% Mizar problem: t16_cat_2,cat_2,319,57 
fof(t16_cat_2,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_cat_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(B))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] : 
                              ( m1_cat_1(G,B,C,D)
                             => ( ( C = E
                                  & D = F )
                               => ( k6_cat_1(B,C,D) = k1_xboole_0
                                  | m1_cat_1(G,A,E,F) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relset_1,d2_cat_1,d3_cat_1,d4_cat_2,d5_cat_1,d6_cat_1,d7_cat_1,dt_k10_cat_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cat_1,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k5_cat_1,dt_k6_cat_1,dt_k8_funct_2,dt_l1_cat_1,dt_m1_cat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_cat_2,dt_u1_cat_1,dt_u2_cat_1,dt_u3_cat_1,dt_u4_cat_1,dt_u5_cat_1,dt_u6_cat_1,existence_l1_cat_1,existence_m1_cat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_cat_2,fc1_subset_1,fc1_xboole_0,fc4_subset_1,fraenkel_a_3_0_cat_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,redefinition_k10_cat_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t21_cat_1,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(cat_2,t16_cat_2)]).

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

fof(cc1_relset_1,axiom,(
    ! [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),
    []).

fof(d2_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) ) ) ),
    file(cat_1,d2_cat_1),
    []).

fof(d3_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k3_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) ) ) ),
    file(cat_1,d3_cat_1),
    []).

fof(d4_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( m3_cat_2(B,A)
          <=> ( r1_tarski(u1_cat_1(B),u1_cat_1(A))
              & ! [C] : 
                  ( m1_subset_1(C,u1_cat_1(B))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_cat_1(B))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_cat_1(A))
                         => ! [F] : 
                              ( m1_subset_1(F,u1_cat_1(A))
                             => ( ( C = E
                                  & D = F )
                               => r1_tarski(k6_cat_1(B,C,D),k6_cat_1(A,E,F)) ) ) ) ) )
              & r1_tarski(u5_cat_1(B),u5_cat_1(A))
              & ! [C] : 
                  ( m1_subset_1(C,u1_cat_1(B))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_cat_1(A))
                     => ( C = D
                       => k10_cat_1(B,C) = k10_cat_1(A,D) ) ) ) ) ) ) ) ),
    file(cat_2,d4_cat_2),
    []).

fof(d5_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => k5_cat_1(A,B) = k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) ) ) ),
    file(cat_1,d5_cat_1),
    []).

fof(d6_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => k6_cat_1(A,B,C) = a_3_0_cat_1(A,B,C) ) ) ) ),
    file(cat_1,d6_cat_1),
    []).

fof(d7_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k6_cat_1(A,B,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,u2_cat_1(A))
                   => ( m1_cat_1(D,A,B,C)
                    <=> r2_hidden(D,k6_cat_1(A,B,C)) ) ) ) ) ) ) ),
    file(cat_1,d7_cat_1),
    []).

fof(dt_k10_cat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_cat_1(k10_cat_1(A,B),A,B,B) ) ),
    file(cat_1,k10_cat_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

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

fof(dt_k2_cat_1,axiom,(
    ! [A,B] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k2_cat_1(A,B),u1_cat_1(A)) ) ),
    file(cat_1,k2_cat_1),
    []).

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

fof(dt_k3_cat_1,axiom,(
    ! [A,B] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)) ) ),
    file(cat_1,k3_cat_1),
    []).

fof(dt_k5_cat_1,axiom,(
    ! [A,B] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)) ) ),
    file(cat_1,k5_cat_1),
    []).

fof(dt_k6_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))) ) ),
    file(cat_1,k6_cat_1),
    []).

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

fof(dt_l1_cat_1,axiom,(
    $true ),
    file(cat_1,l1_cat_1),
    []).

fof(dt_m1_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => ! [D] : 
          ( m1_cat_1(D,A,B,C)
         => m1_subset_1(D,u2_cat_1(A)) ) ) ),
    file(cat_1,m1_cat_1),
    []).

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

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

fof(dt_m3_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_cat_2(B,A)
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) ),
    file(cat_2,m3_cat_2),
    []).

fof(dt_u1_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u1_cat_1(A)) ) ),
    file(cat_1,u1_cat_1),
    []).

fof(dt_u2_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u2_cat_1(A)) ) ),
    file(cat_1,u2_cat_1),
    []).

fof(dt_u3_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u3_cat_1(A))
        & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ),
    file(cat_1,u3_cat_1),
    []).

fof(dt_u4_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u4_cat_1(A))
        & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A))
        & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) ) ) ),
    file(cat_1,u4_cat_1),
    []).

fof(dt_u5_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u5_cat_1(A))
        & m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A)) ) ) ),
    file(cat_1,u5_cat_1),
    []).

fof(dt_u6_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_funct_1(u6_cat_1(A))
        & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A))
        & m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) ) ) ),
    file(cat_1,u6_cat_1),
    []).

fof(existence_l1_cat_1,axiom,(
    ? [A] : l1_cat_1(A) ),
    file(cat_1,l1_cat_1),
    []).

fof(existence_m1_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => ? [D] : m1_cat_1(D,A,B,C) ) ),
    file(cat_1,m1_cat_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

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

fof(existence_m3_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ? [B] : m3_cat_2(B,A) ) ),
    file(cat_2,m3_cat_2),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fraenkel_a_3_0_cat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(B))
        & m1_subset_1(D,u1_cat_1(B)) )
     => ( r2_hidden(A,a_3_0_cat_1(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u2_cat_1(B))
            & A = E
            & k2_cat_1(B,E) = C
            & k3_cat_1(B,E) = D ) ) ) ),
    file(cat_1,a_3_0_cat_1),
    []).

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

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

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

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

fof(redefinition_k10_cat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => k10_cat_1(A,B) = k5_cat_1(A,B) ) ),
    file(cat_1,k10_cat_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

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

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

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

fof(t21_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( r2_hidden(D,k6_cat_1(A,B,C))
                 => m1_cat_1(D,A,B,C) ) ) ) ) ),
    file(cat_1,t21_cat_1),
    []).

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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

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

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

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

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

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