% Mizar ND problem: t9_group_2,group_2,118,42 
fof(dh_c1_6__group_2,definition,
    ( ( ( ~ v3_struct_0(c1_6__group_2)
        & v3_group_1(c1_6__group_2)
        & v4_group_1(c1_6__group_2)
        & l1_group_1(c1_6__group_2) )
     => k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2))) = u1_struct_0(c1_6__group_2) )
   => ! [A] : 
        ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & l1_group_1(A) )
       => k1_group_2(A,k2_subset_1(u1_struct_0(A))) = u1_struct_0(A) ) ),
    introduced(definition,[new_symbol(c1_6__group_2),file(group_2,c1_6__group_2)]),
    [interesting(0.8),axiom,file(group_2,c1_6__group_2)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc1_finsub_1,theorem,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,cc1_finsub_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_finsub_1,theorem,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,cc2_finsub_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

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_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(fc1_finsub_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    [interesting(0.9),axiom,file(finsub_1,fc1_finsub_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(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k1_group_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_group_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(group_2,k1_group_2),
    [interesting(0.9),axiom,file(group_2,k1_group_2)]).

fof(dt_k2_subset_1,axiom,(
    ! [A] : m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A)) ),
    file(subset_1,k2_subset_1),
    [interesting(0.9),axiom,file(subset_1,k2_subset_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__group_2,assumption,
    ( ~ v3_struct_0(c1_6__group_2)
    & v3_group_1(c1_6__group_2)
    & v4_group_1(c1_6__group_2)
    & l1_group_1(c1_6__group_2) ),
    introduced(assumption,[file(group_2,c1_6__group_2)]),
    [interesting(0.8),axiom,file(group_2,c1_6__group_2)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

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

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

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_k3_group_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k3_group_1(A,B),u1_struct_0(A)) ) ),
    file(group_1,k3_group_1),
    [interesting(0.9),axiom,file(group_1,k3_group_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(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(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(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(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_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_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(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_2_0_group_2,definition,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_group_2(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_struct_0(B))
            & A = k3_group_1(B,D)
            & r2_hidden(D,C) ) ) ) ),
    file(group_2,a_2_0_group_2),
    [interesting(0.9),axiom,file(group_2,a_2_0_group_2)]).

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(d1_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_group_2(A,B) = a_2_0_group_2(A,B) ) ) ),
    file(group_2,d1_group_2),
    [interesting(0.9),axiom,file(group_2,d1_group_2)]).

fof(e1_6__group_2,plain,(
    r1_tarski(k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2))),u1_struct_0(c1_6__group_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__group_2])],[dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,antisymmetry_r2_hidden,dt_k3_group_1,cc15_membered,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc2_finsub_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,t1_subset,t2_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_subset_1,cc1_group_1,fc1_finsub_1,fc1_struct_0,fc1_subset_1,rc3_struct_0,t2_tarski,fraenkel_a_2_0_group_2,reflexivity_r1_tarski,dt_k1_group_2,dt_k2_subset_1,dt_u1_struct_0,dt_c1_6__group_2,t3_subset,d1_group_2]),
    [interesting(0.8),file(group_2,e1_6__group_2),[file(group_2,e1_6__group_2)]]).

fof(dt_c2_6__group_2,assumption,(
    $true ),
    introduced(assumption,[file(group_2,c2_6__group_2)]),
    [interesting(0.8),axiom,file(group_2,c2_6__group_2)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c2_6__group_2,definition,
    ( ~ ( r2_hidden(c2_6__group_2,u1_struct_0(c1_6__group_2))
        & ~ r2_hidden(c2_6__group_2,k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2)))) )
   => ! [A] : 
        ~ ( r2_hidden(A,u1_struct_0(c1_6__group_2))
          & ~ r2_hidden(A,k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2)))) ) ),
    introduced(definition,[new_symbol(c2_6__group_2),file(group_2,c2_6__group_2)]),
    [interesting(0.8),axiom,file(group_2,c2_6__group_2)]).

fof(e2_6__group_2,assumption,(
    r2_hidden(c2_6__group_2,u1_struct_0(c1_6__group_2)) ),
    introduced(assumption,[file(group_2,e2_6__group_2)]),
    [interesting(0.8),axiom,file(group_2,e2_6__group_2)]).

fof(de_c3_6__group_2,definition,(
    c3_6__group_2 = c2_6__group_2 ),
    introduced(definition,[new_symbol(c3_6__group_2),file(group_2,c3_6__group_2)]),
    [interesting(0.8),axiom,file(group_2,c3_6__group_2)]).

fof(e3_6__group_2,plain,(
    m1_subset_1(c2_6__group_2,u1_struct_0(c1_6__group_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__group_2,dt_c2_6__group_2,e2_6__group_2])],[dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,t8_boole,existence_l1_group_1,existence_l1_struct_0,dt_l1_group_1,dt_l1_struct_0,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_struct_0,rc3_struct_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__group_2,dt_c2_6__group_2,t1_subset,t7_boole,e2_6__group_2]),
    [interesting(0.8),file(group_2,e3_6__group_2),[file(group_2,e3_6__group_2)]]).

fof(dt_c3_6__group_2,plain,(
    m1_subset_1(c3_6__group_2,u1_struct_0(c1_6__group_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__group_2,dt_c2_6__group_2,e2_6__group_2])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,t1_subset,cc15_membered,cc1_finset_1,cc1_funct_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_l1_struct_0,dt_l1_group_1,dt_l1_struct_0,cc1_group_1,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__group_2,dt_c2_6__group_2,de_c3_6__group_2,e3_6__group_2]),
    [interesting(0.8),file(group_2,c3_6__group_2),[file(group_2,c3_6__group_2)]]).

fof(e4_6__group_2,plain,(
    r2_hidden(k3_group_1(c1_6__group_2,c3_6__group_2),u1_struct_0(c1_6__group_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__group_2,dt_c2_6__group_2,e2_6__group_2])],[dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,existence_l1_group_1,existence_l1_struct_0,existence_m1_subset_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_subset_1,dt_c2_6__group_2,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_struct_0,rc3_struct_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_group_1,dt_u1_struct_0,dt_c1_6__group_2,dt_c3_6__group_2,de_c3_6__group_2,t1_subset,t7_boole]),
    [interesting(0.8),file(group_2,e4_6__group_2),[file(group_2,e4_6__group_2)]]).

fof(d4_subset_1,definition,(
    ! [A] : k2_subset_1(A) = A ),
    file(subset_1,d4_subset_1),
    [interesting(0.9),axiom,file(subset_1,d4_subset_1)]).

fof(e5_6__group_2,plain,(
    r2_hidden(k3_group_1(c1_6__group_2,c3_6__group_2),k2_subset_1(u1_struct_0(c1_6__group_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__group_2,dt_c2_6__group_2,e2_6__group_2])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finsub_1,cc1_membered,cc20_membered,cc2_finset_1,cc2_finsub_1,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,existence_l1_group_1,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_subset_1,dt_c2_6__group_2,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_finsub_1,fc1_struct_0,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_subset_1,dt_k3_group_1,dt_u1_struct_0,dt_c1_6__group_2,dt_c3_6__group_2,de_c3_6__group_2,t1_subset,t7_boole,e4_6__group_2,d4_subset_1]),
    [interesting(0.8),file(group_2,e5_6__group_2),[file(group_2,e5_6__group_2)]]).

fof(e6_6__group_2,plain,(
    r2_hidden(k3_group_1(c1_6__group_2,k3_group_1(c1_6__group_2,c3_6__group_2)),k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__group_2,dt_c2_6__group_2,e2_6__group_2])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finsub_1,cc1_membered,cc20_membered,cc2_finset_1,cc2_finsub_1,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,existence_l1_group_1,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_subset_1,dt_c2_6__group_2,cc15_membered,cc1_finset_1,cc1_funct_1,cc1_group_1,fc1_finsub_1,fc1_struct_0,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_2_0_group_2,antisymmetry_r2_hidden,dt_k1_group_2,dt_k2_subset_1,dt_k3_group_1,dt_u1_struct_0,dt_c1_6__group_2,dt_c3_6__group_2,de_c3_6__group_2,t1_subset,t7_boole,d1_group_2,e5_6__group_2]),
    [interesting(0.8),file(group_2,e6_6__group_2),[file(group_2,e6_6__group_2)]]).

fof(t19_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_group_1(A,k3_group_1(A,B)) = B ) ) ),
    file(group_1,t19_group_1),
    [interesting(0.9),axiom,file(group_1,t19_group_1)]).

fof(e7_6__group_2,plain,(
    r2_hidden(c2_6__group_2,k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__group_2,dt_c2_6__group_2,e2_6__group_2])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finsub_1,cc1_membered,cc20_membered,cc2_finset_1,cc2_finsub_1,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,existence_l1_struct_0,dt_k1_zfmisc_1,dt_l1_struct_0,cc15_membered,cc1_finset_1,cc1_funct_1,fc1_finsub_1,fc1_struct_0,fc1_subset_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_2_0_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_subset_1,dt_k1_group_2,dt_k2_subset_1,dt_k3_group_1,dt_l1_group_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_6__group_2,dt_c2_6__group_2,dt_c3_6__group_2,de_c3_6__group_2,cc1_group_1,t1_subset,t7_boole,d1_group_2,e6_6__group_2,t19_group_1]),
    [interesting(0.8),file(group_2,e7_6__group_2),[file(group_2,e7_6__group_2)]]).

fof(i5_6__group_2,theorem,(
    $true ),
    introduced(tautology,[file(group_2,i5_6__group_2)]),
    [interesting(0.8),trivial,file(group_2,i5_6__group_2)]).

fof(i4_6__group_2,plain,(
    r2_hidden(c2_6__group_2,k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2)))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__group_2,dt_c2_6__group_2,e2_6__group_2])],[e7_6__group_2,i5_6__group_2]),
    [interesting(0.8),file(group_2,i4_6__group_2),[file(group_2,i4_6__group_2)]]).

fof(i3_6__group_2,plain,(
    ~ ( r2_hidden(c2_6__group_2,u1_struct_0(c1_6__group_2))
      & ~ r2_hidden(c2_6__group_2,k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__group_2,dt_c2_6__group_2]),discharge_asm(discharge,[e2_6__group_2])],[e2_6__group_2,i4_6__group_2]),
    [interesting(0.8),file(group_2,i3_6__group_2),[file(group_2,i3_6__group_2)]]).

fof(i3_6_tmp__group_2,plain,(
    ~ ( r2_hidden(c2_6__group_2,u1_struct_0(c1_6__group_2))
      & ~ r2_hidden(c2_6__group_2,k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2)))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__group_2]),discharge_asm(discharge,[dt_c2_6__group_2])],[dt_c2_6__group_2,i3_6__group_2]),
    [interesting(0.8),i2_6__group_2]).

fof(i2_6__group_2,plain,(
    r1_tarski(u1_struct_0(c1_6__group_2),k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2)))) ),
    inference(let,[status(thm),assumptions([dt_c1_6__group_2])],[i3_6_tmp__group_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc2_finsub_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,dt_k1_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_subset_1,cc1_group_1,fc1_finsub_1,fc1_struct_0,fc1_subset_1,rc3_struct_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_group_2,dt_k2_subset_1,dt_u1_struct_0,dt_c1_6__group_2,d3_tarski,dh_c2_6__group_2]),
    [interesting(0.8),file(group_2,i2_6__group_2),[file(group_2,i2_6__group_2)]]).

fof(i1_6__group_2,plain,(
    k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2))) = u1_struct_0(c1_6__group_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__group_2])],[cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,rc1_finset_1,rc1_membered,rc3_finset_1,rc4_finset_1,cc15_membered,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc2_finsub_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,dt_k1_zfmisc_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_subset_1,cc1_group_1,fc1_finsub_1,fc1_struct_0,fc1_subset_1,rc3_struct_0,reflexivity_r1_tarski,dt_k1_group_2,dt_k2_subset_1,dt_u1_struct_0,dt_c1_6__group_2,d10_xboole_0,e1_6__group_2,i2_6__group_2]),
    [interesting(0.8),file(group_2,i1_6__group_2),[file(group_2,i1_6__group_2)]]).

fof(i1_6_tmp__group_2,plain,
    ( ( ~ v3_struct_0(c1_6__group_2)
      & v3_group_1(c1_6__group_2)
      & v4_group_1(c1_6__group_2)
      & l1_group_1(c1_6__group_2) )
   => k1_group_2(c1_6__group_2,k2_subset_1(u1_struct_0(c1_6__group_2))) = u1_struct_0(c1_6__group_2) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__group_2])],[dt_c1_6__group_2,i1_6__group_2]),
    [interesting(1),t9_group_2]).

fof(t9_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k1_group_2(A,k2_subset_1(u1_struct_0(A))) = u1_struct_0(A) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__group_2,dh_c1_6__group_2]),
    [interesting(1),file(group_2,t9_group_2),[file(group_2,t9_group_2)]]).