% Mizar problem: t1_bvfunc14,bvfunc14,29,54 
fof(t1_bvfunc14,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k22_bvfunc_1(A,B,k2_partit1(A,C,D)) = k5_subset_1(A,k22_bvfunc_1(A,B,C),k22_bvfunc_1(A,B,D)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_eqrel_1,cc2_eqrel_1,commutativity_k2_partit1,commutativity_k3_setfam_1,commutativity_k3_xboole_0,commutativity_k5_subset_1,d10_xboole_0,d1_t_1topsp,d3_tarski,d3_xboole_0,d4_partit1,d4_xboole_0,d5_setfam_1,d6_eqrel_1,dt_k1_t_1topsp,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k2_partit1,dt_k3_setfam_1,dt_k3_tarski,dt_k3_xboole_0,dt_k4_xboole_0,dt_k5_setfam_1,dt_k5_subset_1,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m1_subset_1,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m1_subset_1,fc1_subset_1,fc1_xboole_0,fc2_subset_1,idempotence_k3_xboole_0,idempotence_k5_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,redefinition_k22_bvfunc_1,redefinition_k5_setfam_1,redefinition_k5_subset_1,redefinition_m1_bvfunc_1,reflexivity_r1_tarski,symmetry_r1_xboole_0,t1_subset,t2_boole,t2_subset,t3_boole,t3_bvfunc11,t3_subset,t3_xboole_0,t4_boole,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t9_t_1topsp]),
    [file(bvfunc14,t1_bvfunc14)]).

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_k3_setfam_1,axiom,(
    ! [A,B] : k3_setfam_1(A,B) = k3_setfam_1(B,A) ),
    file(setfam_1,k3_setfam_1),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_t_1topsp,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( D = k1_t_1topsp(A,B,C)
                  <=> ( r2_hidden(B,D)
                      & r2_hidden(D,C) ) ) ) ) ) ) ),
    file(t_1topsp,d1_t_1topsp),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_partit1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => k2_partit1(A,B,C) = k4_xboole_0(k3_setfam_1(B,C),k1_tarski(k1_xboole_0)) ) ) ) ),
    file(partit1,d4_partit1),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_setfam_1,axiom,(
    ! [A,B,C] : 
      ( C = k3_setfam_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k3_xboole_0(E,F) ) ) ) ),
    file(setfam_1,d5_setfam_1),
    []).

fof(d6_eqrel_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    []).

fof(dt_k1_t_1topsp,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_subset_1(k1_t_1topsp(A,B,C),k1_zfmisc_1(A)) ) ),
    file(t_1topsp,k1_t_1topsp),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_k22_bvfunc_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => m1_bvfunc_1(k22_bvfunc_1(A,B,C),A,C) ) ),
    file(bvfunc_1,k22_bvfunc_1),
    []).

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_k3_setfam_1,axiom,(
    $true ),
    file(setfam_1,k3_setfam_1),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_m1_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ! [C] : 
          ( m1_bvfunc_1(C,A,B)
         => m1_subset_1(C,k1_zfmisc_1(A)) ) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    []).

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(existence_m1_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ? [C] : m1_bvfunc_1(C,A,B) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    []).

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(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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

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_k22_bvfunc_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_eqrel_1(C,A) )
     => k22_bvfunc_1(A,B,C) = k1_t_1topsp(A,B,C) ) ),
    file(bvfunc_1,k22_bvfunc_1),
    []).

fof(redefinition_k5_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k5_setfam_1(A,B) = k3_tarski(B) ) ),
    file(setfam_1,k5_setfam_1),
    []).

fof(redefinition_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(redefinition_m1_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_eqrel_1(B,A) )
     => ! [C] : 
          ( m1_bvfunc_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(bvfunc_1,m1_bvfunc_1),
    []).

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

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

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

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

fof(t3_bvfunc11,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => r1_tarski(k22_bvfunc_1(A,B,k2_partit1(A,C,D)),k22_bvfunc_1(A,B,C)) ) ) ) ) ),
    file(bvfunc11,t3_bvfunc11),
    []).

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

fof(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(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),
    []).

fof(t9_t_1topsp,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ( ~ r1_xboole_0(k1_t_1topsp(A,C,B),k1_t_1topsp(A,D,B))
                   => k1_t_1topsp(A,C,B) = k1_t_1topsp(A,D,B) ) ) ) ) ) ),
    file(t_1topsp,t9_t_1topsp),
    []).