SET007 Axioms: SET007+174.ax


%------------------------------------------------------------------------------
% File     : SET007+174 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Binary Arithmetics, Addition and Subtraction of Integers
% 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    : binari_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   35 (   2 unit)
%            Number of atoms       :  163 (  37 equality)
%            Maximal formula depth :   13 (   7 average)
%            Number of connectives :  154 (  26 ~  ;   1  |;  39  &)
%                                         (   2 <=>;  86 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   1 propositional; 0-3 arity)
%            Number of functors    :   39 (   8 constant; 0-6 arity)
%            Number of variables   :   94 (   0 singleton;  94 !;   0 ?)
%            Maximal term depth    :    9 (   2 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(d1_binari_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ( B = k2_binari_2(A)
          <=> ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r2_hidden(C,k2_finseq_1(A))
                 => k4_finseq_4(k5_numbers,k6_margrel1,B,C) = k2_cqc_lang(k6_margrel1,C,np__1,k8_margrel1,k7_margrel1) ) ) ) ) ) )).

fof(d2_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => k3_binari_2(A,B) = k10_binarith(A,k6_binarith(A,B),k2_binari_2(A)) ) ) )).

fof(d3_binari_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ( ( k4_finseq_4(k5_numbers,k6_margrel1,B,A) = k7_margrel1
             => k4_binari_2(A,B) = k9_binarith(A,B) )
            & ( k4_finseq_4(k5_numbers,k6_margrel1,B,A) != k7_margrel1
             => k4_binari_2(A,B) = k10_binop_2(k9_binarith(A,B),k3_series_1(np__2,A)) ) ) ) ) )).

fof(d4_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => k5_binari_2(A,B,C) = k12_margrel1(k12_margrel1(k11_margrel1(k4_finseq_4(k5_numbers,k6_margrel1,B,A)),k11_margrel1(k4_finseq_4(k5_numbers,k6_margrel1,C,A))),k4_finseq_4(k5_numbers,k6_margrel1,k7_binarith(A,B,C),A)) ) ) ) )).

fof(d5_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => k6_binari_2(A,B,C) = k12_margrel1(k12_margrel1(k4_finseq_4(k5_numbers,k6_margrel1,B,A),k4_finseq_4(k5_numbers,k6_margrel1,C,A)),k11_margrel1(k4_finseq_4(k5_numbers,k6_margrel1,k7_binarith(A,B,C),A))) ) ) ) )).

fof(t1_binari_2,axiom,(
    $true )).

fof(t2_binari_2,axiom,(
    $true )).

fof(t3_binari_2,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(np__2,k6_margrel1))
     => ( A = k12_binarith(np__1,np__1,k6_margrel1,k13_binarith(k6_margrel1,k7_margrel1),k13_binarith(k6_margrel1,k7_margrel1))
       => k4_binari_2(np__2,A) = np__0 ) ) )).

fof(t4_binari_2,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(np__2,k6_margrel1))
     => ( A = k12_binarith(np__1,np__1,k6_margrel1,k13_binarith(k6_margrel1,k8_margrel1),k13_binarith(k6_margrel1,k7_margrel1))
       => k4_binari_2(np__2,A) = np__1 ) ) )).

fof(t5_binari_2,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(np__2,k6_margrel1))
     => ( A = k12_binarith(np__1,np__1,k6_margrel1,k13_binarith(k6_margrel1,k7_margrel1),k13_binarith(k6_margrel1,k8_margrel1))
       => k4_binari_2(np__2,A) = k7_binop_2(np__2) ) ) )).

fof(t6_binari_2,axiom,(
    ! [A] :
      ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(np__2,k6_margrel1))
     => ( A = k12_binarith(np__1,np__1,k6_margrel1,k13_binarith(k6_margrel1,k8_margrel1),k13_binarith(k6_margrel1,k8_margrel1))
       => k4_binari_2(np__2,A) = k7_binop_2(np__1) ) ) )).

fof(t7_binari_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( r2_hidden(B,k2_finseq_1(A))
              & B = np__1 )
           => k4_finseq_4(k5_numbers,k6_margrel1,k2_binari_2(A),B) = k8_margrel1 ) ) ) )).

fof(t8_binari_2,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(B,k2_finseq_1(A))
           => ( B = np__1
              | k4_finseq_4(k5_numbers,k6_margrel1,k2_binari_2(A),B) = k7_margrel1 ) ) ) ) )).

fof(t9_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => k2_binari_2(k23_binop_2(A,np__1)) = k12_binarith(A,np__1,k6_margrel1,k2_binari_2(A),k13_binarith(k6_margrel1,k7_margrel1)) ) )).

fof(t10_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,k2_binari_2(A),k13_binarith(k6_margrel1,k7_margrel1))) = np__1 ) )).

fof(t11_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k6_margrel1)
             => k6_binarith(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,C))) = k12_binarith(A,np__1,k6_margrel1,k6_binarith(A,B),k13_binarith(k6_margrel1,k11_margrel1(C))) ) ) ) )).

fof(t12_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k6_margrel1)
             => k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,C))) = k10_binop_2(k9_binarith(A,B),k2_cqc_lang(k5_numbers,C,k7_margrel1,np__0,k3_series_1(np__2,A))) ) ) ) )).

fof(t13_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => ! [D] :
                  ( m1_subset_1(D,k6_margrel1)
                 => ! [E] :
                      ( m1_subset_1(E,k6_margrel1)
                     => k6_xcmplx_0(k2_xcmplx_0(k4_binari_2(k23_binop_2(A,np__1),k10_binarith(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E)))),k2_cqc_lang(k5_numbers,k5_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E))),k7_margrel1,np__0,k3_series_1(np__2,k23_binop_2(A,np__1)))),k2_cqc_lang(k5_numbers,k6_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E))),k7_margrel1,np__0,k3_series_1(np__2,k23_binop_2(A,np__1)))) = k2_xcmplx_0(k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D))),k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E)))) ) ) ) ) ) )).

fof(t14_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => ! [D] :
                  ( m1_subset_1(D,k6_margrel1)
                 => ! [E] :
                      ( m1_subset_1(E,k6_margrel1)
                     => k4_binari_2(k23_binop_2(A,np__1),k10_binarith(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E)))) = k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D))),k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E)))),k2_cqc_lang(k5_numbers,k5_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E))),k7_margrel1,np__0,k3_series_1(np__2,k23_binop_2(A,np__1)))),k2_cqc_lang(k5_numbers,k6_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E))),k7_margrel1,np__0,k3_series_1(np__2,k23_binop_2(A,np__1)))) ) ) ) ) ) )).

fof(t15_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => k9_binarith(A,k6_binarith(A,B)) = k10_binop_2(k9_binop_2(k7_binop_2(k9_binarith(A,B)),k3_series_1(np__2,A)),np__1) ) ) )).

fof(t16_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k6_margrel1)
             => k3_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,C))) = k12_binarith(A,np__1,k6_margrel1,k3_binari_2(A,B),k13_binarith(k6_margrel1,k4_binarith(k11_margrel1(C),k11_binarith(A,k6_binarith(A,B),k2_binari_2(A))))) ) ) ) )).

fof(t17_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k6_margrel1)
             => k2_xcmplx_0(k4_binari_2(k23_binop_2(A,np__1),k3_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,C)))),k2_cqc_lang(k5_numbers,k5_binari_2(k23_binop_2(A,np__1),k6_binarith(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,C))),k2_binari_2(k23_binop_2(A,np__1))),k7_margrel1,np__0,k3_series_1(np__2,k23_binop_2(A,np__1)))) = k4_xcmplx_0(k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,C)))) ) ) ) )).

fof(t18_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m1_subset_1(C,k6_margrel1)
             => k3_binari_2(k23_binop_2(A,np__1),k3_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,C)))) = k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,C)) ) ) ) )).

fof(d6_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => ! [D] :
                  ( m2_finseq_2(D,k6_margrel1,k4_finseq_2(A,k6_margrel1))
                 => ( D = k7_binari_2(A,B,C)
                  <=> ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r2_hidden(E,k2_finseq_1(A))
                         => k4_finseq_4(k5_numbers,k6_margrel1,D,E) = k4_binarith(k4_binarith(k4_finseq_4(k5_numbers,k6_margrel1,B,E),k4_finseq_4(k5_numbers,k6_margrel1,k3_binari_2(A,C),E)),k4_finseq_4(k5_numbers,k6_margrel1,k7_binarith(A,B,k3_binari_2(A,C)),E)) ) ) ) ) ) ) ) )).

fof(t19_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => k7_binari_2(A,B,C) = k10_binarith(A,B,k3_binari_2(A,C)) ) ) ) )).

fof(t20_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => ! [D] :
                  ( m1_subset_1(D,k6_margrel1)
                 => ! [E] :
                      ( m1_subset_1(E,k6_margrel1)
                     => k7_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E))) = k12_binarith(A,np__1,k6_margrel1,k10_binarith(A,B,k3_binari_2(A,C)),k13_binarith(k6_margrel1,k4_binarith(k4_binarith(k4_binarith(D,k11_margrel1(E)),k11_binarith(A,k6_binarith(A,C),k2_binari_2(A))),k11_binarith(A,B,k3_binari_2(A,C))))) ) ) ) ) ) )).

fof(t21_binari_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & m2_subset_1(A,k1_numbers,k5_numbers) )
     => ! [B] :
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] :
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => ! [D] :
                  ( m1_subset_1(D,k6_margrel1)
                 => ! [E] :
                      ( m1_subset_1(E,k6_margrel1)
                     => k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_binari_2(k23_binop_2(A,np__1),k7_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E)))),k2_cqc_lang(k5_numbers,k5_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k3_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E)))),k7_margrel1,np__0,k3_series_1(np__2,k23_binop_2(A,np__1)))),k2_cqc_lang(k5_numbers,k6_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D)),k3_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E)))),k7_margrel1,np__0,k3_series_1(np__2,k23_binop_2(A,np__1)))),k2_cqc_lang(k5_numbers,k5_binari_2(k23_binop_2(A,np__1),k6_binarith(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E))),k2_binari_2(k23_binop_2(A,np__1))),k7_margrel1,np__0,k3_series_1(np__2,k23_binop_2(A,np__1)))) = k6_xcmplx_0(k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,B,k13_binarith(k6_margrel1,D))),k4_binari_2(k23_binop_2(A,np__1),k12_binarith(A,np__1,k6_margrel1,C,k13_binarith(k6_margrel1,E)))) ) ) ) ) ) )).

fof(dt_k1_binari_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(E,B)
        & m1_subset_1(F,B) )
     => m2_subset_1(k1_binari_2(A,B,C,D,E,F),A,B) ) )).

fof(redefinition_k1_binari_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(E,B)
        & m1_subset_1(F,B) )
     => k1_binari_2(A,B,C,D,E,F) = k1_cqc_lang(C,D,E,F) ) )).

fof(dt_k2_binari_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m2_finseq_2(k2_binari_2(A),k6_margrel1,k4_finseq_2(A,k6_margrel1)) ) )).

fof(dt_k3_binari_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k4_finseq_2(A,k6_margrel1)) )
     => m2_finseq_2(k3_binari_2(A,B),k6_margrel1,k4_finseq_2(A,k6_margrel1)) ) )).

fof(dt_k4_binari_2,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k4_finseq_2(A,k6_margrel1)) )
     => v1_int_1(k4_binari_2(A,B)) ) )).

fof(dt_k5_binari_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k4_finseq_2(A,k6_margrel1))
        & m1_subset_1(C,k4_finseq_2(A,k6_margrel1)) )
     => m1_subset_1(k5_binari_2(A,B,C),k6_margrel1) ) )).

fof(dt_k6_binari_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k4_finseq_2(A,k6_margrel1))
        & m1_subset_1(C,k4_finseq_2(A,k6_margrel1)) )
     => m1_subset_1(k6_binari_2(A,B,C),k6_margrel1) ) )).

fof(dt_k7_binari_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k4_finseq_2(A,k6_margrel1))
        & m1_subset_1(C,k4_finseq_2(A,k6_margrel1)) )
     => m2_finseq_2(k7_binari_2(A,B,C),k6_margrel1,k4_finseq_2(A,k6_margrel1)) ) )).
%------------------------------------------------------------------------------