% Mizar ND problem: t5_autgroup,autgroup,211,43 
fof(dh_c1_6__autgroup,definition,
    ( ( ( ~ v3_struct_0(c1_6__autgroup)
        & v1_group_1(c1_6__autgroup)
        & v3_group_1(c1_6__autgroup)
        & v4_group_1(c1_6__autgroup)
        & l1_group_1(c1_6__autgroup) )
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup))
            & v1_group_6(A,c1_6__autgroup,c1_6__autgroup)
            & m2_relset_1(A,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup)) )
         => ( r2_hidden(A,k1_autgroup(c1_6__autgroup))
          <=> v4_group_6(A,c1_6__autgroup,c1_6__autgroup) ) ) )
   => ! [B] : 
        ( ( ~ v3_struct_0(B)
          & v1_group_1(B)
          & v3_group_1(B)
          & v4_group_1(B)
          & l1_group_1(B) )
       => ! [C] : 
            ( ( v1_funct_1(C)
              & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
              & v1_group_6(C,B,B)
              & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
           => ( r2_hidden(C,k1_autgroup(B))
            <=> v4_group_6(C,B,B) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__autgroup),file(autgroup,c1_6__autgroup)]),
    [interesting(0.8),axiom,file(autgroup,c1_6__autgroup)]).

fof(dh_c2_6__autgroup,definition,
    ( ( ( v1_funct_1(c2_6__autgroup)
        & v1_funct_2(c2_6__autgroup,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup))
        & v1_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup)
        & m2_relset_1(c2_6__autgroup,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup)) )
     => ( r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup))
      <=> v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup))
          & v1_group_6(A,c1_6__autgroup,c1_6__autgroup)
          & m2_relset_1(A,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup)) )
       => ( r2_hidden(A,k1_autgroup(c1_6__autgroup))
        <=> v4_group_6(A,c1_6__autgroup,c1_6__autgroup) ) ) ),
    introduced(definition,[new_symbol(c2_6__autgroup),file(autgroup,c2_6__autgroup)]),
    [interesting(0.8),axiom,file(autgroup,c2_6__autgroup)]).

fof(e1_6_1__autgroup,assumption,(
    r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup)) ),
    introduced(assumption,[file(autgroup,e1_6_1__autgroup)]),
    [interesting(0.65),axiom,file(autgroup,e1_6_1__autgroup)]).

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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(cc1_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

fof(rc2_group_6,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ? [C] : 
          ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
          & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
          & v1_group_6(C,A,B) ) ) ),
    file(group_6,rc2_group_6),
    [interesting(0.9),axiom,file(group_6,rc2_group_6)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(free_g1_group_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C,D] : 
          ( g1_group_1(A,B) = g1_group_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(group_1,g1_group_1),
    [interesting(0.9),axiom,file(group_1,g1_group_1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_g1_group_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_group_1(g1_group_1(A,B))
        & l1_group_1(g1_group_1(A,B)) ) ) ),
    file(group_1,g1_group_1),
    [interesting(0.9),axiom,file(group_1,g1_group_1)]).

fof(dt_u1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_funct_1(u1_group_1(A))
        & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(group_1,u1_group_1),
    [interesting(0.9),axiom,file(group_1,u1_group_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc5_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

fof(fc1_group_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g1_group_1(A,B))
        & v1_group_1(g1_group_1(A,B)) ) ) ),
    file(group_1,fc1_group_1),
    [interesting(0.9),axiom,file(group_1,fc1_group_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc1_funct_2,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(abstractness_v1_group_1,theorem,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_group_1(A)
       => A = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ),
    file(group_1,v1_group_1),
    [interesting(0.9),axiom,file(group_1,v1_group_1)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

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

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_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(rc1_group_1,theorem,(
    ? [A] : 
      ( l1_group_1(A)
      & v1_group_1(A) ) ),
    file(group_1,rc1_group_1),
    [interesting(0.9),axiom,file(group_1,rc1_group_1)]).

fof(rc2_group_1,theorem,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v1_group_1(A) ) ),
    file(group_1,rc2_group_1),
    [interesting(0.9),axiom,file(group_1,rc2_group_1)]).

fof(rc3_group_1,theorem,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v1_group_1(A)
      & v2_group_1(A)
      & v3_group_1(A)
      & v4_group_1(A) ) ),
    file(group_1,rc3_group_1),
    [interesting(0.9),axiom,file(group_1,rc3_group_1)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    [interesting(0.9),axiom,file(group_1,l1_group_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(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_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    [interesting(0.9),axiom,file(group_1,l1_group_1)]).

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(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_6__autgroup,assumption,
    ( ~ v3_struct_0(c1_6__autgroup)
    & v1_group_1(c1_6__autgroup)
    & v3_group_1(c1_6__autgroup)
    & v4_group_1(c1_6__autgroup)
    & l1_group_1(c1_6__autgroup) ),
    introduced(assumption,[file(autgroup,c1_6__autgroup)]),
    [interesting(0.8),axiom,file(autgroup,c1_6__autgroup)]).

fof(dt_c2_6__autgroup,assumption,
    ( v1_funct_1(c2_6__autgroup)
    & v1_funct_2(c2_6__autgroup,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup))
    & v1_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup)
    & m2_relset_1(c2_6__autgroup,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup)) ),
    introduced(assumption,[file(autgroup,c2_6__autgroup)]),
    [interesting(0.8),axiom,file(autgroup,c2_6__autgroup)]).

fof(cc1_group_1,theorem,(
    ! [A] : 
      ( l1_group_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(group_1,cc1_group_1),
    [interesting(0.9),axiom,file(group_1,cc1_group_1)]).

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(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_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_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_autgroup,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(autgroup,k1_autgroup),
    [interesting(0.9),axiom,file(autgroup,k1_autgroup)]).

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_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(d1_autgroup,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k1_autgroup(A)
          <=> ( ! [C] : 
                  ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B)
                 => ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & v1_group_6(C,A,A)
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) )
              & ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & v1_group_6(C,A,A)
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => ( r2_hidden(C,B)
                  <=> ( v2_funct_1(C)
                      & v3_group_6(C,A,A) ) ) ) ) ) ) ) ),
    file(autgroup,d1_autgroup),
    [interesting(0.9),axiom,file(autgroup,d1_autgroup)]).

fof(e3_6_1__autgroup,plain,(
    v2_funct_1(c2_6__autgroup) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_1__autgroup])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc1_funct_2,cc2_funct_1,fc1_xboole_0,rc1_funct_1,rc1_funct_2,rc1_partfun1,rc2_funct_1,rc2_group_6,rc2_partfun1,rc3_funct_1,free_g1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_g1_group_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_u1_group_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_group_1,fc1_struct_0,rc1_fraenkel,rc1_xboole_0,rc2_xboole_0,rc3_group_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,abstractness_v1_group_1,existence_l1_group_1,existence_m1_fraenkel,existence_m2_fraenkel,existence_m2_relset_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_autgroup,dt_l1_group_1,dt_m1_fraenkel,dt_m2_fraenkel,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__autgroup,dt_c2_6__autgroup,cc1_group_1,rc1_group_1,rc2_group_1,t1_subset,t7_boole,e1_6_1__autgroup,d1_autgroup]),
    [interesting(0.65),file(autgroup,e3_6_1__autgroup),[file(autgroup,e3_6_1__autgroup)]]).

fof(d12_group_6,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v2_group_6(C,A,B)
              <=> v2_funct_1(C) ) ) ) ) ),
    file(group_6,d12_group_6),
    [interesting(0.9),axiom,file(group_6,d12_group_6)]).

fof(e4_6_1__autgroup,plain,(
    v2_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_1__autgroup])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,fc1_xboole_0,rc2_group_6,t1_subset,t4_subset,t5_subset,free_g1_group_1,reflexivity_r1_tarski,dt_g1_group_1,dt_u1_group_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_group_1,rc1_funct_1,rc1_funct_2,rc1_partfun1,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_xboole_0,rc3_funct_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_struct_0,rc1_group_1,rc2_group_1,rc3_group_1,rc3_struct_0,t3_subset,existence_l1_group_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_l1_group_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__autgroup,dt_c2_6__autgroup,cc1_group_1,e3_6_1__autgroup,d12_group_6]),
    [interesting(0.65),file(autgroup,e4_6_1__autgroup),[file(autgroup,e4_6_1__autgroup)]]).

fof(e2_6_1__autgroup,plain,(
    v3_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_1__autgroup])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc1_funct_2,cc2_funct_1,fc1_xboole_0,rc1_funct_1,rc1_funct_2,rc1_partfun1,rc2_funct_1,rc2_group_6,rc2_partfun1,rc3_funct_1,free_g1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_g1_group_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_u1_group_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_group_1,fc1_struct_0,rc1_fraenkel,rc1_xboole_0,rc2_xboole_0,rc3_group_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,abstractness_v1_group_1,existence_l1_group_1,existence_m1_fraenkel,existence_m2_fraenkel,existence_m2_relset_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_autgroup,dt_l1_group_1,dt_m1_fraenkel,dt_m2_fraenkel,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__autgroup,dt_c2_6__autgroup,cc1_group_1,rc1_group_1,rc2_group_1,t1_subset,t7_boole,e1_6_1__autgroup,d1_autgroup]),
    [interesting(0.65),file(autgroup,e2_6_1__autgroup),[file(autgroup,e2_6_1__autgroup)]]).

fof(d14_group_6,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v4_group_6(C,A,B)
              <=> ( v3_group_6(C,A,B)
                  & v2_group_6(C,A,B) ) ) ) ) ) ),
    file(group_6,d14_group_6),
    [interesting(0.9),axiom,file(group_6,d14_group_6)]).

fof(e5_6_1__autgroup,plain,(
    v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_1__autgroup])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,fc1_xboole_0,rc1_partfun1,rc2_group_6,rc3_funct_1,t1_subset,t4_subset,t5_subset,free_g1_group_1,reflexivity_r1_tarski,dt_g1_group_1,dt_u1_group_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_group_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_struct_0,rc1_group_1,rc2_group_1,rc3_group_1,rc3_struct_0,t3_subset,existence_l1_group_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_l1_group_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__autgroup,dt_c2_6__autgroup,cc1_group_1,e4_6_1__autgroup,e2_6_1__autgroup,d14_group_6]),
    [interesting(0.65),file(autgroup,e5_6_1__autgroup),[file(autgroup,e5_6_1__autgroup)]]).

fof(i2_6_1__autgroup,theorem,(
    $true ),
    introduced(tautology,[file(autgroup,i2_6_1__autgroup)]),
    [interesting(0.65),trivial,file(autgroup,i2_6_1__autgroup)]).

fof(i1_6_1__autgroup,plain,(
    v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_1__autgroup])],[e5_6_1__autgroup,i2_6_1__autgroup]),
    [interesting(0.65),file(autgroup,i1_6_1__autgroup),[file(autgroup,i1_6_1__autgroup)]]).

fof(e1_6__autgroup,plain,
    ( r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup))
   => v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup]),discharge_asm(discharge,[e1_6_1__autgroup])],[e1_6_1__autgroup,i1_6_1__autgroup]),
    [interesting(0.8),file(autgroup,e1_6__autgroup),[file(autgroup,e1_6__autgroup)]]).

fof(e1_6_2__autgroup,assumption,(
    v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ),
    introduced(assumption,[file(autgroup,e1_6_2__autgroup)]),
    [interesting(0.65),axiom,file(autgroup,e1_6_2__autgroup)]).

fof(e2_6_2__autgroup,plain,
    ( v3_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup)
    & v2_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_2__autgroup])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,fc1_xboole_0,rc1_partfun1,rc2_group_6,rc3_funct_1,t1_subset,t4_subset,t5_subset,free_g1_group_1,reflexivity_r1_tarski,dt_g1_group_1,dt_u1_group_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_group_1,rc1_funct_1,rc1_funct_2,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_struct_0,rc1_group_1,rc2_group_1,rc3_group_1,rc3_struct_0,t3_subset,existence_l1_group_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_l1_group_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__autgroup,dt_c2_6__autgroup,cc1_group_1,e1_6_2__autgroup,d14_group_6]),
    [interesting(0.65),file(autgroup,e2_6_2__autgroup),[file(autgroup,e2_6_2__autgroup)]]).

fof(e3_6_2__autgroup,plain,(
    v2_funct_1(c2_6__autgroup) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_2__autgroup])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_funct_2,fc1_xboole_0,rc2_group_6,t1_subset,t4_subset,t5_subset,free_g1_group_1,reflexivity_r1_tarski,dt_g1_group_1,dt_u1_group_1,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_group_1,rc1_funct_1,rc1_funct_2,rc1_partfun1,rc1_xboole_0,rc2_funct_1,rc2_partfun1,rc2_xboole_0,rc3_funct_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,abstractness_v1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_struct_0,rc1_group_1,rc2_group_1,rc3_group_1,rc3_struct_0,t3_subset,existence_l1_group_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_l1_group_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__autgroup,dt_c2_6__autgroup,cc1_group_1,e2_6_2__autgroup,d12_group_6]),
    [interesting(0.65),file(autgroup,e3_6_2__autgroup),[file(autgroup,e3_6_2__autgroup)]]).

fof(e4_6_2__autgroup,plain,(
    r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_2__autgroup])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc1_funct_2,cc2_funct_1,fc1_xboole_0,rc1_funct_1,rc1_funct_2,rc1_partfun1,rc2_funct_1,rc2_group_6,rc2_partfun1,rc3_funct_1,free_g1_group_1,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_g1_group_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_u1_group_1,cc1_fraenkel,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_group_1,fc1_struct_0,rc1_fraenkel,rc1_xboole_0,rc2_xboole_0,rc3_group_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,abstractness_v1_group_1,existence_l1_group_1,existence_m1_fraenkel,existence_m2_fraenkel,existence_m2_relset_1,redefinition_m2_fraenkel,redefinition_m2_relset_1,dt_k1_autgroup,dt_l1_group_1,dt_m1_fraenkel,dt_m2_fraenkel,dt_m2_relset_1,dt_u1_struct_0,dt_c1_6__autgroup,dt_c2_6__autgroup,cc1_group_1,rc1_group_1,rc2_group_1,t1_subset,t7_boole,e3_6_2__autgroup,e2_6_2__autgroup,d1_autgroup]),
    [interesting(0.65),file(autgroup,e4_6_2__autgroup),[file(autgroup,e4_6_2__autgroup)]]).

fof(i2_6_2__autgroup,theorem,(
    $true ),
    introduced(tautology,[file(autgroup,i2_6_2__autgroup)]),
    [interesting(0.65),trivial,file(autgroup,i2_6_2__autgroup)]).

fof(i1_6_2__autgroup,plain,(
    r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup,e1_6_2__autgroup])],[e4_6_2__autgroup,i2_6_2__autgroup]),
    [interesting(0.65),file(autgroup,i1_6_2__autgroup),[file(autgroup,i1_6_2__autgroup)]]).

fof(e2_6__autgroup,plain,
    ( v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup)
   => r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup]),discharge_asm(discharge,[e1_6_2__autgroup])],[e1_6_2__autgroup,i1_6_2__autgroup]),
    [interesting(0.8),file(autgroup,e2_6__autgroup),[file(autgroup,e2_6__autgroup)]]).

fof(i4_6__autgroup,theorem,(
    $true ),
    introduced(tautology,[file(autgroup,i4_6__autgroup)]),
    [interesting(0.8),trivial,file(autgroup,i4_6__autgroup)]).

fof(i3_6__autgroup,plain,
    ( v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup)
   => r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup])],[e2_6__autgroup,i4_6__autgroup]),
    [interesting(0.8),file(autgroup,i3_6__autgroup),[file(autgroup,i3_6__autgroup)]]).

fof(i2_6__autgroup,plain,
    ( r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup))
  <=> v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__autgroup,dt_c2_6__autgroup])],[e1_6__autgroup,i3_6__autgroup]),
    [interesting(0.8),file(autgroup,i2_6__autgroup),[file(autgroup,i2_6__autgroup)]]).

fof(i2_6_tmp__autgroup,plain,
    ( ( v1_funct_1(c2_6__autgroup)
      & v1_funct_2(c2_6__autgroup,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup))
      & v1_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup)
      & m2_relset_1(c2_6__autgroup,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup)) )
   => ( r2_hidden(c2_6__autgroup,k1_autgroup(c1_6__autgroup))
    <=> v4_group_6(c2_6__autgroup,c1_6__autgroup,c1_6__autgroup) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__autgroup]),discharge_asm(discharge,[dt_c2_6__autgroup])],[dt_c2_6__autgroup,i2_6__autgroup]),
    [interesting(0.8),i1_6__autgroup]).

fof(i1_6__autgroup,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup))
        & v1_group_6(A,c1_6__autgroup,c1_6__autgroup)
        & m2_relset_1(A,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup)) )
     => ( r2_hidden(A,k1_autgroup(c1_6__autgroup))
      <=> v4_group_6(A,c1_6__autgroup,c1_6__autgroup) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__autgroup])],[i2_6_tmp__autgroup,dh_c2_6__autgroup]),
    [interesting(0.8),file(autgroup,i1_6__autgroup),[file(autgroup,i1_6__autgroup)]]).

fof(i1_6_tmp__autgroup,plain,
    ( ( ~ v3_struct_0(c1_6__autgroup)
      & v1_group_1(c1_6__autgroup)
      & v3_group_1(c1_6__autgroup)
      & v4_group_1(c1_6__autgroup)
      & l1_group_1(c1_6__autgroup) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup))
          & v1_group_6(A,c1_6__autgroup,c1_6__autgroup)
          & m2_relset_1(A,u1_struct_0(c1_6__autgroup),u1_struct_0(c1_6__autgroup)) )
       => ( r2_hidden(A,k1_autgroup(c1_6__autgroup))
        <=> v4_group_6(A,c1_6__autgroup,c1_6__autgroup) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__autgroup])],[dt_c1_6__autgroup,i1_6__autgroup]),
    [interesting(1),t5_autgroup]).

fof(t5_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v1_group_6(B,A,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r2_hidden(B,k1_autgroup(A))
          <=> v4_group_6(B,A,A) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__autgroup,dh_c1_6__autgroup]),
    [interesting(1),file(autgroup,t5_autgroup),[file(autgroup,t5_autgroup)]]).