )).

fof(fc3_binop_2,axiom,
    ( v1_funct_1(k33_binop_2)
    & v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & v1_binop_1(k33_binop_2,k1_numbers)
    & v2_binop_1(k33_binop_2,k1_numbers) )).

fof(fc4_binop_2,axiom,
    ( v1_funct_1(k35_binop_2)
    & v1_funct_2(k35_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & v1_binop_1(k35_binop_2,k1_numbers)
    & v2_binop_1(k35_binop_2,k1_numbers) )).

fof(fc5_binop_2,axiom,
    ( v1_funct_1(k39_binop_2)
    & v1_funct_2(k39_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
    & v1_binop_1(k39_binop_2,k3_numbers)
    & v2_binop_1(k39_binop_2,k3_numbers) )).

fof(fc6_binop_2,axiom,
    ( v1_funct_1(k41_binop_2)
    & v1_funct_2(k41_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
    & v1_binop_1(k41_binop_2,k3_numbers)
    & v2_binop_1(k41_binop_2,k3_numbers) )).

fof(fc7_binop_2,axiom,
    ( v1_funct_1(k44_binop_2)
    & v1_funct_2(k44_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
    & v1_binop_1(k44_binop_2,k4_numbers)
    & v2_binop_1(k44_binop_2,k4_numbers) )).

fof(fc8_binop_2,axiom,
    ( v1_funct_1(k46_binop_2)
    & v1_funct_2(k46_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
    & v1_binop_1(k46_binop_2,k4_numbers)
    & v2_binop_1(k46_binop_2,k4_numbers) )).

fof(fc9_binop_2,axiom,
    ( v1_funct_1(k47_binop_2)
    & v1_funct_2(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
    & v1_binop_1(k47_binop_2,k5_numbers)
    & v2_binop_1(k47_binop_2,k5_numbers) )).

fof(fc10_binop_2,axiom,
    ( v1_funct_1(k48_binop_2)
    & v1_funct_2(k48_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
    & v1_binop_1(k48_binop_2,k5_numbers)
    & v2_binop_1(k48_binop_2,k5_numbers) )).

fof(fc11_binop_2,axiom,
    ( v1_funct_1(k27_binop_2)
    & v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
    & v1_binop_1(k27_binop_2,k2_numbers)
    & v2_binop_1(k27_binop_2,k2_numbers)
    & v1_setwiseo(k27_binop_2,k2_numbers) )).

fof(fc12_binop_2,axiom,
    ( v1_funct_1(k33_binop_2)
    & v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & v1_binop_1(k33_binop_2,k1_numbers)
    & v2_binop_1(k33_binop_2,k1_numbers)
    & v1_setwiseo(k33_binop_2,k1_numbers) )).

fof(fc13_binop_2,axiom,
    ( v1_funct_1(k39_binop_2)
    & v1_funct_2(k39_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
    & v1_binop_1(k39_binop_2,k3_numbers)
    & v2_binop_1(k39_binop_2,k3_numbers)
    & v1_setwiseo(k39_binop_2,k3_numbers) )).

fof(fc14_binop_2,axiom,
    ( v1_funct_1(k44_binop_2)
    & v1_funct_2(k44_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
    & v1_binop_1(k44_binop_2,k4_numbers)
    & v2_binop_1(k44_binop_2,k4_numbers)
    & v1_setwiseo(k44_binop_2,k4_numbers) )).

fof(fc15_binop_2,axiom,
    ( v1_funct_1(k47_binop_2)
    & v1_funct_2(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
    & v1_binop_1(k47_binop_2,k5_numbers)
    & v2_binop_1(k47_binop_2,k5_numbers)
    & v1_setwiseo(k47_binop_2,k5_numbers) )).

fof(fc16_binop_2,axiom,
    ( v1_funct_1(k29_binop_2)
    & v1_funct_2(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
    & v1_binop_1(k29_binop_2,k2_numbers)
    & v2_binop_1(k29_binop_2,k2_numbers)
    & v1_setwiseo(k29_binop_2,k2_numbers) )).

fof(fc17_binop_2,axiom,
    ( v1_funct_1(k35_binop_2)
    & v1_funct_2(k35_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & v1_binop_1(k35_binop_2,k1_numbers)
    & v2_binop_1(k35_binop_2,k1_numbers)
    & v1_setwiseo(k35_binop_2,k1_numbers) )).

fof(fc18_binop_2,axiom,
    ( v1_funct_1(k41_binop_2)
    & v1_funct_2(k41_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
    & v1_binop_1(k41_binop_2,k3_numbers)
    & v2_binop_1(k41_binop_2,k3_numbers)
    & v1_setwiseo(k41_binop_2,k3_numbers) )).

fof(fc19_binop_2,axiom,
    ( v1_funct_1(k46_binop_2)
    & v1_funct_2(k46_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
    & v1_binop_1(k46_binop_2,k4_numbers)
    & v2_binop_1(k46_binop_2,k4_numbers)
    & v1_setwiseo(k46_binop_2,k4_numbers) )).

fof(fc20_binop_2,axiom,
    ( v1_funct_1(k48_binop_2)
    & v1_funct_2(k48_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
    & v1_binop_1(k48_binop_2,k5_numbers)
    & v2_binop_1(k48_binop_2,k5_numbers)
    & v1_setwiseo(k48_binop_2,k5_numbers) )).

fof(d1_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_numbers,k2_numbers)
        & m2_relset_1(A,k2_numbers,k2_numbers) )
     => ( A = k25_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k2_numbers)
           => k8_funct_2(k2_numbers,k2_numbers,A,B) = k1_binop_2(B) ) ) ) )).

fof(d2_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_numbers,k2_numbers)
        & m2_relset_1(A,k2_numbers,k2_numbers) )
     => ( A = k26_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k2_numbers)
           => k8_funct_2(k2_numbers,k2_numbers,A,B) = k2_binop_2(B) ) ) ) )).

fof(d3_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )
     => ( A = k27_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k2_numbers)
           => ! [C] :
                ( m1_subset_1(C,k2_numbers)
               => k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k3_binop_2(B,C) ) ) ) ) )).

fof(d4_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )
     => ( A = k28_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k2_numbers)
           => ! [C] :
                ( m1_subset_1(C,k2_numbers)
               => k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k4_binop_2(B,C) ) ) ) ) )).

fof(d5_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )
     => ( A = k29_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k2_numbers)
           => ! [C] :
                ( m1_subset_1(C,k2_numbers)
               => k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k5_binop_2(B,C) ) ) ) ) )).

fof(d6_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )
     => ( A = k30_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k2_numbers)
           => ! [C] :
                ( m1_subset_1(C,k2_numbers)
               => k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k6_binop_2(B,C) ) ) ) ) )).

fof(d7_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k1_numbers,k1_numbers)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( A = k31_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => k8_funct_2(k1_numbers,k1_numbers,A,B) = k7_binop_2(B) ) ) ) )).

fof(d8_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k1_numbers,k1_numbers)
        & m2_relset_1(A,k1_numbers,k1_numbers) )
     => ( A = k32_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => k8_funct_2(k1_numbers,k1_numbers,A,B) = k8_binop_2(B) ) ) ) )).

fof(d9_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
     => ( A = k33_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C) ) ) ) ) )).

fof(d10_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
     => ( A = k34_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k10_binop_2(B,C) ) ) ) ) )).

fof(d11_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
     => ( A = k35_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k11_binop_2(B,C) ) ) ) ) )).

fof(d12_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
     => ( A = k36_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k1_numbers)
           => ! [C] :
                ( m1_subset_1(C,k1_numbers)
               => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k12_binop_2(B,C) ) ) ) ) )).

fof(d13_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k3_numbers,k3_numbers)
        & m2_relset_1(A,k3_numbers,k3_numbers) )
     => ( A = k37_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k3_numbers)
           => k8_funct_2(k3_numbers,k3_numbers,A,B) = k13_binop_2(B) ) ) ) )).

fof(d14_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k3_numbers,k3_numbers)
        & m2_relset_1(A,k3_numbers,k3_numbers) )
     => ( A = k38_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k3_numbers)
           => k8_funct_2(k3_numbers,k3_numbers,A,B) = k14_binop_2(B) ) ) ) )).

fof(d15_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )
     => ( A = k39_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k3_numbers)
           => ! [C] :
                ( m1_subset_1(C,k3_numbers)
               => k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k15_binop_2(B,C) ) ) ) ) )).

fof(d16_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )
     => ( A = k40_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k3_numbers)
           => ! [C] :
                ( m1_subset_1(C,k3_numbers)
               => k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k16_binop_2(B,C) ) ) ) ) )).

fof(d17_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )
     => ( A = k41_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k3_numbers)
           => ! [C] :
                ( m1_subset_1(C,k3_numbers)
               => k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k17_binop_2(B,C) ) ) ) ) )).

fof(d18_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )
     => ( A = k42_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k3_numbers)
           => ! [C] :
                ( m1_subset_1(C,k3_numbers)
               => k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k18_binop_2(B,C) ) ) ) ) )).

fof(d19_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_numbers,k4_numbers)
        & m2_relset_1(A,k4_numbers,k4_numbers) )
     => ( A = k43_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k4_numbers)
           => k8_funct_2(k4_numbers,k4_numbers,A,B) = k19_binop_2(B) ) ) ) )).

fof(d20_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )
     => ( A = k44_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k4_numbers)
           => ! [C] :
                ( m1_subset_1(C,k4_numbers)
               => k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k20_binop_2(B,C) ) ) ) ) )).

fof(d21_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )
     => ( A = k45_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k4_numbers)
           => ! [C] :
                ( m1_subset_1(C,k4_numbers)
               => k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k21_binop_2(B,C) ) ) ) ) )).

fof(d22_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )
     => ( A = k46_binop_2
      <=> ! [B] :
            ( m1_subset_1(B,k4_numbers)
           => ! [C] :
                ( m1_subset_1(C,k4_numbers)
               => k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k22_binop_2(B,C) ) ) ) ) )).

fof(d23_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) )
     => ( A = k47_binop_2
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k23_binop_2(B,C) ) ) ) ) )).

fof(d24_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
        & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) )
     => ( A = k48_binop_2
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k24_binop_2(B,C) ) ) ) ) )).

fof(t1_binop_2,axiom,(
    k3_binop_1(k2_numbers,k27_binop_2) = np__0 )).

fof(t2_binop_2,axiom,(
    k3_binop_1(k1_numbers,k33_binop_2) = np__0 )).

fof(t3_binop_2,axiom,(
    k3_binop_1(k3_numbers,k39_binop_2) = np__0 )).

fof(t4_binop_2,axiom,(
    k3_binop_1(k4_numbers,k44_binop_2) = np__0 )).

fof(t5_binop_2,axiom,(
    k3_binop_1(k5_numbers,k47_binop_2) = np__0 )).

fof(t6_binop_2,axiom,(
    k3_binop_1(k2_numbers,k29_binop_2) = np__1 )).

fof(t7_binop_2,axiom,(
    k3_binop_1(k1_numbers,k35_binop_2) = np__1 )).

fof(t8_binop_2,axiom,(
    k3_binop_1(k3_numbers,k41_binop_2) = np__1 )).

fof(t9_binop_2,axiom,(
    k3_binop_1(k4_numbers,k46_binop_2) = np__1 )).

fof(t10_binop_2,axiom,(
    k3_binop_1(k5_numbers,k48_binop_2) = np__1 )).

fof(s1_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,f1_s1_binop_2,f2_s1_binop_2)
        & m2_relset_1(A,f1_s1_binop_2,f2_s1_binop_2) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,f1_s1_binop_2,f2_s1_binop_2)
            & m2_relset_1(B,f1_s1_binop_2,f2_s1_binop_2) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,f1_s1_binop_2)
                 => k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,A,C) = f3_s1_binop_2(C) )
              & ! [C] :
                  ( m1_subset_1(C,f1_s1_binop_2)
                 => k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,B,C) = f3_s1_binop_2(C) ) )
           => A = B ) ) ) )).

fof(s2_binop_2,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2)
        & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2)
            & m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) )
         => ( ( ! [C] :
                  ( m1_subset_1(C,f1_s2_binop_2)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s2_binop_2)
                     => k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,A,C,D) = f2_s2_binop_2(C,D) ) )
              & ! [C] :
                  ( m1_subset_1(C,f1_s2_binop_2)
                 => ! [D] :
                      ( m1_subset_1(D,f1_s2_binop_2)
                     => k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,B,C,D) = f2_s2_binop_2(C,D) ) ) )
           => A = B ) ) ) )).

fof(dt_k1_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => m1_subset_1(k1_binop_2(A),k2_numbers) ) )).

fof(involutiveness_k1_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => k1_binop_2(k1_binop_2(A)) = A ) )).

fof(redefinition_k1_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => k1_binop_2(A) = k4_xcmplx_0(A) ) )).

fof(dt_k2_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => m1_subset_1(k2_binop_2(A),k2_numbers) ) )).

fof(involutiveness_k2_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => k2_binop_2(k2_binop_2(A)) = A ) )).

fof(redefinition_k2_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_numbers)
     => k2_binop_2(A) = k5_xcmplx_0(A) ) )).

fof(dt_k3_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k3_binop_2(A,B),k2_numbers) ) )).

fof(commutativity_k3_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k3_binop_2(A,B) = k3_binop_2(B,A) ) )).

fof(redefinition_k3_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k3_binop_2(A,B) = k2_xcmplx_0(A,B) ) )).

fof(dt_k4_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k4_binop_2(A,B),k2_numbers) ) )).

fof(redefinition_k4_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k4_binop_2(A,B) = k6_xcmplx_0(A,B) ) )).

fof(dt_k5_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k5_binop_2(A,B),k2_numbers) ) )).

fof(commutativity_k5_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k5_binop_2(A,B) = k5_binop_2(B,A) ) )).

fof(redefinition_k5_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k5_binop_2(A,B) = k3_xcmplx_0(A,B) ) )).

fof(dt_k6_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => m1_subset_1(k6_binop_2(A,B),k2_numbers) ) )).

fof(redefinition_k6_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k2_numbers)
        & m1_subset_1(B,k2_numbers) )
     => k6_binop_2(A,B) = k7_xcmplx_0(A,B) ) )).

fof(dt_k7_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(k7_binop_2(A),k1_numbers) ) )).

fof(involutiveness_k7_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k7_binop_2(k7_binop_2(A)) = A ) )).

fof(redefinition_k7_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k7_binop_2(A) = k4_xcmplx_0(A) ) )).

fof(dt_k8_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(k8_binop_2(A),k1_numbers) ) )).

fof(involutiveness_k8_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k8_binop_2(k8_binop_2(A)) = A ) )).

fof(redefinition_k8_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => k8_binop_2(A) = k5_xcmplx_0(A) ) )).

fof(dt_k9_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k9_binop_2(A,B),k1_numbers) ) )).

fof(commutativity_k9_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k9_binop_2(A,B) = k9_binop_2(B,A) ) )).

fof(redefinition_k9_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k9_binop_2(A,B) = k2_xcmplx_0(A,B) ) )).

fof(dt_k10_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k10_binop_2(A,B),k1_numbers) ) )).

fof(redefinition_k10_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k10_binop_2(A,B) = k6_xcmplx_0(A,B) ) )).

fof(dt_k11_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k11_binop_2(A,B),k1_numbers) ) )).

fof(commutativity_k11_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k11_binop_2(A,B) = k11_binop_2(B,A) ) )).

fof(redefinition_k11_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k11_binop_2(A,B) = k3_xcmplx_0(A,B) ) )).

fof(dt_k12_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k12_binop_2(A,B),k1_numbers) ) )).

fof(redefinition_k12_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k12_binop_2(A,B) = k7_xcmplx_0(A,B) ) )).

fof(dt_k13_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_numbers)
     => m1_subset_1(k13_binop_2(A),k3_numbers) ) )).

fof(involutiveness_k13_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_numbers)
     => k13_binop_2(k13_binop_2(A)) = A ) )).

fof(redefinition_k13_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_numbers)
     => k13_binop_2(A) = k4_xcmplx_0(A) ) )).

fof(dt_k14_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_numbers)
     => m1_subset_1(k14_binop_2(A),k3_numbers) ) )).

fof(involutiveness_k14_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_numbers)
     => k14_binop_2(k14_binop_2(A)) = A ) )).

fof(redefinition_k14_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_numbers)
     => k14_binop_2(A) = k5_xcmplx_0(A) ) )).

fof(dt_k15_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => m1_subset_1(k15_binop_2(A,B),k3_numbers) ) )).

fof(commutativity_k15_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => k15_binop_2(A,B) = k15_binop_2(B,A) ) )).

fof(redefinition_k15_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => k15_binop_2(A,B) = k2_xcmplx_0(A,B) ) )).

fof(dt_k16_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => m1_subset_1(k16_binop_2(A,B),k3_numbers) ) )).

fof(redefinition_k16_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => k16_binop_2(A,B) = k6_xcmplx_0(A,B) ) )).

fof(dt_k17_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => m1_subset_1(k17_binop_2(A,B),k3_numbers) ) )).

fof(commutativity_k17_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => k17_binop_2(A,B) = k17_binop_2(B,A) ) )).

fof(redefinition_k17_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => k17_binop_2(A,B) = k3_xcmplx_0(A,B) ) )).

fof(dt_k18_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => m1_subset_1(k18_binop_2(A,B),k3_numbers) ) )).

fof(redefinition_k18_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k3_numbers)
        & m1_subset_1(B,k3_numbers) )
     => k18_binop_2(A,B) = k7_xcmplx_0(A,B) ) )).

fof(dt_k19_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_numbers)
     => m1_subset_1(k19_binop_2(A),k4_numbers) ) )).

fof(involutiveness_k19_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_numbers)
     => k19_binop_2(k19_binop_2(A)) = A ) )).

fof(redefinition_k19_binop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_numbers)
     => k19_binop_2(A) = k4_xcmplx_0(A) ) )).

fof(dt_k20_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_numbers)
        & m1_subset_1(B,k4_numbers) )
     => m1_subset_1(k20_binop_2(A,B),k4_numbers) ) )).

fof(commutativity_k20_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_numbers)
        & m1_subset_1(B,k4_numbers) )
     => k20_binop_2(A,B) = k20_binop_2(B,A) ) )).

fof(redefinition_k20_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_numbers)
        & m1_subset_1(B,k4_numbers) )
     => k20_binop_2(A,B) = k2_xcmplx_0(A,B) ) )).

fof(dt_k21_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_numbers)
        & m1_subset_1(B,k4_numbers) )
     => m1_subset_1(k21_binop_2(A,B),k4_numbers) ) )).

fof(redefinition_k21_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_numbers)
        & m1_subset_1(B,k4_numbers) )
     => k21_binop_2(A,B) = k6_xcmplx_0(A,B) ) )).

fof(dt_k22_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_numbers)
        & m1_subset_1(B,k4_numbers) )
     => m1_subset_1(k22_binop_2(A,B),k4_numbers) ) )).

fof(commutativity_k22_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_numbers)
        & m1_subset_1(B,k4_numbers) )
     => k22_binop_2(A,B) = k22_binop_2(B,A) ) )).

fof(redefinition_k22_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_numbers)
        & m1_subset_1(B,k4_numbers) )
     => k22_binop_2(A,B) = k3_xcmplx_0(A,B) ) )).

fof(dt_k23_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers) ) )).

fof(commutativity_k23_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k23_binop_2(A,B) = k23_binop_2(B,A) ) )).

fof(redefinition_k23_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k23_binop_2(A,B) = k2_xcmplx_0(A,B) ) )).

fof(dt_k24_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k24_binop_2(A,B),k1_numbers,k5_numbers) ) )).

fof(commutativity_k24_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k24_binop_2(A,B) = k24_binop_2(B,A) ) )).

fof(redefinition_k24_binop_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k24_binop_2(A,B) = k3_xcmplx_0(A,B) ) )).

fof(dt_k25_binop_2,axiom,
    ( v1_funct_1(k25_binop_2)
    & v1_funct_2(k25_binop_2,k2_numbers,k2_numbers)
    & m2_relset_1(k25_binop_2,k2_numbers,k2_numbers) )).

fof(dt_k26_binop_2,axiom,
    ( v1_funct_1(k26_binop_2)
    & v1_funct_2(k26_binop_2,k2_numbers,k2_numbers)
    & m2_relset_1(k26_binop_2,k2_numbers,k2_numbers) )).

fof(dt_k27_binop_2,axiom,
    ( v1_funct_1(k27_binop_2)
    & v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
    & m2_relset_1(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )).

fof(dt_k28_binop_2,axiom,
    ( v1_funct_1(k28_binop_2)
    & v1_funct_2(k28_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
    & m2_relset_1(k28_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )).

fof(dt_k29_binop_2,axiom,
    ( v1_funct_1(k29_binop_2)
    & v1_funct_2(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
    & m2_relset_1(k29_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )).

fof(dt_k30_binop_2,axiom,
    ( v1_funct_1(k30_binop_2)
    & v1_funct_2(k30_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)
    & m2_relset_1(k30_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) )).

fof(dt_k31_binop_2,axiom,
    ( v1_funct_1(k31_binop_2)
    & v1_funct_2(k31_binop_2,k1_numbers,k1_numbers)
    & m2_relset_1(k31_binop_2,k1_numbers,k1_numbers) )).

fof(dt_k32_binop_2,axiom,
    ( v1_funct_1(k32_binop_2)
    & v1_funct_2(k32_binop_2,k1_numbers,k1_numbers)
    & m2_relset_1(k32_binop_2,k1_numbers,k1_numbers) )).

fof(dt_k33_binop_2,axiom,
    ( v1_funct_1(k33_binop_2)
    & v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & m2_relset_1(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )).

fof(dt_k34_binop_2,axiom,
    ( v1_funct_1(k34_binop_2)
    & v1_funct_2(k34_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & m2_relset_1(k34_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )).

fof(dt_k35_binop_2,axiom,
    ( v1_funct_1(k35_binop_2)
    & v1_funct_2(k35_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & m2_relset_1(k35_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )).

fof(dt_k36_binop_2,axiom,
    ( v1_funct_1(k36_binop_2)
    & v1_funct_2(k36_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
    & m2_relset_1(k36_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )).

fof(dt_k37_binop_2,axiom,
    ( v1_funct_1(k37_binop_2)
    & v1_funct_2(k37_binop_2,k3_numbers,k3_numbers)
    & m2_relset_1(k37_binop_2,k3_numbers,k3_numbers) )).

fof(dt_k38_binop_2,axiom,
    ( v1_funct_1(k38_binop_2)
    & v1_funct_2(k38_binop_2,k3_numbers,k3_numbers)
    & m2_relset_1(k38_binop_2,k3_numbers,k3_numbers) )).

fof(dt_k39_binop_2,axiom,
    ( v1_funct_1(k39_binop_2)
    & v1_funct_2(k39_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
    & m2_relset_1(k39_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )).

fof(dt_k40_binop_2,axiom,
    ( v1_funct_1(k40_binop_2)
    & v1_funct_2(k40_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
    & m2_relset_1(k40_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )).

fof(dt_k41_binop_2,axiom,
    ( v1_funct_1(k41_binop_2)
    & v1_funct_2(k41_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
    & m2_relset_1(k41_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )).

fof(dt_k42_binop_2,axiom,
    ( v1_funct_1(k42_binop_2)
    & v1_funct_2(k42_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers)
    & m2_relset_1(k42_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) )).

fof(dt_k43_binop_2,axiom,
    ( v1_funct_1(k43_binop_2)
    & v1_funct_2(k43_binop_2,k4_numbers,k4_numbers)
    & m2_relset_1(k43_binop_2,k4_numbers,k4_numbers) )).

fof(dt_k44_binop_2,axiom,
    ( v1_funct_1(k44_binop_2)
    & v1_funct_2(k44_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
    & m2_relset_1(k44_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )).

fof(dt_k45_binop_2,axiom,
    ( v1_funct_1(k45_binop_2)
    & v1_funct_2(k45_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
    & m2_relset_1(k45_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )).

fof(dt_k46_binop_2,axiom,
    ( v1_funct_1(k46_binop_2)
    & v1_funct_2(k46_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers)
    & m2_relset_1(k46_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) )).

fof(dt_k47_binop_2,axiom,
    ( v1_funct_1(k47_binop_2)
    & v1_funct_2(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
    & m2_relset_1(k47_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) )).

fof(dt_k48_binop_2,axiom,
    ( v1_funct_1(k48_binop_2)
    & v1_funct_2(k48_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers)
    & m2_relset_1(k48_binop_2,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) )).
%------------------------------------------------------------------------------