SET007 Axioms: SET007+635.ax


%------------------------------------------------------------------------------
% File     : SET007+635 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Predicate Calculus for Boolean Valued Functions. Part XII
% 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    : bvfunc24 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   50 (  10 unit)
%            Number of atoms       : 1409 (1064 equality)
%            Maximal formula depth :   67 (  39 average)
%            Number of connectives : 1575 ( 216 ~  ; 780  |; 221  &)
%                                         (   2 <=>; 356 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   10 (   1 propositional; 0-2 arity)
%            Number of functors    :   22 (   1 constant; 0-9 arity)
%            Number of variables   :  550 (   0 singleton; 550 !;   0 ?)
%            Maximal term depth    :   10 (   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(t1_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ( B = k5_enumset1(C,D,E,F,G,H,I)
                                       => ( C = D
                                          | C = E
                                          | C = F
                                          | C = G
                                          | C = H
                                          | C = I
                                          | D = E
                                          | D = F
                                          | D = G
                                          | D = H
                                          | D = I
                                          | E = F
                                          | E = G
                                          | E = H
                                          | E = I
                                          | F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | k5_bvfunc_2(A,C,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t2_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ( B = k5_enumset1(C,D,E,F,G,H,I)
                                       => ( C = D
                                          | C = E
                                          | C = F
                                          | C = G
                                          | C = H
                                          | C = I
                                          | D = E
                                          | D = F
                                          | D = G
                                          | D = H
                                          | D = I
                                          | E = F
                                          | E = G
                                          | E = H
                                          | E = I
                                          | F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | k5_bvfunc_2(A,D,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,E),F),G),H),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t3_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ( B = k5_enumset1(C,D,E,F,G,H,I)
                                       => ( C = D
                                          | C = E
                                          | C = F
                                          | C = G
                                          | C = H
                                          | C = I
                                          | D = E
                                          | D = F
                                          | D = G
                                          | D = H
                                          | D = I
                                          | E = F
                                          | E = G
                                          | E = H
                                          | E = I
                                          | F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | k5_bvfunc_2(A,E,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),F),G),H),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t4_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ( B = k5_enumset1(C,D,E,F,G,H,I)
                                       => ( C = D
                                          | C = E
                                          | C = F
                                          | C = G
                                          | C = H
                                          | C = I
                                          | D = E
                                          | D = F
                                          | D = G
                                          | D = H
                                          | D = I
                                          | E = F
                                          | E = G
                                          | E = H
                                          | E = I
                                          | F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | k5_bvfunc_2(A,F,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),G),H),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t5_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ( B = k5_enumset1(C,D,E,F,G,H,I)
                                       => ( C = D
                                          | C = E
                                          | C = F
                                          | C = G
                                          | C = H
                                          | C = I
                                          | D = E
                                          | D = F
                                          | D = G
                                          | D = H
                                          | D = I
                                          | E = F
                                          | E = G
                                          | E = H
                                          | E = I
                                          | F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | k5_bvfunc_2(A,G,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),H),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ( B = k5_enumset1(C,D,E,F,G,H,I)
                                       => ( C = D
                                          | C = E
                                          | C = F
                                          | C = G
                                          | C = H
                                          | C = I
                                          | D = E
                                          | D = F
                                          | D = G
                                          | D = H
                                          | D = I
                                          | E = F
                                          | E = G
                                          | E = H
                                          | E = I
                                          | F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | k5_bvfunc_2(A,H,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t7_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ( B = k5_enumset1(C,D,E,F,G,H,I)
                                       => ( C = D
                                          | C = E
                                          | C = F
                                          | C = G
                                          | C = H
                                          | C = I
                                          | D = E
                                          | D = F
                                          | D = G
                                          | D = H
                                          | D = I
                                          | E = F
                                          | E = G
                                          | E = H
                                          | E = I
                                          | F = G
                                          | F = H
                                          | F = I
                                          | G = H
                                          | G = I
                                          | H = I
                                          | k5_bvfunc_2(A,I,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t8_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( v1_relat_1(H)
        & v1_funct_1(H) )
     => ! [I,J,K,L,M,N,O] :
          ( H = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,J),k3_cqc_lang(C,K)),k3_cqc_lang(D,L)),k3_cqc_lang(E,M)),k3_cqc_lang(F,N)),k3_cqc_lang(G,O)),k3_cqc_lang(A,I))
         => ( A = B
            | A = C
            | A = D
            | A = E
            | A = F
            | A = G
            | B = C
            | B = D
            | B = E
            | B = F
            | B = G
            | C = D
            | C = E
            | C = F
            | C = G
            | D = E
            | D = F
            | D = G
            | E = F
            | E = G
            | F = G
            | ( k1_funct_1(H,A) = I
              & k1_funct_1(H,B) = J
              & k1_funct_1(H,C) = K
              & k1_funct_1(H,D) = L
              & k1_funct_1(H,E) = M
              & k1_funct_1(H,F) = N
              & k1_funct_1(H,G) = O ) ) ) ) )).

fof(t9_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( v1_relat_1(H)
        & v1_funct_1(H) )
     => ! [I,J,K,L,M,N,O] :
          ( H = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,J),k3_cqc_lang(C,K)),k3_cqc_lang(D,L)),k3_cqc_lang(E,M)),k3_cqc_lang(F,N)),k3_cqc_lang(G,O)),k3_cqc_lang(A,I))
         => k1_relat_1(H) = k5_enumset1(A,B,C,D,E,F,G) ) ) )).

fof(t10_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H] :
      ( ( v1_relat_1(H)
        & v1_funct_1(H) )
     => ! [I,J,K,L,M,N,O] :
          ( H = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,J),k3_cqc_lang(C,K)),k3_cqc_lang(D,L)),k3_cqc_lang(E,M)),k3_cqc_lang(F,N)),k3_cqc_lang(G,O)),k3_cqc_lang(A,I))
         => k2_relat_1(H) = k5_enumset1(k1_funct_1(H,A),k1_funct_1(H,B),k1_funct_1(H,C),k1_funct_1(H,D),k1_funct_1(H,E),k1_funct_1(H,F),k1_funct_1(H,G)) ) ) )).

fof(t11_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_subset_1(J,A)
                                         => ! [K] :
                                              ( m1_subset_1(K,A)
                                             => ~ ( v2_bvfunc_2(B,A)
                                                  & B = k5_enumset1(C,D,E,F,G,H,I)
                                                  & C != D
                                                  & C != E
                                                  & C != F
                                                  & C != G
                                                  & C != H
                                                  & C != I
                                                  & D != E
                                                  & D != F
                                                  & D != G
                                                  & D != H
                                                  & D != I
                                                  & E != F
                                                  & E != G
                                                  & E != H
                                                  & E != I
                                                  & F != G
                                                  & F != H
                                                  & F != I
                                                  & G != H
                                                  & G != I
                                                  & H != I
                                                  & r1_xboole_0(k22_bvfunc_1(A,K,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I)),k22_bvfunc_1(A,J,C)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_subset_1(J,A)
                                         => ! [K] :
                                              ( m1_subset_1(K,A)
                                             => ~ ( v2_bvfunc_2(B,A)
                                                  & B = k5_enumset1(C,D,E,F,G,H,I)
                                                  & C != D
                                                  & C != E
                                                  & C != F
                                                  & C != G
                                                  & C != H
                                                  & C != I
                                                  & D != E
                                                  & D != F
                                                  & D != G
                                                  & D != H
                                                  & D != I
                                                  & E != F
                                                  & E != G
                                                  & E != H
                                                  & E != I
                                                  & F != G
                                                  & F != H
                                                  & F != I
                                                  & G != H
                                                  & G != I
                                                  & H != I
                                                  & k22_bvfunc_1(A,J,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I)) = k22_bvfunc_1(A,K,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I))
                                                  & r1_xboole_0(k22_bvfunc_1(A,K,k5_bvfunc_2(A,C,B)),k22_bvfunc_1(A,J,k5_bvfunc_2(A,D,B))) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ( B = k6_enumset1(C,D,E,F,G,H,I,J)
                                           => ( C = D
                                              | C = E
                                              | C = F
                                              | C = G
                                              | C = H
                                              | C = I
                                              | C = J
                                              | D = E
                                              | D = F
                                              | D = G
                                              | D = H
                                              | D = I
                                              | D = J
                                              | E = F
                                              | E = G
                                              | E = H
                                              | E = I
                                              | E = J
                                              | F = G
                                              | F = H
                                              | F = I
                                              | F = J
                                              | G = H
                                              | G = I
                                              | G = J
                                              | H = I
                                              | H = J
                                              | I = J
                                              | k5_bvfunc_2(A,C,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ( B = k6_enumset1(C,D,E,F,G,H,I,J)
                                           => ( C = D
                                              | C = E
                                              | C = F
                                              | C = G
                                              | C = H
                                              | C = I
                                              | C = J
                                              | D = E
                                              | D = F
                                              | D = G
                                              | D = H
                                              | D = I
                                              | D = J
                                              | E = F
                                              | E = G
                                              | E = H
                                              | E = I
                                              | E = J
                                              | F = G
                                              | F = H
                                              | F = I
                                              | F = J
                                              | G = H
                                              | G = I
                                              | G = J
                                              | H = I
                                              | H = J
                                              | I = J
                                              | k5_bvfunc_2(A,D,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,E),F),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t15_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ( B = k6_enumset1(C,D,E,F,G,H,I,J)
                                           => ( C = D
                                              | C = E
                                              | C = F
                                              | C = G
                                              | C = H
                                              | C = I
                                              | C = J
                                              | D = E
                                              | D = F
                                              | D = G
                                              | D = H
                                              | D = I
                                              | D = J
                                              | E = F
                                              | E = G
                                              | E = H
                                              | E = I
                                              | E = J
                                              | F = G
                                              | F = H
                                              | F = I
                                              | F = J
                                              | G = H
                                              | G = I
                                              | G = J
                                              | H = I
                                              | H = J
                                              | I = J
                                              | k5_bvfunc_2(A,E,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),F),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ( B = k6_enumset1(C,D,E,F,G,H,I,J)
                                           => ( C = D
                                              | C = E
                                              | C = F
                                              | C = G
                                              | C = H
                                              | C = I
                                              | C = J
                                              | D = E
                                              | D = F
                                              | D = G
                                              | D = H
                                              | D = I
                                              | D = J
                                              | E = F
                                              | E = G
                                              | E = H
                                              | E = I
                                              | E = J
                                              | F = G
                                              | F = H
                                              | F = I
                                              | F = J
                                              | G = H
                                              | G = I
                                              | G = J
                                              | H = I
                                              | H = J
                                              | I = J
                                              | k5_bvfunc_2(A,F,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t17_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ( B = k6_enumset1(C,D,E,F,G,H,I,J)
                                           => ( C = D
                                              | C = E
                                              | C = F
                                              | C = G
                                              | C = H
                                              | C = I
                                              | C = J
                                              | D = E
                                              | D = F
                                              | D = G
                                              | D = H
                                              | D = I
                                              | D = J
                                              | E = F
                                              | E = G
                                              | E = H
                                              | E = I
                                              | E = J
                                              | F = G
                                              | F = H
                                              | F = I
                                              | F = J
                                              | G = H
                                              | G = I
                                              | G = J
                                              | H = I
                                              | H = J
                                              | I = J
                                              | k5_bvfunc_2(A,G,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t18_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ( B = k6_enumset1(C,D,E,F,G,H,I,J)
                                           => ( C = D
                                              | C = E
                                              | C = F
                                              | C = G
                                              | C = H
                                              | C = I
                                              | C = J
                                              | D = E
                                              | D = F
                                              | D = G
                                              | D = H
                                              | D = I
                                              | D = J
                                              | E = F
                                              | E = G
                                              | E = H
                                              | E = I
                                              | E = J
                                              | F = G
                                              | F = H
                                              | F = I
                                              | F = J
                                              | G = H
                                              | G = I
                                              | G = J
                                              | H = I
                                              | H = J
                                              | I = J
                                              | k5_bvfunc_2(A,H,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),I),J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ( B = k6_enumset1(C,D,E,F,G,H,I,J)
                                           => ( C = D
                                              | C = E
                                              | C = F
                                              | C = G
                                              | C = H
                                              | C = I
                                              | C = J
                                              | D = E
                                              | D = F
                                              | D = G
                                              | D = H
                                              | D = I
                                              | D = J
                                              | E = F
                                              | E = G
                                              | E = H
                                              | E = I
                                              | E = J
                                              | F = G
                                              | F = H
                                              | F = I
                                              | F = J
                                              | G = H
                                              | G = I
                                              | G = J
                                              | H = I
                                              | H = J
                                              | I = J
                                              | k5_bvfunc_2(A,I,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),J) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ( B = k6_enumset1(C,D,E,F,G,H,I,J)
                                           => ( C = D
                                              | C = E
                                              | C = F
                                              | C = G
                                              | C = H
                                              | C = I
                                              | C = J
                                              | D = E
                                              | D = F
                                              | D = G
                                              | D = H
                                              | D = I
                                              | D = J
                                              | E = F
                                              | E = G
                                              | E = H
                                              | E = I
                                              | E = J
                                              | F = G
                                              | F = H
                                              | F = I
                                              | F = J
                                              | G = H
                                              | G = I
                                              | G = J
                                              | H = I
                                              | H = J
                                              | I = J
                                              | k5_bvfunc_2(A,J,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),I) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t21_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( v1_relat_1(I)
        & v1_funct_1(I) )
     => ! [J,K,L,M,N,O,P,Q] :
          ( I = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,K),k3_cqc_lang(C,L)),k3_cqc_lang(D,M)),k3_cqc_lang(E,N)),k3_cqc_lang(F,O)),k3_cqc_lang(G,P)),k3_cqc_lang(H,Q)),k3_cqc_lang(A,J))
         => ( A = B
            | A = C
            | A = D
            | A = E
            | A = F
            | A = G
            | A = H
            | B = C
            | B = D
            | B = E
            | B = F
            | B = G
            | B = H
            | C = D
            | C = E
            | C = F
            | C = G
            | C = H
            | D = E
            | D = F
            | D = G
            | D = H
            | E = F
            | E = G
            | E = H
            | F = G
            | F = H
            | G = H
            | ( k1_funct_1(I,B) = K
              & k1_funct_1(I,C) = L
              & k1_funct_1(I,D) = M
              & k1_funct_1(I,E) = N
              & k1_funct_1(I,F) = O
              & k1_funct_1(I,G) = P ) ) ) ) )).

fof(t22_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( v1_relat_1(I)
        & v1_funct_1(I) )
     => ! [J,K,L,M,N,O,P,Q] :
          ( I = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,K),k3_cqc_lang(C,L)),k3_cqc_lang(D,M)),k3_cqc_lang(E,N)),k3_cqc_lang(F,O)),k3_cqc_lang(G,P)),k3_cqc_lang(H,Q)),k3_cqc_lang(A,J))
         => k1_relat_1(I) = k6_enumset1(A,B,C,D,E,F,G,H) ) ) )).

fof(t23_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] :
      ( ( v1_relat_1(I)
        & v1_funct_1(I) )
     => ! [J,K,L,M,N,O,P,Q] :
          ( I = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,K),k3_cqc_lang(C,L)),k3_cqc_lang(D,M)),k3_cqc_lang(E,N)),k3_cqc_lang(F,O)),k3_cqc_lang(G,P)),k3_cqc_lang(H,Q)),k3_cqc_lang(A,J))
         => k2_relat_1(I) = k6_enumset1(k1_funct_1(I,A),k1_funct_1(I,B),k1_funct_1(I,C),k1_funct_1(I,D),k1_funct_1(I,E),k1_funct_1(I,F),k1_funct_1(I,G),k1_funct_1(I,H)) ) ) )).

fof(t24_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_subset_1(K,A)
                                             => ! [L] :
                                                  ( m1_subset_1(L,A)
                                                 => ~ ( v2_bvfunc_2(B,A)
                                                      & B = k6_enumset1(C,D,E,F,G,H,I,J)
                                                      & C != D
                                                      & C != E
                                                      & C != F
                                                      & C != G
                                                      & C != H
                                                      & C != I
                                                      & C != J
                                                      & D != E
                                                      & D != F
                                                      & D != G
                                                      & D != H
                                                      & D != I
                                                      & D != J
                                                      & E != F
                                                      & E != G
                                                      & E != H
                                                      & E != I
                                                      & E != J
                                                      & F != G
                                                      & F != H
                                                      & F != I
                                                      & F != J
                                                      & G != H
                                                      & G != I
                                                      & G != J
                                                      & H != I
                                                      & H != J
                                                      & I != J
                                                      & k5_subset_1(A,k22_bvfunc_1(A,L,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I),J)),k22_bvfunc_1(A,K,C)) = k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_subset_1(K,A)
                                             => ! [L] :
                                                  ( m1_subset_1(L,A)
                                                 => ~ ( v2_bvfunc_2(B,A)
                                                      & B = k6_enumset1(C,D,E,F,G,H,I,J)
                                                      & C != D
                                                      & C != E
                                                      & C != F
                                                      & C != G
                                                      & C != H
                                                      & C != I
                                                      & C != J
                                                      & D != E
                                                      & D != F
                                                      & D != G
                                                      & D != H
                                                      & D != I
                                                      & D != J
                                                      & E != F
                                                      & E != G
                                                      & E != H
                                                      & E != I
                                                      & E != J
                                                      & F != G
                                                      & F != H
                                                      & F != I
                                                      & F != J
                                                      & G != H
                                                      & G != I
                                                      & G != J
                                                      & H != I
                                                      & H != J
                                                      & I != J
                                                      & k22_bvfunc_1(A,K,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J)) = k22_bvfunc_1(A,L,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J))
                                                      & r1_xboole_0(k22_bvfunc_1(A,L,k5_bvfunc_2(A,C,B)),k22_bvfunc_1(A,K,k5_bvfunc_2(A,D,B))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( J = k1_bvfunc24(A,B,C,D,E,F,G,H,I)
    <=> ! [K] :
          ( r2_hidden(K,J)
        <=> ~ ( K != A
              & K != B
              & K != C
              & K != D
              & K != E
              & K != F
              & K != G
              & K != H
              & K != I ) ) ) )).

fof(t26_bvfunc24,axiom,(
    $true )).

fof(t27_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k1_tarski(A),k6_enumset1(B,C,D,E,F,G,H,I)) )).

fof(t28_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k2_tarski(A,B),k5_enumset1(C,D,E,F,G,H,I)) )).

fof(t29_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k1_enumset1(A,B,C),k4_enumset1(D,E,F,G,H,I)) )).

fof(t30_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k2_enumset1(A,B,C,D),k3_enumset1(E,F,G,H,I)) )).

fof(t31_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_enumset1(F,G,H,I)) )).

fof(t32_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_enumset1(G,H,I)) )).

fof(t33_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k2_tarski(H,I)) )).

fof(t34_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k6_enumset1(A,B,C,D,E,F,G,H),k1_tarski(I)) )).

fof(t35_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,C,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,D,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,E),F),G),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t37_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,E,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),F),G),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t38_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,F,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),G),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t39_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,G,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t40_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,H,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t41_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,I,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t42_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,J,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),I),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t43_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                               => ( C = D
                                                  | C = E
                                                  | C = F
                                                  | C = G
                                                  | C = H
                                                  | C = I
                                                  | C = J
                                                  | C = K
                                                  | D = E
                                                  | D = F
                                                  | D = G
                                                  | D = H
                                                  | D = I
                                                  | D = J
                                                  | D = K
                                                  | E = F
                                                  | E = G
                                                  | E = H
                                                  | E = I
                                                  | E = J
                                                  | E = K
                                                  | F = G
                                                  | F = H
                                                  | F = I
                                                  | F = J
                                                  | F = K
                                                  | G = H
                                                  | G = I
                                                  | G = J
                                                  | G = K
                                                  | H = I
                                                  | H = J
                                                  | H = K
                                                  | I = J
                                                  | I = K
                                                  | J = K
                                                  | k5_bvfunc_2(A,K,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t44_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ( v1_relat_1(J)
        & v1_funct_1(J) )
     => ! [K,L,M,N,O,P,Q,R,S] :
          ( J = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,L),k3_cqc_lang(C,M)),k3_cqc_lang(D,N)),k3_cqc_lang(E,O)),k3_cqc_lang(F,P)),k3_cqc_lang(G,Q)),k3_cqc_lang(H,R)),k3_cqc_lang(I,S)),k3_cqc_lang(A,K))
         => ( A = B
            | A = C
            | A = D
            | A = E
            | A = F
            | A = G
            | A = H
            | A = I
            | B = C
            | B = D
            | B = E
            | B = F
            | B = G
            | B = H
            | B = I
            | C = D
            | C = E
            | C = F
            | C = G
            | C = H
            | C = I
            | D = E
            | D = F
            | D = G
            | D = H
            | D = I
            | E = F
            | E = G
            | E = H
            | E = I
            | F = G
            | F = H
            | F = I
            | G = H
            | G = I
            | H = I
            | ( k1_funct_1(J,A) = K
              & k1_funct_1(J,B) = L
              & k1_funct_1(J,C) = M
              & k1_funct_1(J,D) = N
              & k1_funct_1(J,E) = O
              & k1_funct_1(J,F) = P
              & k1_funct_1(J,G) = Q
              & k1_funct_1(J,H) = R
              & k1_funct_1(J,I) = S ) ) ) ) )).

fof(t45_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ( v1_relat_1(J)
        & v1_funct_1(J) )
     => ! [K,L,M,N,O,P,Q,R,S] :
          ( J = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,L),k3_cqc_lang(C,M)),k3_cqc_lang(D,N)),k3_cqc_lang(E,O)),k3_cqc_lang(F,P)),k3_cqc_lang(G,Q)),k3_cqc_lang(H,R)),k3_cqc_lang(I,S)),k3_cqc_lang(A,K))
         => k1_relat_1(J) = k1_bvfunc24(A,B,C,D,E,F,G,H,I) ) ) )).

fof(t46_bvfunc24,axiom,(
    ! [A,B,C,D,E,F,G,H,I,J] :
      ( ( v1_relat_1(J)
        & v1_funct_1(J) )
     => ! [K,L,M,N,O,P,Q,R,S] :
          ( J = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,L),k3_cqc_lang(C,M)),k3_cqc_lang(D,N)),k3_cqc_lang(E,O)),k3_cqc_lang(F,P)),k3_cqc_lang(G,Q)),k3_cqc_lang(H,R)),k3_cqc_lang(I,S)),k3_cqc_lang(A,K))
         => k2_relat_1(J) = k1_bvfunc24(k1_funct_1(J,A),k1_funct_1(J,B),k1_funct_1(J,C),k1_funct_1(J,D),k1_funct_1(J,E),k1_funct_1(J,F),k1_funct_1(J,G),k1_funct_1(J,H),k1_funct_1(J,I)) ) ) )).

fof(t47_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ! [L] :
                                                  ( m1_subset_1(L,A)
                                                 => ! [M] :
                                                      ( m1_subset_1(M,A)
                                                     => ~ ( v2_bvfunc_2(B,A)
                                                          & B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                                          & C != D
                                                          & C != E
                                                          & C != F
                                                          & C != G
                                                          & C != H
                                                          & C != I
                                                          & C != J
                                                          & C != K
                                                          & D != E
                                                          & D != F
                                                          & D != G
                                                          & D != H
                                                          & D != I
                                                          & D != J
                                                          & D != K
                                                          & E != F
                                                          & E != G
                                                          & E != H
                                                          & E != I
                                                          & E != J
                                                          & E != K
                                                          & F != G
                                                          & F != H
                                                          & F != I
                                                          & F != J
                                                          & F != K
                                                          & G != H
                                                          & G != I
                                                          & G != J
                                                          & G != K
                                                          & H != I
                                                          & H != J
                                                          & H != K
                                                          & I != J
                                                          & I != K
                                                          & J != K
                                                          & k5_subset_1(A,k22_bvfunc_1(A,M,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I),J),K)),k22_bvfunc_1(A,L,C)) = k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t48_bvfunc24,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] :
              ( m1_eqrel_1(C,A)
             => ! [D] :
                  ( m1_eqrel_1(D,A)
                 => ! [E] :
                      ( m1_eqrel_1(E,A)
                     => ! [F] :
                          ( m1_eqrel_1(F,A)
                         => ! [G] :
                              ( m1_eqrel_1(G,A)
                             => ! [H] :
                                  ( m1_eqrel_1(H,A)
                                 => ! [I] :
                                      ( m1_eqrel_1(I,A)
                                     => ! [J] :
                                          ( m1_eqrel_1(J,A)
                                         => ! [K] :
                                              ( m1_eqrel_1(K,A)
                                             => ! [L] :
                                                  ( m1_subset_1(L,A)
                                                 => ! [M] :
                                                      ( m1_subset_1(M,A)
                                                     => ~ ( v2_bvfunc_2(B,A)
                                                          & B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
                                                          & C != D
                                                          & C != E
                                                          & C != F
                                                          & C != G
                                                          & C != H
                                                          & C != I
                                                          & C != J
                                                          & C != K
                                                          & D != E
                                                          & D != F
                                                          & D != G
                                                          & D != H
                                                          & D != I
                                                          & D != J
                                                          & D != K
                                                          & E != F
                                                          & E != G
                                                          & E != H
                                                          & E != I
                                                          & E != J
                                                          & E != K
                                                          & F != G
                                                          & F != H
                                                          & F != I
                                                          & F != J
                                                          & F != K
                                                          & G != H
                                                          & G != I
                                                          & G != J
                                                          & G != K
                                                          & H != I
                                                          & H != J
                                                          & H != K
                                                          & I != J
                                                          & I != K
                                                          & J != K
                                                          & k22_bvfunc_1(A,L,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J),K)) = k22_bvfunc_1(A,M,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J),K))
                                                          & r1_xboole_0(k22_bvfunc_1(A,M,k5_bvfunc_2(A,C,B)),k22_bvfunc_1(A,L,k5_bvfunc_2(A,D,B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_bvfunc24,axiom,(
    $true )).
%------------------------------------------------------------------------------