% Mizar problem: t55_ens_1,ens_1,1683,39 
fof(t55_ens_1,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => k22_ens_1(A,B,C) = k1_partfun1(k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)),k19_ens_1(A,k2_cat_1(A,C),B),k18_ens_1(A,k2_cat_1(A,B),C)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_1,cc1_funct_2,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,d1_funct_2,d20_ens_1,d21_ens_1,d24_ens_1,d2_cat_1,d3_cat_1,d6_cat_1,dt_k18_ens_1,dt_k19_ens_1,dt_k1_funct_1,dt_k1_partfun1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k22_ens_1,dt_k2_cat_1,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k4_cat_1,dt_k4_relset_1,dt_k5_relat_1,dt_k6_cat_1,dt_k8_funct_2,dt_l1_cat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_cat_1,dt_u2_cat_1,dt_u3_cat_1,dt_u4_cat_1,existence_l1_cat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_relat_1,fc12_relat_1,fc1_funct_1,fc1_subset_1,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,fraenkel_a_3_0_cat_1,rc1_funct_1,rc1_funct_2,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,redefinition_k1_partfun1,redefinition_k4_relset_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t18_cat_1,t19_cat_1,t19_funct_2,t1_subset,t22_funct_1,t2_subset,t2_tarski,t3_subset,t42_cat_1,t43_cat_1,t4_subset,t51_ens_1,t52_cat_1,t5_subset,t6_boole,t7_boole,t8_boole,t9_funct_1]),
    [file(ens_1,t55_ens_1)]).

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

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

fof(cc1_funct_2,axiom,(
    ! [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),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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(cc2_funct_1,axiom,(
    ! [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),
    []).

fof(cc5_funct_2,axiom,(
    ! [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),
    []).

fof(cc6_funct_2,axiom,(
    ! [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),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d20_ens_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C)))
                    & m2_relset_1(D,k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) )
                 => ( D = k18_ens_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u2_cat_1(A))
                       => ( r2_hidden(E,k6_cat_1(A,B,k2_cat_1(A,C)))
                         => k1_funct_1(D,E) = k4_cat_1(A,E,C) ) ) ) ) ) ) ) ),
    file(ens_1,d20_ens_1),
    []).

fof(d21_ens_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B))
                    & m2_relset_1(D,k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)) )
                 => ( D = k19_ens_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u2_cat_1(A))
                       => ( r2_hidden(E,k6_cat_1(A,k3_cat_1(A,C),B))
                         => k1_funct_1(D,E) = k4_cat_1(A,C,E) ) ) ) ) ) ) ) ),
    file(ens_1,d21_ens_1),
    []).

fof(d24_ens_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)))
                    & m2_relset_1(D,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))) )
                 => ( D = k22_ens_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u2_cat_1(A))
                       => ( r2_hidden(E,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)))
                         => k1_funct_1(D,E) = k4_cat_1(A,B,k4_cat_1(A,E,C)) ) ) ) ) ) ) ) ),
    file(ens_1,d24_ens_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(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(dt_k18_ens_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => ( v1_funct_1(k18_ens_1(A,B,C))
        & v1_funct_2(k18_ens_1(A,B,C),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C)))
        & m2_relset_1(k18_ens_1(A,B,C),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) ) ) ),
    file(ens_1,k18_ens_1),
    []).

fof(dt_k19_ens_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => ( v1_funct_1(k19_ens_1(A,B,C))
        & v1_funct_2(k19_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B))
        & m2_relset_1(k19_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)) ) ) ),
    file(ens_1,k19_ens_1),
    []).

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

fof(dt_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F))
        & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ),
    file(partfun1,k1_partfun1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_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_k22_ens_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => ( v1_funct_1(k22_ens_1(A,B,C))
        & v1_funct_2(k22_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)))
        & m2_relset_1(k22_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))) ) ) ),
    file(ens_1,k22_ens_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_k4_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)) ) ),
    file(cat_1,k4_cat_1),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_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_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_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(existence_l1_cat_1,axiom,(
    ? [A] : l1_cat_1(A) ),
    file(cat_1,l1_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(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

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

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

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(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [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),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_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(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(redefinition_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(partfun1,k1_partfun1),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_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(t18_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] : 
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_hidden(D,k6_cat_1(A,B,C))
                  <=> ( k2_cat_1(A,D) = B
                      & k3_cat_1(A,D) = C ) ) ) ) ) ) ),
    file(cat_1,t18_cat_1),
    []).

fof(t19_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)) != k1_xboole_0 ) ) ),
    file(cat_1,t19_cat_1),
    []).

fof(t19_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ~ ( B = k1_xboole_0
                & C != k1_xboole_0
                & A != k1_xboole_0 )
           => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
              & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)
              & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) ) ) ) ) ),
    file(funct_2,t19_funct_2),
    []).

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

fof(t22_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_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(t42_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,C) = k3_cat_1(A,B)
               => ( k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B)
                  & k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) ) ) ) ) ) ),
    file(cat_1,t42_cat_1),
    []).

fof(t43_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( ( k2_cat_1(A,D) = k3_cat_1(A,C)
                      & k2_cat_1(A,C) = k3_cat_1(A,B) )
                   => k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D)) ) ) ) ) ) ),
    file(cat_1,t43_cat_1),
    []).

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(t51_ens_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)) = k1_xboole_0
               => k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)) = k1_xboole_0 ) ) ) ) ),
    file(ens_1,t51_ens_1),
    []).

fof(t52_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,C,D) != k1_xboole_0
                      & k6_cat_1(A,B,D) = k1_xboole_0 ) ) ) ) ) ),
    file(cat_1,t52_cat_1),
    []).

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),
    []).

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).