% Mizar ND problem: t2_bvfunc_3,bvfunc_3,55,45 
fof(dh_c1_2__bvfunc_3,definition,
    ( ( ~ v1_xboole_0(c1_2__bvfunc_3)
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc_3)))
         => ! [B] : 
              ( m2_fraenkel(B,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
             => ! [C] : 
                  ( m2_fraenkel(C,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
                 => ! [D] : 
                      ( m1_eqrel_1(D,c1_2__bvfunc_3)
                     => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,B,A,D),k6_bvfunc_2(c1_2__bvfunc_3,C,A,D)),k6_valuat_1(c1_2__bvfunc_3,B,C)) ) ) ) ) )
   => ! [E] : 
        ( ~ v1_xboole_0(E)
       => ! [F] : 
            ( m1_subset_1(F,k1_zfmisc_1(k1_bvfunc_2(E)))
           => ! [G] : 
                ( m2_fraenkel(G,E,k6_margrel1,k1_fraenkel(E,k6_margrel1))
               => ! [H] : 
                    ( m2_fraenkel(H,E,k6_margrel1,k1_fraenkel(E,k6_margrel1))
                   => ! [I] : 
                        ( m1_eqrel_1(I,E)
                       => r1_bvfunc_1(E,k6_valuat_1(E,k6_bvfunc_2(E,G,F,I),k6_bvfunc_2(E,H,F,I)),k6_valuat_1(E,G,H)) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_2__bvfunc_3),file(bvfunc_3,c1_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c1_2__bvfunc_3)]).

fof(dh_c2_2__bvfunc_3,definition,
    ( ( m1_subset_1(c2_2__bvfunc_3,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc_3)))
     => ! [A] : 
          ( m2_fraenkel(A,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
         => ! [B] : 
              ( m2_fraenkel(B,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
             => ! [C] : 
                  ( m1_eqrel_1(C,c1_2__bvfunc_3)
                 => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,A,c2_2__bvfunc_3,C),k6_bvfunc_2(c1_2__bvfunc_3,B,c2_2__bvfunc_3,C)),k6_valuat_1(c1_2__bvfunc_3,A,B)) ) ) ) )
   => ! [D] : 
        ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc_3)))
       => ! [E] : 
            ( m2_fraenkel(E,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
           => ! [F] : 
                ( m2_fraenkel(F,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
               => ! [G] : 
                    ( m1_eqrel_1(G,c1_2__bvfunc_3)
                   => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,E,D,G),k6_bvfunc_2(c1_2__bvfunc_3,F,D,G)),k6_valuat_1(c1_2__bvfunc_3,E,F)) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_2__bvfunc_3),file(bvfunc_3,c2_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c2_2__bvfunc_3)]).

fof(dh_c3_2__bvfunc_3,definition,
    ( ( m2_fraenkel(c3_2__bvfunc_3,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
     => ! [A] : 
          ( m2_fraenkel(A,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
         => ! [B] : 
              ( m1_eqrel_1(B,c1_2__bvfunc_3)
             => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,B),k6_bvfunc_2(c1_2__bvfunc_3,A,c2_2__bvfunc_3,B)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,A)) ) ) )
   => ! [C] : 
        ( m2_fraenkel(C,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
       => ! [D] : 
            ( m2_fraenkel(D,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
           => ! [E] : 
                ( m1_eqrel_1(E,c1_2__bvfunc_3)
               => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,C,c2_2__bvfunc_3,E),k6_bvfunc_2(c1_2__bvfunc_3,D,c2_2__bvfunc_3,E)),k6_valuat_1(c1_2__bvfunc_3,C,D)) ) ) ) ),
    introduced(definition,[new_symbol(c3_2__bvfunc_3),file(bvfunc_3,c3_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c3_2__bvfunc_3)]).

fof(dh_c4_2__bvfunc_3,definition,
    ( ( m2_fraenkel(c4_2__bvfunc_3,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
     => ! [A] : 
          ( m1_eqrel_1(A,c1_2__bvfunc_3)
         => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,A),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,A)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3)) ) )
   => ! [B] : 
        ( m2_fraenkel(B,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
       => ! [C] : 
            ( m1_eqrel_1(C,c1_2__bvfunc_3)
           => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,C),k6_bvfunc_2(c1_2__bvfunc_3,B,c2_2__bvfunc_3,C)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,B)) ) ) ),
    introduced(definition,[new_symbol(c4_2__bvfunc_3),file(bvfunc_3,c4_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c4_2__bvfunc_3)]).

fof(dh_c5_2__bvfunc_3,definition,
    ( ( m1_eqrel_1(c5_2__bvfunc_3,c1_2__bvfunc_3)
     => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3)) )
   => ! [A] : 
        ( m1_eqrel_1(A,c1_2__bvfunc_3)
       => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,A),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,A)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3)) ) ),
    introduced(definition,[new_symbol(c5_2__bvfunc_3),file(bvfunc_3,c5_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c5_2__bvfunc_3)]).

fof(dt_k1_partit1,axiom,(
    $true ),
    file(partit1,k1_partit1),
    [interesting(0.9),axiom,file(partit1,k1_partit1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_m1_t_1topsp,axiom,(
    $true ),
    file(t_1topsp,m1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]).

fof(cc1_fraenkel,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]).

fof(rc1_fraenkel,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]).

fof(commutativity_k4_valuat_1,theorem,(
    ! [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) )
     => k4_valuat_1(A,B) = k4_valuat_1(B,A) ) ),
    file(valuat_1,k4_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k4_valuat_1)]).

fof(redefinition_k1_bvfunc_2,definition,(
    ! [A] : k1_bvfunc_2(A) = k1_partit1(A) ),
    file(bvfunc_2,k1_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,k1_bvfunc_2)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_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),
    [interesting(0.9),axiom,file(bvfunc_2,k1_bvfunc_2)]).

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    [interesting(0.9),axiom,file(funct_2,k1_funct_2)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k4_valuat_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(k4_valuat_1(A,B))
        & v1_funct_1(k4_valuat_1(A,B)) ) ) ),
    file(valuat_1,k4_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k4_valuat_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),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(fraenkel,m1_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),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(fc1_fraenkel,theorem,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,fc1_fraenkel)]).

fof(fc2_valuat_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(valuat_1,fc2_valuat_1)]).

fof(fc4_valuat_1,theorem,(
    ! [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(k4_valuat_1(A,B))
        & v1_funct_1(k4_valuat_1(A,B))
        & v1_valuat_1(k4_valuat_1(A,B)) ) ) ),
    file(valuat_1,fc4_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,fc4_valuat_1)]).

fof(rc1_valuat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_valuat_1(A) ) ),
    file(valuat_1,rc1_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,rc1_valuat_1)]).

fof(rc2_margrel1,theorem,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc2_margrel1)]).

fof(commutativity_k6_valuat_1,theorem,(
    ! [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)) )
     => k6_valuat_1(A,B,C) = k6_valuat_1(A,C,B) ) ),
    file(valuat_1,k6_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k6_valuat_1)]).

fof(reflexivity_r1_bvfunc_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(bvfunc_1,r1_bvfunc_1)]).

fof(redefinition_k1_fraenkel,definition,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,k1_fraenkel)]).

fof(redefinition_k6_valuat_1,definition,(
    ! [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)) )
     => k6_valuat_1(A,B,C) = k4_valuat_1(B,C) ) ),
    file(valuat_1,k6_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k6_valuat_1)]).

fof(redefinition_m2_fraenkel,definition,(
    ! [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),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,k1_fraenkel)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_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),
    [interesting(0.9),axiom,file(bvfunc_2,k6_bvfunc_2)]).

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    [interesting(0.9),axiom,file(margrel1,k6_margrel1)]).

fof(dt_k6_valuat_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(k6_valuat_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(valuat_1,k6_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,k6_valuat_1)]).

fof(dt_k8_margrel1,axiom,(
    m1_subset_1(k8_margrel1,k6_margrel1) ),
    file(margrel1,k8_margrel1),
    [interesting(0.9),axiom,file(margrel1,k8_margrel1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(dt_c1_2__bvfunc_3,assumption,(
    ~ v1_xboole_0(c1_2__bvfunc_3) ),
    introduced(assumption,[file(bvfunc_3,c1_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c1_2__bvfunc_3)]).

fof(dt_c2_2__bvfunc_3,assumption,(
    m1_subset_1(c2_2__bvfunc_3,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc_3))) ),
    introduced(assumption,[file(bvfunc_3,c2_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c2_2__bvfunc_3)]).

fof(dt_c3_2__bvfunc_3,assumption,(
    m2_fraenkel(c3_2__bvfunc_3,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1)) ),
    introduced(assumption,[file(bvfunc_3,c3_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c3_2__bvfunc_3)]).

fof(dt_c4_2__bvfunc_3,assumption,(
    m2_fraenkel(c4_2__bvfunc_3,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1)) ),
    introduced(assumption,[file(bvfunc_3,c4_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c4_2__bvfunc_3)]).

fof(dt_c5_2__bvfunc_3,assumption,(
    m1_eqrel_1(c5_2__bvfunc_3,c1_2__bvfunc_3) ),
    introduced(assumption,[file(bvfunc_3,c5_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c5_2__bvfunc_3)]).

fof(dt_c6_2__bvfunc_3,assumption,(
    m1_subset_1(c6_2__bvfunc_3,c1_2__bvfunc_3) ),
    introduced(assumption,[file(bvfunc_3,c6_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c6_2__bvfunc_3)]).

fof(cc1_margrel1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,cc1_margrel1)]).

fof(cc1_valuat_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
     => v1_valuat_1(B) ) ),
    file(valuat_1,cc1_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,cc1_valuat_1)]).

fof(fc3_margrel1,theorem,(
    ~ v1_xboole_0(k6_margrel1) ),
    file(margrel1,fc3_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc3_margrel1)]).

fof(d15_bvfunc_1,definition,(
    ! [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)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ( k1_funct_1(B,D) = k8_margrel1
                     => k1_funct_1(C,D) = k8_margrel1 ) ) ) ) ) ) ),
    file(bvfunc_1,d15_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,d15_bvfunc_1)]).

fof(dh_c6_2__bvfunc_3,definition,
    ( ( m1_subset_1(c6_2__bvfunc_3,c1_2__bvfunc_3)
     => ~ ( k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),c6_2__bvfunc_3) = k8_margrel1
          & k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3),c6_2__bvfunc_3) != k8_margrel1 ) )
   => ! [A] : 
        ( m1_subset_1(A,c1_2__bvfunc_3)
       => ~ ( k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),A) = k8_margrel1
            & k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3),A) != k8_margrel1 ) ) ),
    introduced(definition,[new_symbol(c6_2__bvfunc_3),file(bvfunc_3,c6_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,c6_2__bvfunc_3)]).

fof(e1_2__bvfunc_3,assumption,(
    k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),c6_2__bvfunc_3) = k8_margrel1 ),
    introduced(assumption,[file(bvfunc_3,e1_2__bvfunc_3)]),
    [interesting(0.8),axiom,file(bvfunc_3,e1_2__bvfunc_3)]).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(fc5_margrel1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => v2_margrel1(k10_margrel1(A,B)) ) ),
    file(margrel1,fc5_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc5_margrel1)]).

fof(commutativity_k10_margrel1,theorem,(
    ! [A,B] : 
      ( ( v2_margrel1(A)
        & v2_margrel1(B) )
     => k10_margrel1(A,B) = k10_margrel1(B,A) ) ),
    file(margrel1,k10_margrel1),
    [interesting(0.9),axiom,file(margrel1,k10_margrel1)]).

fof(commutativity_k12_margrel1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => k12_margrel1(A,B) = k12_margrel1(B,A) ) ),
    file(margrel1,k12_margrel1),
    [interesting(0.9),axiom,file(margrel1,k12_margrel1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(fraenkel,m2_fraenkel)]).

fof(redefinition_k12_margrel1,definition,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => k12_margrel1(A,B) = k10_margrel1(A,B) ) ),
    file(margrel1,k12_margrel1),
    [interesting(0.9),axiom,file(margrel1,k12_margrel1)]).

fof(redefinition_k8_funct_2,definition,(
    ! [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),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(dt_k10_margrel1,axiom,(
    $true ),
    file(margrel1,k10_margrel1),
    [interesting(0.9),axiom,file(margrel1,k10_margrel1)]).

fof(dt_k12_margrel1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_margrel1)
        & m1_subset_1(B,k6_margrel1) )
     => m1_subset_1(k12_margrel1(A,B),k6_margrel1) ) ),
    file(margrel1,k12_margrel1),
    [interesting(0.9),axiom,file(margrel1,k12_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),
    [interesting(0.9),axiom,file(funct_2,k8_funct_2)]).

fof(d6_valuat_1,definition,(
    ! [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 = k6_valuat_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k12_margrel1(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) ),
    file(valuat_1,d6_valuat_1),
    [interesting(0.9),axiom,file(valuat_1,d6_valuat_1)]).

fof(e1_2_3__bvfunc_3,plain,(
    k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3),c6_2__bvfunc_3) = k10_margrel1(k1_funct_1(c3_2__bvfunc_3,c6_2__bvfunc_3),k1_funct_1(c4_2__bvfunc_3,c6_2__bvfunc_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c6_2__bvfunc_3])],[dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc1_fraenkel,rc1_fraenkel,commutativity_k4_valuat_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k4_valuat_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,fc4_valuat_1,fc5_margrel1,rc1_valuat_1,rc2_margrel1,commutativity_k10_margrel1,commutativity_k12_margrel1,commutativity_k6_valuat_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k12_margrel1,redefinition_k1_fraenkel,redefinition_k6_valuat_1,redefinition_k8_funct_2,redefinition_m2_fraenkel,dt_k10_margrel1,dt_k12_margrel1,dt_k1_fraenkel,dt_k1_funct_1,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_funct_2,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c6_2__bvfunc_3,cc1_margrel1,cc1_valuat_1,fc3_margrel1,d6_valuat_1]),
    [interesting(0.65),file(bvfunc_3,e1_2_3__bvfunc_3),[file(bvfunc_3,e1_2_3__bvfunc_3)]]).

fof(existence_m1_t_1topsp,axiom,(
    ! [A] : 
    ? [B] : m1_t_1topsp(B,A) ),
    file(t_1topsp,m1_t_1topsp),
    [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]).

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),
    [interesting(0.9),axiom,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),
    [interesting(0.9),axiom,file(eqrel_1,m1_eqrel_1)]).

fof(redefinition_m1_bvfunc_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(bvfunc_1,m1_bvfunc_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),
    [interesting(0.9),axiom,file(t_1topsp,k1_t_1topsp)]).

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),
    [interesting(0.9),axiom,file(bvfunc_1,m1_bvfunc_1)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(redefinition_k22_bvfunc_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(bvfunc_1,k22_bvfunc_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),
    [interesting(0.9),axiom,file(bvfunc_1,k22_bvfunc_1)]).

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),
    [interesting(0.9),axiom,file(bvfunc_2,k5_bvfunc_2)]).

fof(d1_t_1topsp,definition,(
    ! [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),
    [interesting(0.9),axiom,file(t_1topsp,d1_t_1topsp)]).

fof(e3_2__bvfunc_3,plain,
    ( r2_hidden(c6_2__bvfunc_3,k22_bvfunc_1(c1_2__bvfunc_3,c6_2__bvfunc_3,k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)))
    & r2_hidden(k22_bvfunc_1(c1_2__bvfunc_3,c6_2__bvfunc_3,k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)),k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,existence_m1_bvfunc_1,redefinition_k1_bvfunc_2,redefinition_m1_bvfunc_1,dt_k1_bvfunc_2,dt_m1_bvfunc_1,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k22_bvfunc_1,dt_k5_bvfunc_2,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,d1_t_1topsp]),
    [interesting(0.8),file(bvfunc_3,e3_2__bvfunc_3),[file(bvfunc_3,e3_2__bvfunc_3)]]).

fof(e1_2_1__bvfunc_3,assumption,(
    ? [A] : 
      ( m1_subset_1(A,c1_2__bvfunc_3)
      & r2_hidden(A,k22_bvfunc_1(c1_2__bvfunc_3,c6_2__bvfunc_3,k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)))
      & k1_funct_1(c3_2__bvfunc_3,A) != k8_margrel1 ) ),
    introduced(assumption,[file(bvfunc_3,e1_2_1__bvfunc_3)]),
    [interesting(0.65),axiom,file(bvfunc_3,e1_2_1__bvfunc_3)]).

fof(dt_k7_margrel1,axiom,(
    m1_subset_1(k7_margrel1,k6_margrel1) ),
    file(margrel1,k7_margrel1),
    [interesting(0.9),axiom,file(margrel1,k7_margrel1)]).

fof(dt_k23_bvfunc_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
        & m1_eqrel_1(C,A) )
     => m2_fraenkel(k23_bvfunc_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ),
    file(bvfunc_1,k23_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,k23_bvfunc_1)]).

fof(d19_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k23_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => ( ( ! [F] : 
                                ( m1_subset_1(F,A)
                               => ( r2_hidden(F,k22_bvfunc_1(A,E,C))
                                 => k1_funct_1(B,F) = k8_margrel1 ) )
                           => k1_funct_1(D,E) = k8_margrel1 )
                          & ( ? [F] : 
                                ( m1_subset_1(F,A)
                                & r2_hidden(F,k22_bvfunc_1(A,E,C))
                                & k1_funct_1(B,F) != k8_margrel1 )
                           => k1_funct_1(D,E) = k7_margrel1 ) ) ) ) ) ) ) ) ),
    file(bvfunc_1,d19_bvfunc_1),
    [interesting(0.9),axiom,file(bvfunc_1,d19_bvfunc_1)]).

fof(e2_2_1__bvfunc_3,plain,(
    k1_funct_1(k23_bvfunc_1(c1_2__bvfunc_3,c3_2__bvfunc_3,k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)),c6_2__bvfunc_3) = k7_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,e1_2_1__bvfunc_3])],[existence_m1_relset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_t_1topsp,cc1_fraenkel,rc1_fraenkel,existence_m1_bvfunc_1,existence_m1_fraenkel,existence_m2_relset_1,redefinition_k1_bvfunc_2,redefinition_m1_bvfunc_1,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_funct_2,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_m1_bvfunc_1,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,rc2_margrel1,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_k22_bvfunc_1,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k1_funct_1,dt_k22_bvfunc_1,dt_k23_bvfunc_1,dt_k5_bvfunc_2,dt_k6_margrel1,dt_k7_margrel1,dt_k8_margrel1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,cc1_margrel1,cc1_valuat_1,fc3_margrel1,e1_2_1__bvfunc_3,d19_bvfunc_1]),
    [interesting(0.65),file(bvfunc_3,e2_2_1__bvfunc_3),[file(bvfunc_3,e2_2_1__bvfunc_3)]]).

fof(d9_bvfunc_2,definition,(
    ! [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)
                 => k6_bvfunc_2(A,B,C,D) = k23_bvfunc_1(A,B,k5_bvfunc_2(A,D,C)) ) ) ) ) ),
    file(bvfunc_2,d9_bvfunc_2),
    [interesting(0.9),axiom,file(bvfunc_2,d9_bvfunc_2)]).

fof(e3_2_1__bvfunc_3,plain,(
    k1_funct_1(k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),c6_2__bvfunc_3) = k7_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,e1_2_1__bvfunc_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_partit1,dt_m1_fraenkel,dt_m1_t_1topsp,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,rc2_margrel1,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k23_bvfunc_1,dt_k5_bvfunc_2,dt_k6_bvfunc_2,dt_k6_margrel1,dt_k7_margrel1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,cc1_margrel1,cc1_valuat_1,fc3_margrel1,e2_2_1__bvfunc_3,d9_bvfunc_2]),
    [interesting(0.65),file(bvfunc_3,e3_2_1__bvfunc_3),[file(bvfunc_3,e3_2_1__bvfunc_3)]]).

fof(t43_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A != k8_margrel1
      <=> A = k7_margrel1 ) ) ),
    file(margrel1,t43_margrel1),
    [interesting(0.9),axiom,file(margrel1,t43_margrel1)]).

fof(e4_2_1__bvfunc_3,plain,(
    k1_funct_1(k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),c6_2__bvfunc_3) != k8_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,e1_2_1__bvfunc_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_partit1,dt_m1_fraenkel,dt_m1_t_1topsp,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_zfmisc_1,dt_k6_margrel1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,fc3_margrel1,dt_k1_funct_1,dt_k6_bvfunc_2,dt_k7_margrel1,dt_k8_margrel1,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,rc2_margrel1,e3_2_1__bvfunc_3,t43_margrel1]),
    [interesting(0.65),file(bvfunc_3,e4_2_1__bvfunc_3),[file(bvfunc_3,e4_2_1__bvfunc_3)]]).

fof(e2_2__bvfunc_3,plain,(
    k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),c6_2__bvfunc_3) = k10_margrel1(k1_funct_1(k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),c6_2__bvfunc_3),k1_funct_1(k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),c6_2__bvfunc_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[existence_m1_t_1topsp,dt_k1_partit1,dt_k2_zfmisc_1,dt_m1_t_1topsp,cc1_fraenkel,rc1_fraenkel,commutativity_k4_valuat_1,existence_m1_eqrel_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m2_relset_1,redefinition_k1_bvfunc_2,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_funct_2,dt_k1_zfmisc_1,dt_k4_valuat_1,dt_m1_eqrel_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,fc4_valuat_1,fc5_margrel1,rc1_valuat_1,rc2_margrel1,commutativity_k10_margrel1,commutativity_k12_margrel1,commutativity_k6_valuat_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k12_margrel1,redefinition_k1_fraenkel,redefinition_k6_valuat_1,redefinition_k8_funct_2,redefinition_m2_fraenkel,dt_k10_margrel1,dt_k12_margrel1,dt_k1_fraenkel,dt_k1_funct_1,dt_k6_bvfunc_2,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_funct_2,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,cc1_margrel1,cc1_valuat_1,fc3_margrel1,d6_valuat_1]),
    [interesting(0.8),file(bvfunc_3,e2_2__bvfunc_3),[file(bvfunc_3,e2_2__bvfunc_3)]]).

fof(t45_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ( ( k10_margrel1(A,B) = k8_margrel1
             => ( A = k8_margrel1
                & B = k8_margrel1 ) )
            & ( ( A = k8_margrel1
                & B = k8_margrel1 )
             => k10_margrel1(A,B) = k8_margrel1 )
            & ~ ( k10_margrel1(A,B) = k7_margrel1
                & A != k7_margrel1
                & B != k7_margrel1 )
            & ( ( A = k7_margrel1
                | B = k7_margrel1 )
             => k10_margrel1(A,B) = k7_margrel1 ) ) ) ) ),
    file(margrel1,t45_margrel1),
    [interesting(0.9),axiom,file(margrel1,t45_margrel1)]).

fof(e5_2_1__bvfunc_3,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_2_1__bvfunc_3,e1_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_partit1,dt_m1_fraenkel,dt_m1_t_1topsp,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,fc4_valuat_1,rc1_valuat_1,commutativity_k4_valuat_1,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_zfmisc_1,dt_k4_valuat_1,dt_k6_margrel1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,fc3_margrel1,commutativity_k10_margrel1,commutativity_k6_valuat_1,redefinition_k6_valuat_1,dt_k10_margrel1,dt_k1_funct_1,dt_k6_bvfunc_2,dt_k6_valuat_1,dt_k7_margrel1,dt_k8_margrel1,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,fc5_margrel1,rc2_margrel1,e4_2_1__bvfunc_3,e1_2__bvfunc_3,e2_2__bvfunc_3,t45_margrel1]),
    [interesting(0.65),file(bvfunc_3,e5_2_1__bvfunc_3),[file(bvfunc_3,e5_2_1__bvfunc_3)]]).

fof(i2_2_1__bvfunc_3,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_3,i2_2_1__bvfunc_3)]),
    [interesting(0.65),trivial,file(bvfunc_3,i2_2_1__bvfunc_3)]).

fof(i1_2_1__bvfunc_3,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_2_1__bvfunc_3,e1_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[e5_2_1__bvfunc_3,i2_2_1__bvfunc_3]),
    [interesting(0.65),file(bvfunc_3,i1_2_1__bvfunc_3),[file(bvfunc_3,i1_2_1__bvfunc_3)]]).

fof(e4_2__bvfunc_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,c1_2__bvfunc_3)
     => ( r2_hidden(A,k22_bvfunc_1(c1_2__bvfunc_3,c6_2__bvfunc_3,k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)))
       => k1_funct_1(c3_2__bvfunc_3,A) = k8_margrel1 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3]),discharge_asm(discharge,[e1_2_1__bvfunc_3])],[e1_2_1__bvfunc_3,i1_2_1__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,e4_2__bvfunc_3),[file(bvfunc_3,e4_2__bvfunc_3)]]).

fof(e1_2_2__bvfunc_3,assumption,(
    ? [A] : 
      ( m1_subset_1(A,c1_2__bvfunc_3)
      & r2_hidden(A,k22_bvfunc_1(c1_2__bvfunc_3,c6_2__bvfunc_3,k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)))
      & k1_funct_1(c4_2__bvfunc_3,A) != k8_margrel1 ) ),
    introduced(assumption,[file(bvfunc_3,e1_2_2__bvfunc_3)]),
    [interesting(0.65),axiom,file(bvfunc_3,e1_2_2__bvfunc_3)]).

fof(e2_2_2__bvfunc_3,plain,(
    k1_funct_1(k23_bvfunc_1(c1_2__bvfunc_3,c4_2__bvfunc_3,k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)),c6_2__bvfunc_3) = k7_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,e1_2_2__bvfunc_3])],[existence_m1_relset_1,existence_m1_t_1topsp,dt_k1_partit1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_t_1topsp,cc1_fraenkel,rc1_fraenkel,existence_m1_bvfunc_1,existence_m1_fraenkel,existence_m2_relset_1,redefinition_k1_bvfunc_2,redefinition_m1_bvfunc_1,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_funct_2,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_m1_bvfunc_1,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,rc2_margrel1,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_fraenkel,redefinition_k22_bvfunc_1,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k1_funct_1,dt_k22_bvfunc_1,dt_k23_bvfunc_1,dt_k5_bvfunc_2,dt_k6_margrel1,dt_k7_margrel1,dt_k8_margrel1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,cc1_margrel1,cc1_valuat_1,fc3_margrel1,e1_2_2__bvfunc_3,d19_bvfunc_1]),
    [interesting(0.65),file(bvfunc_3,e2_2_2__bvfunc_3),[file(bvfunc_3,e2_2_2__bvfunc_3)]]).

fof(e3_2_2__bvfunc_3,plain,(
    k1_funct_1(k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),c6_2__bvfunc_3) = k7_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,e1_2_2__bvfunc_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_partit1,dt_m1_fraenkel,dt_m1_t_1topsp,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,rc2_margrel1,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k23_bvfunc_1,dt_k5_bvfunc_2,dt_k6_bvfunc_2,dt_k6_margrel1,dt_k7_margrel1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,cc1_margrel1,cc1_valuat_1,fc3_margrel1,e2_2_2__bvfunc_3,d9_bvfunc_2]),
    [interesting(0.65),file(bvfunc_3,e3_2_2__bvfunc_3),[file(bvfunc_3,e3_2_2__bvfunc_3)]]).

fof(e4_2_2__bvfunc_3,plain,(
    k1_funct_1(k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),c6_2__bvfunc_3) != k8_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,e1_2_2__bvfunc_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_partit1,dt_m1_fraenkel,dt_m1_t_1topsp,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_zfmisc_1,dt_k6_margrel1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,fc3_margrel1,dt_k1_funct_1,dt_k6_bvfunc_2,dt_k7_margrel1,dt_k8_margrel1,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,rc2_margrel1,e3_2_2__bvfunc_3,t43_margrel1]),
    [interesting(0.65),file(bvfunc_3,e4_2_2__bvfunc_3),[file(bvfunc_3,e4_2_2__bvfunc_3)]]).

fof(e5_2_2__bvfunc_3,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_2_2__bvfunc_3,e1_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_partit1,dt_m1_fraenkel,dt_m1_t_1topsp,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,fc4_valuat_1,rc1_valuat_1,commutativity_k4_valuat_1,existence_m1_eqrel_1,existence_m1_subset_1,existence_m2_fraenkel,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_m2_fraenkel,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_zfmisc_1,dt_k4_valuat_1,dt_k6_margrel1,dt_m1_eqrel_1,dt_m1_subset_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,fc3_margrel1,commutativity_k10_margrel1,commutativity_k6_valuat_1,redefinition_k6_valuat_1,dt_k10_margrel1,dt_k1_funct_1,dt_k6_bvfunc_2,dt_k6_valuat_1,dt_k7_margrel1,dt_k8_margrel1,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,fc5_margrel1,rc2_margrel1,e4_2_2__bvfunc_3,e1_2__bvfunc_3,e2_2__bvfunc_3,t45_margrel1]),
    [interesting(0.65),file(bvfunc_3,e5_2_2__bvfunc_3),[file(bvfunc_3,e5_2_2__bvfunc_3)]]).

fof(i2_2_2__bvfunc_3,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_3,i2_2_2__bvfunc_3)]),
    [interesting(0.65),trivial,file(bvfunc_3,i2_2_2__bvfunc_3)]).

fof(i1_2_2__bvfunc_3,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_2_2__bvfunc_3,e1_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[e5_2_2__bvfunc_3,i2_2_2__bvfunc_3]),
    [interesting(0.65),file(bvfunc_3,i1_2_2__bvfunc_3),[file(bvfunc_3,i1_2_2__bvfunc_3)]]).

fof(e5_2__bvfunc_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,c1_2__bvfunc_3)
     => ( r2_hidden(A,k22_bvfunc_1(c1_2__bvfunc_3,c6_2__bvfunc_3,k5_bvfunc_2(c1_2__bvfunc_3,c5_2__bvfunc_3,c2_2__bvfunc_3)))
       => k1_funct_1(c4_2__bvfunc_3,A) = k8_margrel1 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3]),discharge_asm(discharge,[e1_2_2__bvfunc_3])],[e1_2_2__bvfunc_3,i1_2_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,e5_2__bvfunc_3),[file(bvfunc_3,e5_2__bvfunc_3)]]).

fof(e6_2__bvfunc_3,plain,(
    k1_funct_1(c4_2__bvfunc_3,c6_2__bvfunc_3) = k8_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([e1_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_partit1,dt_m1_fraenkel,dt_m1_t_1topsp,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,rc2_margrel1,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m2_fraenkel,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_m1_bvfunc_1,redefinition_m2_fraenkel,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k6_margrel1,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,fc3_margrel1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k22_bvfunc_1,dt_k1_funct_1,dt_k22_bvfunc_1,dt_k5_bvfunc_2,dt_k8_margrel1,dt_m1_subset_1,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,e5_2__bvfunc_3,e3_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,e6_2__bvfunc_3),[file(bvfunc_3,e6_2__bvfunc_3)]]).

fof(e2_2_3__bvfunc_3,plain,(
    k10_margrel1(k1_funct_1(c3_2__bvfunc_3,c6_2__bvfunc_3),k1_funct_1(c4_2__bvfunc_3,c6_2__bvfunc_3)) = k12_margrel1(k8_margrel1,k8_margrel1) ),
    inference(mizar_by,[status(thm),assumptions([e1_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_fraenkel,rc1_fraenkel,existence_m1_fraenkel,existence_m1_t_1topsp,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_2,dt_k1_partit1,dt_m1_fraenkel,dt_m1_t_1topsp,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,rc1_valuat_1,existence_m1_bvfunc_1,existence_m1_eqrel_1,existence_m2_fraenkel,redefinition_k1_bvfunc_2,redefinition_k1_fraenkel,redefinition_m1_bvfunc_1,redefinition_m2_fraenkel,dt_k1_bvfunc_2,dt_k1_fraenkel,dt_k1_t_1topsp,dt_k1_zfmisc_1,dt_k6_margrel1,dt_m1_bvfunc_1,dt_m1_eqrel_1,dt_m2_fraenkel,cc1_margrel1,cc1_valuat_1,fc3_margrel1,fc5_margrel1,rc2_margrel1,commutativity_k10_margrel1,commutativity_k12_margrel1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k12_margrel1,redefinition_k22_bvfunc_1,dt_k10_margrel1,dt_k12_margrel1,dt_k1_funct_1,dt_k22_bvfunc_1,dt_k5_bvfunc_2,dt_k8_margrel1,dt_m1_subset_1,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3,e3_2__bvfunc_3,e4_2__bvfunc_3,e6_2__bvfunc_3]),
    [interesting(0.65),file(bvfunc_3,e2_2_3__bvfunc_3),[file(bvfunc_3,e2_2_3__bvfunc_3)]]).

fof(e3_2_3__bvfunc_3,plain,(
    k12_margrel1(k8_margrel1,k8_margrel1) = k8_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_k6_margrel1,dt_m1_subset_1,cc1_margrel1,fc3_margrel1,commutativity_k10_margrel1,commutativity_k12_margrel1,redefinition_k12_margrel1,dt_k10_margrel1,dt_k12_margrel1,dt_k7_margrel1,dt_k8_margrel1,fc5_margrel1,rc2_margrel1,t45_margrel1]),
    [interesting(0.65),file(bvfunc_3,e3_2_3__bvfunc_3),[file(bvfunc_3,e3_2_3__bvfunc_3)]]).

fof(e7_2__bvfunc_3,plain,(
    k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3),c6_2__bvfunc_3) = k8_margrel1 ),
    inference(iterative_eq,[status(thm),assumptions([e1_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[e1_2_3__bvfunc_3,e2_2_3__bvfunc_3,e3_2_3__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,e7_2__bvfunc_3),[file(bvfunc_3,e7_2__bvfunc_3)]]).

fof(i8_2__bvfunc_3,theorem,(
    $true ),
    introduced(tautology,[file(bvfunc_3,i8_2__bvfunc_3)]),
    [interesting(0.8),trivial,file(bvfunc_3,i8_2__bvfunc_3)]).

fof(i7_2__bvfunc_3,plain,(
    k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3),c6_2__bvfunc_3) = k8_margrel1 ),
    inference(conclusion,[status(thm),assumptions([e1_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3])],[e7_2__bvfunc_3,i8_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,i7_2__bvfunc_3),[file(bvfunc_3,i7_2__bvfunc_3)]]).

fof(i6_2__bvfunc_3,plain,(
    ~ ( k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),c6_2__bvfunc_3) = k8_margrel1
      & k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3),c6_2__bvfunc_3) != k8_margrel1 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3,dt_c6_2__bvfunc_3]),discharge_asm(discharge,[e1_2__bvfunc_3])],[e1_2__bvfunc_3,i7_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,i6_2__bvfunc_3),[file(bvfunc_3,i6_2__bvfunc_3)]]).

fof(i6_2_tmp__bvfunc_3,plain,
    ( m1_subset_1(c6_2__bvfunc_3,c1_2__bvfunc_3)
   => ~ ( k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),c6_2__bvfunc_3) = k8_margrel1
        & k1_funct_1(k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3),c6_2__bvfunc_3) != k8_margrel1 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3]),discharge_asm(discharge,[dt_c6_2__bvfunc_3])],[dt_c6_2__bvfunc_3,i6_2__bvfunc_3]),
    [interesting(0.8),i5_2__bvfunc_3]).

fof(i5_2__bvfunc_3,plain,(
    r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3)) ),
    inference(let,[status(thm),assumptions([dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c5_2__bvfunc_3])],[i6_2_tmp__bvfunc_3,dt_k1_partit1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_t_1topsp,cc1_fraenkel,rc1_fraenkel,commutativity_k4_valuat_1,redefinition_k1_bvfunc_2,redefinition_m2_relset_1,dt_k1_bvfunc_2,dt_k1_funct_2,dt_k1_zfmisc_1,dt_k4_valuat_1,dt_m1_eqrel_1,dt_m1_fraenkel,dt_m2_relset_1,fc1_fraenkel,fc2_valuat_1,fc4_valuat_1,rc1_valuat_1,rc2_margrel1,commutativity_k6_valuat_1,reflexivity_r1_bvfunc_1,redefinition_k1_fraenkel,redefinition_k6_valuat_1,redefinition_m2_fraenkel,dt_k1_fraenkel,dt_k1_funct_1,dt_k6_bvfunc_2,dt_k6_margrel1,dt_k6_valuat_1,dt_k8_margrel1,dt_m1_subset_1,dt_m2_fraenkel,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3,dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c5_2__bvfunc_3,cc1_margrel1,cc1_valuat_1,fc3_margrel1,d15_bvfunc_1,dh_c6_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,i5_2__bvfunc_3),[file(bvfunc_3,i5_2__bvfunc_3)]]).

fof(i5_2_tmp__bvfunc_3,plain,
    ( m1_eqrel_1(c5_2__bvfunc_3,c1_2__bvfunc_3)
   => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,c5_2__bvfunc_3)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3]),discharge_asm(discharge,[dt_c5_2__bvfunc_3])],[dt_c5_2__bvfunc_3,i5_2__bvfunc_3]),
    [interesting(0.8),i4_2__bvfunc_3]).

fof(i4_2__bvfunc_3,plain,(
    ! [A] : 
      ( m1_eqrel_1(A,c1_2__bvfunc_3)
     => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,A),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,A)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3)) ) ),
    inference(let,[status(thm),assumptions([dt_c3_2__bvfunc_3,dt_c4_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3])],[i5_2_tmp__bvfunc_3,dh_c5_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,i4_2__bvfunc_3),[file(bvfunc_3,i4_2__bvfunc_3)]]).

fof(i4_2_tmp__bvfunc_3,plain,
    ( m2_fraenkel(c4_2__bvfunc_3,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
   => ! [A] : 
        ( m1_eqrel_1(A,c1_2__bvfunc_3)
       => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,A),k6_bvfunc_2(c1_2__bvfunc_3,c4_2__bvfunc_3,c2_2__bvfunc_3,A)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,c4_2__bvfunc_3)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3]),discharge_asm(discharge,[dt_c4_2__bvfunc_3])],[dt_c4_2__bvfunc_3,i4_2__bvfunc_3]),
    [interesting(0.8),i3_2__bvfunc_3]).

fof(i3_2__bvfunc_3,plain,(
    ! [A] : 
      ( m2_fraenkel(A,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
     => ! [B] : 
          ( m1_eqrel_1(B,c1_2__bvfunc_3)
         => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,B),k6_bvfunc_2(c1_2__bvfunc_3,A,c2_2__bvfunc_3,B)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,A)) ) ) ),
    inference(let,[status(thm),assumptions([dt_c3_2__bvfunc_3,dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3])],[i4_2_tmp__bvfunc_3,dh_c4_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,i3_2__bvfunc_3),[file(bvfunc_3,i3_2__bvfunc_3)]]).

fof(i3_2_tmp__bvfunc_3,plain,
    ( m2_fraenkel(c3_2__bvfunc_3,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
   => ! [A] : 
        ( m2_fraenkel(A,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
       => ! [B] : 
            ( m1_eqrel_1(B,c1_2__bvfunc_3)
           => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,c3_2__bvfunc_3,c2_2__bvfunc_3,B),k6_bvfunc_2(c1_2__bvfunc_3,A,c2_2__bvfunc_3,B)),k6_valuat_1(c1_2__bvfunc_3,c3_2__bvfunc_3,A)) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3]),discharge_asm(discharge,[dt_c3_2__bvfunc_3])],[dt_c3_2__bvfunc_3,i3_2__bvfunc_3]),
    [interesting(0.8),i2_2__bvfunc_3]).

fof(i2_2__bvfunc_3,plain,(
    ! [A] : 
      ( m2_fraenkel(A,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
     => ! [B] : 
          ( m2_fraenkel(B,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
         => ! [C] : 
              ( m1_eqrel_1(C,c1_2__bvfunc_3)
             => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,A,c2_2__bvfunc_3,C),k6_bvfunc_2(c1_2__bvfunc_3,B,c2_2__bvfunc_3,C)),k6_valuat_1(c1_2__bvfunc_3,A,B)) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__bvfunc_3,dt_c2_2__bvfunc_3])],[i3_2_tmp__bvfunc_3,dh_c3_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,i2_2__bvfunc_3),[file(bvfunc_3,i2_2__bvfunc_3)]]).

fof(i2_2_tmp__bvfunc_3,plain,
    ( m1_subset_1(c2_2__bvfunc_3,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc_3)))
   => ! [A] : 
        ( m2_fraenkel(A,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
       => ! [B] : 
            ( m2_fraenkel(B,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
           => ! [C] : 
                ( m1_eqrel_1(C,c1_2__bvfunc_3)
               => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,A,c2_2__bvfunc_3,C),k6_bvfunc_2(c1_2__bvfunc_3,B,c2_2__bvfunc_3,C)),k6_valuat_1(c1_2__bvfunc_3,A,B)) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__bvfunc_3]),discharge_asm(discharge,[dt_c2_2__bvfunc_3])],[dt_c2_2__bvfunc_3,i2_2__bvfunc_3]),
    [interesting(0.8),i1_2__bvfunc_3]).

fof(i1_2__bvfunc_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc_3)))
     => ! [B] : 
          ( m2_fraenkel(B,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,c1_2__bvfunc_3)
                 => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,B,A,D),k6_bvfunc_2(c1_2__bvfunc_3,C,A,D)),k6_valuat_1(c1_2__bvfunc_3,B,C)) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__bvfunc_3])],[i2_2_tmp__bvfunc_3,dh_c2_2__bvfunc_3]),
    [interesting(0.8),file(bvfunc_3,i1_2__bvfunc_3),[file(bvfunc_3,i1_2__bvfunc_3)]]).

fof(i1_2_tmp__bvfunc_3,plain,
    ( ~ v1_xboole_0(c1_2__bvfunc_3)
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc_3)))
       => ! [B] : 
            ( m2_fraenkel(B,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
           => ! [C] : 
                ( m2_fraenkel(C,c1_2__bvfunc_3,k6_margrel1,k1_fraenkel(c1_2__bvfunc_3,k6_margrel1))
               => ! [D] : 
                    ( m1_eqrel_1(D,c1_2__bvfunc_3)
                   => r1_bvfunc_1(c1_2__bvfunc_3,k6_valuat_1(c1_2__bvfunc_3,k6_bvfunc_2(c1_2__bvfunc_3,B,A,D),k6_bvfunc_2(c1_2__bvfunc_3,C,A,D)),k6_valuat_1(c1_2__bvfunc_3,B,C)) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__bvfunc_3])],[dt_c1_2__bvfunc_3,i1_2__bvfunc_3]),
    [interesting(1),t2_bvfunc_3]).

fof(t2_bvfunc_3,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k6_valuat_1(A,C,D)) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__bvfunc_3,dh_c1_2__bvfunc_3]),
    [interesting(1),file(bvfunc_3,t2_bvfunc_3),[file(bvfunc_3,t2_bvfunc_3)]]).