% Mizar problem: t39_bvfunc24,bvfunc24,2386,19 
fof(t39_bvfunc24,conjecture,(
    ! [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) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_eqrel_1,cc2_eqrel_1,commutativity_k2_partit1,commutativity_k2_tarski,commutativity_k2_xboole_0,dt_k1_bvfunc24,dt_k1_bvfunc_2,dt_k1_enumset1,dt_k1_partit1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_enumset1,dt_k2_partit1,dt_k2_tarski,dt_k2_xboole_0,dt_k4_enumset1,dt_k5_bvfunc_2,dt_m1_eqrel_1,dt_m1_subset_1,dt_m1_t_1topsp,existence_m1_eqrel_1,existence_m1_subset_1,existence_m1_t_1topsp,fc1_subset_1,fc1_xboole_0,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,idempotence_k2_xboole_0,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,redefinition_k1_bvfunc_2,reflexivity_r1_tarski,t1_boole,t1_subset,t29_bvfunc24,t2_subset,t38_bvfunc24,t3_subset,t4_subset,t52_enumset1,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(bvfunc24,t39_bvfunc24)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_eqrel_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(eqrel_1,cc1_eqrel_1),
    []).

fof(cc2_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => v1_setfam_1(B) ) ),
    file(eqrel_1,cc2_eqrel_1),
    []).

fof(commutativity_k2_partit1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A)
        & m1_eqrel_1(C,A) )
     => k2_partit1(A,B,C) = k2_partit1(A,C,B) ) ),
    file(partit1,k2_partit1),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k1_bvfunc24,axiom,(
    $true ),
    file(bvfunc24,k1_bvfunc24),
    []).

fof(dt_k1_bvfunc_2,axiom,(
    ! [A] : 
      ( v1_t_1topsp(k1_bvfunc_2(A),A)
      & m1_t_1topsp(k1_bvfunc_2(A),A) ) ),
    file(bvfunc_2,k1_bvfunc_2),
    []).

fof(dt_k1_enumset1,axiom,(
    $true ),
    file(enumset1,k1_enumset1),
    []).

fof(dt_k1_partit1,axiom,(
    $true ),
    file(partit1,k1_partit1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_enumset1,axiom,(
    $true ),
    file(enumset1,k2_enumset1),
    []).

fof(dt_k2_partit1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_eqrel_1(k2_partit1(A,B,C),A) ) ),
    file(partit1,k2_partit1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k4_enumset1,axiom,(
    $true ),
    file(enumset1,k4_enumset1),
    []).

fof(dt_k5_bvfunc_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) )
     => m1_eqrel_1(k5_bvfunc_2(A,B,C),A) ) ),
    file(bvfunc_2,k5_bvfunc_2),
    []).

fof(dt_m1_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_eqrel_1(B,A)
     => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(eqrel_1,m1_eqrel_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m1_t_1topsp,axiom,(
    $true ),
    file(t_1topsp,m1_t_1topsp),
    []).

fof(existence_m1_eqrel_1,axiom,(
    ! [A] : 
    ? [B] : m1_eqrel_1(B,A) ),
    file(eqrel_1,m1_eqrel_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_t_1topsp,axiom,(
    ! [A] : 
    ? [B] : m1_t_1topsp(B,A) ),
    file(t_1topsp,m1_t_1topsp),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(redefinition_k1_bvfunc_2,axiom,(
    ! [A] : k1_bvfunc_2(A) = k1_partit1(A) ),
    file(bvfunc_2,k1_bvfunc_2),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

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)) ),
    file(bvfunc24,t29_bvfunc24),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

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) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(bvfunc24,t38_bvfunc24),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t52_enumset1,axiom,(
    ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F)) ),
    file(enumset1,t52_enumset1),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).