% Mizar problem: t1_bvfunc13,bvfunc13,26,43 
fof(t1_bvfunc13,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_fraenkel,cc1_margrel1,cc1_valuat_1,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_funct_2,dt_k1_partit1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_valuat_1,dt_k5_valuat_1,dt_k6_bvfunc_2,dt_k6_margrel1,dt_k7_bvfunc_2,dt_m1_eqrel_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m1_t_1topsp,dt_m2_fraenkel,dt_m2_relset_1,existence_m1_eqrel_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m1_t_1topsp,existence_m2_fraenkel,existence_m2_relset_1,fc1_fraenkel,fc3_margrel1,fc3_valuat_1,rc1_fraenkel,rc1_valuat_1,rc2_margrel1,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,reflexivity_r1_bvfunc_1,t11_partit_2,t17_partit_2,t21_bvfunc_2,t8_bvfunc11]),
    [file(bvfunc13,t1_bvfunc13)]).

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

fof(cc1_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    []).

fof(cc1_valuat_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
     => v1_valuat_1(B) ) ),
    file(valuat_1,cc1_valuat_1),
    []).

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_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

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

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

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_valuat_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => ( v1_relat_1(k3_valuat_1(A))
        & v1_funct_1(k3_valuat_1(A)) ) ) ),
    file(valuat_1,k3_valuat_1),
    []).

fof(dt_k5_valuat_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
     => m2_fraenkel(k5_valuat_1(A,B),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(valuat_1,k5_valuat_1),
    []).

fof(dt_k6_bvfunc_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
        & m1_eqrel_1(D,A) )
     => m2_fraenkel(k6_bvfunc_2(A,B,C,D),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(bvfunc_2,k6_bvfunc_2),
    []).

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    []).

fof(dt_k7_bvfunc_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
        & m1_eqrel_1(D,A) )
     => m2_fraenkel(k7_bvfunc_2(A,B,C,D),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(bvfunc_2,k7_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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_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(dt_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_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(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc1_fraenkel,axiom,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    []).

fof(fc3_margrel1,axiom,(
    ~ v1_xboole_0(k6_margrel1) ),
    file(margrel1,fc3_margrel1),
    []).

fof(fc3_valuat_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => ( v1_relat_1(k3_valuat_1(A))
        & v1_funct_1(k3_valuat_1(A))
        & v1_valuat_1(k3_valuat_1(A)) ) ) ),
    file(valuat_1,fc3_valuat_1),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

fof(rc1_valuat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_valuat_1(A) ) ),
    file(valuat_1,rc1_valuat_1),
    []).

fof(rc2_margrel1,axiom,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    []).

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

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k5_valuat_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
     => k5_valuat_1(A,B) = k3_valuat_1(B) ) ),
    file(valuat_1,k5_valuat_1),
    []).

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_bvfunc_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
     => r1_bvfunc_1(A,B,B) ) ),
    file(bvfunc_1,r1_bvfunc_1),
    []).

fof(t11_partit_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( r1_bvfunc_1(A,B,C)
               => r1_bvfunc_1(A,k5_valuat_1(A,C),k5_valuat_1(A,B)) ) ) ) ) ),
    file(partit_2,t11_partit_2),
    []).

fof(t17_partit_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( v2_bvfunc_2(C,A)
                       => k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,D),C,E) = k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D) ) ) ) ) ) ) ),
    file(partit_2,t17_partit_2),
    []).

fof(t21_bvfunc_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k5_valuat_1(A,k7_bvfunc_2(A,C,B,D)) = k6_bvfunc_2(A,k5_valuat_1(A,C),B,D) ) ) ) ) ),
    file(bvfunc_2,t21_bvfunc_2),
    []).

fof(t8_bvfunc11,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A)))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r1_bvfunc_1(A,B,C)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,B,D,E),k7_bvfunc_2(A,C,D,E)) ) ) ) ) ) ) ),
    file(bvfunc11,t8_bvfunc11),
    []).