% Mizar problem: t6_bvfunc_5,bvfunc_5,106,40 
fof(t6_bvfunc_5,conjecture,(
    ! [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))
             => ( k5_valuat_1(A,B) = k19_bvfunc_1(A)
               => k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_fraenkel,cc1_margrel1,cc1_valuat_1,commutativity_k1_binarith,d11_bvfunc_1,d14_bvfunc_1,d5_valuat_1,dt_k11_margrel1,dt_k12_bvfunc_1,dt_k14_bvfunc_1,dt_k19_bvfunc_1,dt_k1_binarith,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_valuat_1,dt_k5_valuat_1,dt_k6_margrel1,dt_k8_funct_2,dt_k8_margrel1,dt_k9_margrel1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,fc1_binarith,fc1_fraenkel,fc1_margrel1,fc2_valuat_1,fc3_margrel1,fc3_valuat_1,fc4_margrel1,involutiveness_k11_margrel1,involutiveness_k9_margrel1,rc1_fraenkel,rc1_margrel1,rc1_valuat_1,rc2_margrel1,redefinition_k11_margrel1,redefinition_k14_bvfunc_1,redefinition_k1_fraenkel,redefinition_k5_valuat_1,redefinition_k8_funct_2,redefinition_m2_fraenkel,redefinition_m2_relset_1,reflexivity_r1_tarski,t19_binarith,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(bvfunc_5,t6_bvfunc_5)]).

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

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(commutativity_k1_binarith,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k1_binarith(A,B) = k1_binarith(B,A) ) ),
    file(binarith,k1_binarith),
    []).

fof(d11_bvfunc_1,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] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k14_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k1_binarith(k9_margrel1(k1_funct_1(B,E)),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(bvfunc_1,d11_bvfunc_1),
    []).

fof(d14_bvfunc_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( B = k19_bvfunc_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => k1_funct_1(B,C) = k8_margrel1 ) ) ) ) ),
    file(bvfunc_1,d14_bvfunc_1),
    []).

fof(d5_valuat_1,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))
             => ( C = k5_valuat_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => k8_funct_2(A,k6_margrel1,C,D) = k11_margrel1(k8_funct_2(A,k6_margrel1,B,D)) ) ) ) ) ) ),
    file(valuat_1,d5_valuat_1),
    []).

fof(dt_k11_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => m1_subset_1(k11_margrel1(A),k6_margrel1) ) ),
    file(margrel1,k11_margrel1),
    []).

fof(dt_k12_bvfunc_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_valuat_1(B) )
     => ( v1_relat_1(k12_bvfunc_1(A,B))
        & v1_funct_1(k12_bvfunc_1(A,B)) ) ) ),
    file(bvfunc_1,k12_bvfunc_1),
    []).

fof(dt_k14_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)) )
     => m2_fraenkel(k14_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(bvfunc_1,k14_bvfunc_1),
    []).

fof(dt_k19_bvfunc_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m2_fraenkel(k19_bvfunc_1(A),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(bvfunc_1,k19_bvfunc_1),
    []).

fof(dt_k1_binarith,axiom,(
    $true ),
    file(binarith,k1_binarith),
    []).

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_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

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_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_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_k8_margrel1,axiom,(
    m1_subset_1(k8_margrel1,k6_margrel1) ),
    file(margrel1,k8_margrel1),
    []).

fof(dt_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_margrel1),
    []).

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_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_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_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_binarith,axiom,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k1_binarith(A,B)) ) ),
    file(binarith,fc1_binarith),
    []).

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

fof(fc1_margrel1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    []).

fof(fc2_valuat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => v2_margrel1(k1_funct_1(A,B)) ) ),
    file(valuat_1,fc2_valuat_1),
    []).

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(fc4_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,fc4_margrel1),
    []).

fof(involutiveness_k11_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => k11_margrel1(k11_margrel1(A)) = A ) ),
    file(margrel1,k11_margrel1),
    []).

fof(involutiveness_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,k9_margrel1),
    []).

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

fof(rc1_margrel1,axiom,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    []).

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_k11_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => k11_margrel1(A) = k9_margrel1(A) ) ),
    file(margrel1,k11_margrel1),
    []).

fof(redefinition_k14_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)) )
     => k14_bvfunc_1(A,B,C) = k12_bvfunc_1(B,C) ) ),
    file(bvfunc_1,k14_bvfunc_1),
    []).

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_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

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

fof(t19_binarith,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k8_margrel1) = k8_margrel1 ) ),
    file(binarith,t19_binarith),
    []).

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

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_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(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),
    []).