% Mizar problem: t38_ens_1,ens_1,1024,41 
fof(t38_ens_1,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k12_ens_1(A)))
         => ( v1_ens_1(k16_ens_1(A,B),A)
           => v4_cat_1(B,k12_ens_1(A)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_cat_1,antisymmetry_r2_hidden,cc1_funct_1,cc1_funct_2,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,commutativity_k2_tarski,d11_cat_1,d14_ens_1,d18_ens_1,d1_ens_1,d2_cat_1,d2_ens_1,d3_cat_1,d4_ens_1,d5_ens_1,d5_tarski,d7_ens_1,d9_ens_1,dt_g1_cat_1,dt_k10_ens_1,dt_k11_ens_1,dt_k12_ens_1,dt_k16_ens_1,dt_k1_domain_1,dt_k1_ens_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_mcart_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cat_1,dt_k2_ens_1,dt_k2_mcart_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k3_ens_1,dt_k3_tarski,dt_k4_cat_1,dt_k4_ens_1,dt_k4_tarski,dt_k5_relat_1,dt_k6_ens_1,dt_k8_ens_1,dt_k8_funct_2,dt_k9_ens_1,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,dt_u5_cat_1,dt_u6_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_ens_1,fc1_funct_1,fc1_funct_2,fc1_subset_1,fc2_ens_1,fc2_funct_2,fc2_subset_1,fc3_ens_1,fc3_subset_1,fc4_ens_1,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,fraenkel_a_1_0_ens_1,fraenkel_a_1_1_ens_1,free_g1_cat_1,l17_ens_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_domain_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t156_funct_1,t1_subset,t26_ens_1,t28_ens_1,t2_subset,t2_tarski,t33_zfmisc_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t8_ens_1]),
    [file(ens_1,t38_ens_1)]).

fof(abstractness_v1_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_cat_1(A)
       => A = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ) ),
    file(cat_1,v1_cat_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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d11_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ( v4_cat_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u2_cat_1(A))
               => ! [D] : 
                    ( m1_subset_1(D,u2_cat_1(A))
                   => ( ( k2_cat_1(A,C) = k3_cat_1(A,B)
                        & k2_cat_1(A,D) = k3_cat_1(A,B)
                        & k3_cat_1(A,C) = k3_cat_1(A,D)
                        & k4_cat_1(A,B,C) = k4_cat_1(A,B,D) )
                     => C = D ) ) ) ) ) ) ),
    file(cat_1,d11_cat_1),
    []).

fof(d14_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k12_ens_1(A) = g1_cat_1(A,k2_ens_1(A),k8_ens_1(A),k9_ens_1(A),k10_ens_1(A),k11_ens_1(A)) ) ),
    file(ens_1,d14_ens_1),
    []).

fof(d18_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k12_ens_1(A)))
         => k16_ens_1(A,B) = B ) ) ),
    file(ens_1,d18_ens_1),
    []).

fof(d1_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k1_ens_1(A) = k3_tarski(a_1_0_ens_1(A)) ) ),
    file(ens_1,d1_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(d2_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k2_ens_1(A) = a_1_1_ens_1(A) ) ),
    file(ens_1,d2_ens_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_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k2_ens_1(A))
         => k3_ens_1(A,B) = k1_mcart_1(k1_mcart_1(B)) ) ) ),
    file(ens_1,d4_ens_1),
    []).

fof(d5_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k2_ens_1(A))
         => k4_ens_1(A,B) = k2_mcart_1(k1_mcart_1(B)) ) ) ),
    file(ens_1,d5_ens_1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d7_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k2_ens_1(A))
         => ! [C] : 
              ( m1_subset_1(C,k2_ens_1(A))
             => ( k4_ens_1(A,B) = k3_ens_1(A,C)
               => k6_ens_1(A,B,C) = k4_tarski(k1_domain_1(A,A,k3_ens_1(A,B),k4_ens_1(A,C)),k5_relat_1(k2_mcart_1(B),k2_mcart_1(C))) ) ) ) ) ),
    file(ens_1,d7_ens_1),
    []).

fof(d9_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k2_ens_1(A))
         => ( v1_ens_1(B,A)
          <=> k2_relat_1(k2_mcart_1(B)) = k4_ens_1(A,B) ) ) ) ),
    file(ens_1,d9_ens_1),
    []).

fof(dt_g1_cat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B) )
     => ( v1_cat_1(g1_cat_1(A,B,C,D,E,F))
        & l1_cat_1(g1_cat_1(A,B,C,D,E,F)) ) ) ),
    file(cat_1,g1_cat_1),
    []).

fof(dt_k10_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k10_ens_1(A))
        & m2_relset_1(k10_ens_1(A),k2_zfmisc_1(k2_ens_1(A),k2_ens_1(A)),k2_ens_1(A)) ) ) ),
    file(ens_1,k10_ens_1),
    []).

fof(dt_k11_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k11_ens_1(A))
        & v1_funct_2(k11_ens_1(A),A,k2_ens_1(A))
        & m2_relset_1(k11_ens_1(A),A,k2_ens_1(A)) ) ) ),
    file(ens_1,k11_ens_1),
    []).

fof(dt_k12_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => l1_cat_1(k12_ens_1(A)) ) ),
    file(ens_1,k12_ens_1),
    []).

fof(dt_k16_ens_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,u2_cat_1(k12_ens_1(A))) )
     => m1_subset_1(k16_ens_1(A,B),k2_ens_1(A)) ) ),
    file(ens_1,k16_ens_1),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(dt_k1_ens_1,axiom,(
    $true ),
    file(ens_1,k1_ens_1),
    []).

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

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

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_ens_1,axiom,(
    $true ),
    file(ens_1,k2_ens_1),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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_k3_ens_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k2_ens_1(A)) )
     => m1_subset_1(k3_ens_1(A,B),A) ) ),
    file(ens_1,k3_ens_1),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

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_ens_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k2_ens_1(A)) )
     => m1_subset_1(k4_ens_1(A,B),A) ) ),
    file(ens_1,k4_ens_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

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_ens_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k2_ens_1(A))
        & m1_subset_1(C,k2_ens_1(A)) )
     => m1_subset_1(k6_ens_1(A,B,C),k2_ens_1(A)) ) ),
    file(ens_1,k6_ens_1),
    []).

fof(dt_k8_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k8_ens_1(A))
        & v1_funct_2(k8_ens_1(A),k2_ens_1(A),A)
        & m2_relset_1(k8_ens_1(A),k2_ens_1(A),A) ) ) ),
    file(ens_1,k8_ens_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_k9_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_funct_1(k9_ens_1(A))
        & v1_funct_2(k9_ens_1(A),k2_ens_1(A),A)
        & m2_relset_1(k9_ens_1(A),k2_ens_1(A),A) ) ) ),
    file(ens_1,k9_ens_1),
    []).

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(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_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_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_ens_1(A))
        & v1_fraenkel(k1_ens_1(A)) ) ) ),
    file(ens_1,fc1_ens_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_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ~ v1_xboole_0(k1_funct_2(A,B)) ) ),
    file(funct_2,fc1_funct_2),
    []).

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

fof(fc2_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_ens_1(A)) ) ),
    file(ens_1,fc2_ens_1),
    []).

fof(fc2_funct_2,axiom,(
    ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ),
    file(funct_2,fc2_funct_2),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_ens_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k2_ens_1(A)) )
     => ( v1_relat_1(k2_mcart_1(B))
        & v1_funct_1(k2_mcart_1(B)) ) ) ),
    file(ens_1,fc3_ens_1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v1_cat_1(k12_ens_1(A))
        & v2_cat_1(k12_ens_1(A)) ) ) ),
    file(ens_1,fc4_ens_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(fc6_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_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(fc8_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_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_1_0_ens_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_0_ens_1(B))
      <=> ? [C,D] : 
            ( m1_subset_1(C,B)
            & m1_subset_1(D,B)
            & A = k1_funct_2(C,D) ) ) ) ),
    file(ens_1,a_1_0_ens_1),
    []).

fof(fraenkel_a_1_1_ens_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_1_ens_1(B))
      <=> ? [C,D,E] : 
            ( m1_subset_1(C,B)
            & m1_subset_1(D,B)
            & m1_subset_1(E,k1_ens_1(B))
            & A = k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E)
            & ( D = k1_xboole_0
             => C = k1_xboole_0 )
            & v1_funct_1(E)
            & v1_funct_2(E,C,D)
            & m2_relset_1(E,C,D) ) ) ) ),
    file(ens_1,a_1_1_ens_1),
    []).

fof(free_g1_cat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B) )
     => ! [G,H,I,J,K,L] : 
          ( g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) ),
    file(cat_1,g1_cat_1),
    []).

fof(l17_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k2_ens_1(A))
         => ( k1_relat_1(k2_mcart_1(B)) = k3_ens_1(A,B)
            & r1_tarski(k2_relat_1(k2_mcart_1(B)),k4_ens_1(A,B)) ) ) ) ),
    file(ens_1,l17_ens_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_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_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(t156_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D) )
             => ( ( A = k2_relat_1(B)
                  & k1_relat_1(C) = A
                  & k1_relat_1(D) = A
                  & k5_relat_1(B,C) = k5_relat_1(B,D) )
               => C = D ) ) ) ) ),
    file(funct_1,t156_funct_1),
    []).

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

fof(t26_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k12_ens_1(A)))
         => ( k2_cat_1(k12_ens_1(A),B) = k3_ens_1(A,k16_ens_1(A,B))
            & k3_cat_1(k12_ens_1(A),B) = k4_ens_1(A,k16_ens_1(A,B)) ) ) ) ),
    file(ens_1,t26_ens_1),
    []).

fof(t28_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k12_ens_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(k12_ens_1(A)))
             => ( k2_cat_1(k12_ens_1(A),B) = k3_cat_1(k12_ens_1(A),C)
               => k4_cat_1(k12_ens_1(A),C,B) = k6_ens_1(A,k16_ens_1(A,C),k16_ens_1(A,B)) ) ) ) ) ),
    file(ens_1,t28_ens_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(t33_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    []).

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),
    []).

fof(t8_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k2_ens_1(A))
         => B = k4_tarski(k1_domain_1(A,A,k3_ens_1(A,B),k4_ens_1(A,B)),k2_mcart_1(B)) ) ) ),
    file(ens_1,t8_ens_1),
    []).