% Mizar problem: t8_yoneda_1,yoneda_1,1249,25 
fof(t8_yoneda_1,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => v2_funct_1(k4_yoneda_1(A)) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_cat_1,antisymmetry_r2_hidden,cc1_funct_1,cc1_relset_1,cc2_funct_1,commutativity_k2_tarski,d18_nattra_1,d1_funct_2,d1_nattra_1,d1_yoneda_1,d22_ens_1,d2_cat_2,d2_yoneda_1,d3_mcart_1,d3_yoneda_1,d4_yoneda_1,d5_nattra_1,d5_tarski,d7_cat_1,d8_funct_1,dt_g1_cat_1,dt_k10_cat_1,dt_k11_cat_2,dt_k11_nattra_1,dt_k12_cat_1,dt_k12_ens_1,dt_k12_nattra_1,dt_k13_cat_1,dt_k13_cat_2,dt_k17_ens_1,dt_k18_ens_1,dt_k19_ens_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_yoneda_1,dt_k1_zfmisc_1,dt_k20_ens_1,dt_k22_ens_1,dt_k2_cat_1,dt_k2_ens_1,dt_k2_mcart_1,dt_k2_tarski,dt_k2_yoneda_1,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k3_mcart_1,dt_k3_nattra_1,dt_k3_yoneda_1,dt_k4_nattra_1,dt_k4_relset_1,dt_k4_tarski,dt_k4_yoneda_1,dt_k5_cat_1,dt_k5_cat_2,dt_k5_nattra_1,dt_k6_cat_1,dt_k7_cat_2,dt_k7_nattra_1,dt_k8_funct_2,dt_k8_nattra_1,dt_l1_cat_1,dt_m1_cat_1,dt_m1_cat_2,dt_m1_nattra_1,dt_m1_oppcat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_cat_1,dt_m2_nattra_1,dt_m2_relset_1,dt_m4_nattra_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_cat_1,existence_m1_cat_2,existence_m1_nattra_1,existence_m1_oppcat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_cat_1,existence_m2_nattra_1,existence_m2_relset_1,existence_m4_nattra_1,fc1_xboole_0,fc2_ens_1,fc3_ens_1,fc4_ens_1,fc5_ens_1,free_g1_cat_1,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_funct_1,redefinition_k10_cat_1,redefinition_k13_cat_2,redefinition_k1_domain_1,redefinition_k4_relset_1,redefinition_k7_cat_2,redefinition_k7_nattra_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_r4_nattra_1,reflexivity_r1_nattra_1,reflexivity_r1_tarski,reflexivity_r4_nattra_1,symmetry_r4_nattra_1,t15_nattra_1,t1_subset,t21_nattra_1,t23_cat_1,t28_mcart_1,t2_subset,t31_oppcat_1,t3_subset,t44_cat_1,t4_subset,t53_ens_1,t55_cat_1,t56_cat_1,t5_subset,t6_boole,t6_yoneda_1,t7_boole,t7_yoneda_1,t8_boole,t9_funct_1]),
    [file(yoneda_1,t8_yoneda_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_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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d18_nattra_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( ( v1_cat_1(C)
                & v2_cat_1(C)
                & l1_cat_1(C) )
             => ( C = k12_nattra_1(A,B)
              <=> ( u1_cat_1(C) = k7_cat_2(A,B)
                  & u2_cat_1(C) = k11_nattra_1(A,B)
                  & ! [D] : 
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ( k2_cat_1(C,D) = k1_mcart_1(k1_mcart_1(D))
                        & k3_cat_1(C,D) = k2_mcart_1(k1_mcart_1(D)) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ! [E] : 
                          ( m1_subset_1(E,u2_cat_1(C))
                         => ( k2_cat_1(C,E) = k3_cat_1(C,D)
                           => r2_hidden(k13_cat_2(C,C,E,D),k1_relat_1(u5_cat_1(C))) ) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u2_cat_1(C))
                     => ! [E] : 
                          ( m1_subset_1(E,u2_cat_1(C))
                         => ~ ( r2_hidden(k13_cat_2(C,C,E,D),k1_relat_1(u5_cat_1(C)))
                              & ! [F] : 
                                  ( m2_cat_1(F,A,B)
                                 => ! [G] : 
                                      ( m2_cat_1(G,A,B)
                                     => ! [H] : 
                                          ( m2_cat_1(H,A,B)
                                         => ! [I] : 
                                              ( m2_nattra_1(I,A,B,F,G)
                                             => ! [J] : 
                                                  ( m2_nattra_1(J,A,B,G,H)
                                                 => ~ ( D = k4_tarski(k4_tarski(F,G),I)
                                                      & E = k4_tarski(k4_tarski(G,H),J)
                                                      & k1_funct_1(u5_cat_1(C),k13_cat_2(C,C,E,D)) = k4_tarski(k4_tarski(F,H),k8_nattra_1(A,B,F,G,H,I,J)) ) ) ) ) ) ) ) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_cat_1(C))
                     => ! [E] : 
                          ( m2_cat_1(E,A,B)
                         => ( E = D
                           => k10_cat_1(C,D) = k4_tarski(k4_tarski(E,E),k7_nattra_1(A,B,E)) ) ) ) ) ) ) ) ) ),
    file(nattra_1,d18_nattra_1),
    []).

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(d1_nattra_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m2_cat_1(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ( k6_cat_1(A,D,E) != k1_xboole_0
                       => ! [F] : 
                            ( m1_cat_1(F,A,D,E)
                           => k3_nattra_1(A,B,C,D,E,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) ) ) ) ) ) ) ) ),
    file(nattra_1,d1_nattra_1),
    []).

fof(d1_yoneda_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)) ) ),
    file(yoneda_1,d1_yoneda_1),
    []).

fof(d22_ens_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A)))
                & m2_relset_1(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) )
             => ( C = k20_ens_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u2_cat_1(A))
                   => k8_funct_2(u2_cat_1(A),k2_ens_1(k17_ens_1(A)),C,D) = k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,B,k2_cat_1(A,D)),k6_cat_1(A,B,k3_cat_1(A,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,B,k2_cat_1(A,D)),k6_cat_1(A,B,k3_cat_1(A,D))),k18_ens_1(A,B,D)) ) ) ) ) ) ),
    file(ens_1,d22_ens_1),
    []).

fof(d2_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( C = k5_cat_2(A,B)
            <=> ! [D] : 
                  ( r2_hidden(D,C)
                <=> m2_cat_1(D,A,B) ) ) ) ) ),
    file(cat_2,d2_cat_2),
    []).

fof(d2_yoneda_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => k2_yoneda_1(A,B) = k20_ens_1(A,B) ) ) ),
    file(yoneda_1,d2_yoneda_1),
    []).

fof(d3_mcart_1,axiom,(
    ! [A,B,C] : k3_mcart_1(A,B,C) = k4_tarski(k4_tarski(A,B),C) ),
    file(mcart_1,d3_mcart_1),
    []).

fof(d3_yoneda_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m2_nattra_1(C,A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B)))
             => ( C = k3_yoneda_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_cat_1(A))
                   => k5_nattra_1(A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B)),C,D) = k4_tarski(k4_tarski(k6_cat_1(A,k3_cat_1(A,B),D),k6_cat_1(A,k2_cat_1(A,B),D)),k22_ens_1(A,B,k10_cat_1(A,D))) ) ) ) ) ) ),
    file(yoneda_1,d3_yoneda_1),
    []).

fof(d4_yoneda_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_oppcat_1(B,A,k12_nattra_1(A,k1_yoneda_1(A)))
         => ( B = k4_yoneda_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u2_cat_1(A))
               => k8_funct_2(u2_cat_1(A),u2_cat_1(k12_nattra_1(A,k1_yoneda_1(A))),B,C) = k4_tarski(k4_tarski(k2_yoneda_1(A,k3_cat_1(A,C)),k2_yoneda_1(A,k2_cat_1(A,C))),k3_yoneda_1(A,C)) ) ) ) ) ),
    file(yoneda_1,d4_yoneda_1),
    []).

fof(d5_nattra_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m2_cat_1(C,A,B)
             => ! [D] : 
                  ( m2_cat_1(D,A,B)
                 => ( r1_nattra_1(A,B,C,D)
                   => ! [E] : 
                        ( m1_nattra_1(E,A,B,C,D)
                       => ! [F] : 
                            ( m1_subset_1(F,u1_cat_1(A))
                           => k5_nattra_1(A,B,C,D,E,F) = k8_funct_2(u1_cat_1(A),u2_cat_1(B),E,F) ) ) ) ) ) ) ) ),
    file(nattra_1,d5_nattra_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_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(d8_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_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_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_k11_cat_2,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ( v2_cat_1(k11_cat_2(A,B))
        & l1_cat_1(k11_cat_2(A,B)) ) ) ),
    file(cat_2,k11_cat_2),
    []).

fof(dt_k11_nattra_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => m4_nattra_1(k11_nattra_1(A,B),A,B) ) ),
    file(nattra_1,k11_nattra_1),
    []).

fof(dt_k12_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
        & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
     => ( v1_funct_1(k12_cat_1(A,B,C))
        & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B))
        & m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) ) ) ),
    file(cat_1,k12_cat_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_k12_nattra_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ( v1_cat_1(k12_nattra_1(A,B))
        & v2_cat_1(k12_nattra_1(A,B))
        & l1_cat_1(k12_nattra_1(A,B)) ) ) ),
    file(nattra_1,k12_nattra_1),
    []).

fof(dt_k13_cat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m1_subset_1(D,u1_cat_1(A)) )
     => m1_subset_1(k13_cat_1(A,B,C,D),u1_cat_1(B)) ) ),
    file(cat_1,k13_cat_1),
    []).

fof(dt_k13_cat_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_subset_1(C,u2_cat_1(A))
        & m1_subset_1(D,u2_cat_1(B)) )
     => m1_subset_1(k13_cat_2(A,B,C,D),u2_cat_1(k11_cat_2(A,B))) ) ),
    file(cat_2,k13_cat_2),
    []).

fof(dt_k17_ens_1,axiom,(
    $true ),
    file(ens_1,k17_ens_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_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_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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_yoneda_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v2_cat_1(k1_yoneda_1(A))
        & l1_cat_1(k1_yoneda_1(A)) ) ) ),
    file(yoneda_1,k1_yoneda_1),
    []).

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

fof(dt_k20_ens_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => ( v1_funct_1(k20_ens_1(A,B))
        & v1_funct_2(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A)))
        & m2_relset_1(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) ) ) ),
    file(ens_1,k20_ens_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_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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_yoneda_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A)) )
     => m2_cat_1(k2_yoneda_1(A,B),A,k1_yoneda_1(A)) ) ),
    file(yoneda_1,k2_yoneda_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_k3_mcart_1,axiom,(
    $true ),
    file(mcart_1,k3_mcart_1),
    []).

fof(dt_k3_nattra_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m1_subset_1(D,u1_cat_1(A))
        & m1_subset_1(E,u1_cat_1(A))
        & m1_cat_1(F,A,D,E) )
     => m1_cat_1(k3_nattra_1(A,B,C,D,E,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) ) ),
    file(nattra_1,k3_nattra_1),
    []).

fof(dt_k3_yoneda_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m2_nattra_1(k3_yoneda_1(A,B),A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B))) ) ),
    file(yoneda_1,k3_yoneda_1),
    []).

fof(dt_k4_nattra_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => m1_nattra_1(k4_nattra_1(A,B,C),A,B,C,C) ) ),
    file(nattra_1,k4_nattra_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_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_yoneda_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m1_oppcat_1(k4_yoneda_1(A),A,k12_nattra_1(A,k1_yoneda_1(A))) ) ),
    file(yoneda_1,k4_yoneda_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_k5_cat_2,axiom,(
    $true ),
    file(cat_2,k5_cat_2),
    []).

fof(dt_k5_nattra_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B)
        & m1_nattra_1(E,A,B,C,D)
        & m1_subset_1(F,u1_cat_1(A)) )
     => m1_cat_1(k5_nattra_1(A,B,C,D,E,F),B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)) ) ),
    file(nattra_1,k5_nattra_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_k7_cat_2,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => m1_cat_2(k7_cat_2(A,B),A,B) ) ),
    file(cat_2,k7_cat_2),
    []).

fof(dt_k7_nattra_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => m2_nattra_1(k7_nattra_1(A,B,C),A,B,C,C) ) ),
    file(nattra_1,k7_nattra_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_k8_nattra_1,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,A,B)
        & m2_nattra_1(F,A,B,C,D)
        & m2_nattra_1(G,A,B,D,E) )
     => m2_nattra_1(k8_nattra_1(A,B,C,D,E,F,G),A,B,C,E) ) ),
    file(nattra_1,k8_nattra_1),
    []).

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_cat_2,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( m1_cat_2(C,A,B)
         => ~ v1_xboole_0(C) ) ) ),
    file(cat_2,m1_cat_2),
    []).

fof(dt_m1_nattra_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ! [E] : 
          ( m1_nattra_1(E,A,B,C,D)
         => ( v1_funct_1(E)
            & v1_funct_2(E,u1_cat_1(A),u2_cat_1(B))
            & m2_relset_1(E,u1_cat_1(A),u2_cat_1(B)) ) ) ) ),
    file(nattra_1,m1_nattra_1),
    []).

fof(dt_m1_oppcat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( m1_oppcat_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
            & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) ) ) ) ),
    file(oppcat_1,m1_oppcat_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_cat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( m2_cat_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
            & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) ) ) ) ),
    file(cat_1,m2_cat_1),
    []).

fof(dt_m2_nattra_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ! [E] : 
          ( m2_nattra_1(E,A,B,C,D)
         => m1_nattra_1(E,A,B,C,D) ) ) ),
    file(nattra_1,m2_nattra_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_m4_nattra_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( m4_nattra_1(C,A,B)
         => ~ v1_xboole_0(C) ) ) ),
    file(nattra_1,m4_nattra_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_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_cat_2,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m1_cat_2(C,A,B) ) ),
    file(cat_2,m1_cat_2),
    []).

fof(existence_m1_nattra_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ? [E] : m1_nattra_1(E,A,B,C,D) ) ),
    file(nattra_1,m1_nattra_1),
    []).

fof(existence_m1_oppcat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m1_oppcat_1(C,A,B) ) ),
    file(oppcat_1,m1_oppcat_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_cat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m2_cat_1(C,A,B) ) ),
    file(cat_1,m2_cat_1),
    []).

fof(existence_m2_nattra_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => ? [E] : m2_nattra_1(E,A,B,C,D) ) ),
    file(nattra_1,m2_nattra_1),
    []).

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

fof(existence_m4_nattra_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m4_nattra_1(C,A,B) ) ),
    file(nattra_1,m4_nattra_1),
    []).

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

fof(fc2_ens_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_ens_1(A)) ) ),
    file(ens_1,fc2_ens_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(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(fc5_ens_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ~ v1_xboole_0(k17_ens_1(A)) ) ),
    file(ens_1,fc5_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(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

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

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_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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(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_k13_cat_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m1_subset_1(C,u2_cat_1(A))
        & m1_subset_1(D,u2_cat_1(B)) )
     => k13_cat_2(A,B,C,D) = k4_tarski(C,D) ) ),
    file(cat_2,k13_cat_2),
    []).

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_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_k7_cat_2,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => k7_cat_2(A,B) = k5_cat_2(A,B) ) ),
    file(cat_2,k7_cat_2),
    []).

fof(redefinition_k7_nattra_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => k7_nattra_1(A,B,C) = k4_nattra_1(A,B,C) ) ),
    file(nattra_1,k7_nattra_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(redefinition_r4_nattra_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & v1_funct_2(F,C,D)
        & m1_relset_1(F,C,D) )
     => ( r4_nattra_1(A,B,C,D,E,F)
      <=> E = F ) ) ),
    file(nattra_1,r4_nattra_1),
    []).

fof(reflexivity_r1_nattra_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B)
        & m2_cat_1(D,A,B) )
     => r1_nattra_1(A,B,C,C) ) ),
    file(nattra_1,r1_nattra_1),
    []).

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

fof(reflexivity_r4_nattra_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & v1_funct_2(F,C,D)
        & m1_relset_1(F,C,D) )
     => r4_nattra_1(A,B,C,D,E,E) ) ),
    file(nattra_1,r4_nattra_1),
    []).

fof(symmetry_r4_nattra_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & v1_funct_2(F,C,D)
        & m1_relset_1(F,C,D) )
     => ( r4_nattra_1(A,B,C,D,E,F)
       => r4_nattra_1(A,B,C,D,F,E) ) ) ),
    file(nattra_1,r4_nattra_1),
    []).

fof(t15_nattra_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m2_cat_1(C,B,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(B))
                 => k3_nattra_1(B,A,C,D,D,k10_cat_1(B,D)) = k10_cat_1(A,k13_cat_1(B,A,C,D)) ) ) ) ) ),
    file(nattra_1,t15_nattra_1),
    []).

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

fof(t21_nattra_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m2_cat_1(C,B,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(B))
                 => k5_nattra_1(B,A,C,C,k4_nattra_1(B,A,C),D) = k10_cat_1(A,k13_cat_1(B,A,C,D)) ) ) ) ) ),
    file(nattra_1,t21_nattra_1),
    []).

fof(t23_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_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => ( k2_cat_1(A,D) = B
                      & k3_cat_1(A,D) = C ) ) ) ) ) ) ),
    file(cat_1,t23_cat_1),
    []).

fof(t28_mcart_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F)
     => ( A = D
        & B = E
        & C = F ) ) ),
    file(mcart_1,t28_mcart_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(t31_oppcat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m1_oppcat_1(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(B))
                     => ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E)
                       => k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E ) ) ) ) ) ) ),
    file(oppcat_1,t31_oppcat_1),
    []).

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

fof(t44_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ( k2_cat_1(A,k5_cat_1(A,B)) = B
            & k3_cat_1(A,k5_cat_1(A,B)) = B ) ) ) ),
    file(cat_1,t44_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(t53_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))
             => ( k22_ens_1(A,k10_cat_1(A,B),C) = k18_ens_1(A,B,C)
                & k22_ens_1(A,C,k10_cat_1(A,B)) = k19_ens_1(A,B,C) ) ) ) ) ),
    file(ens_1,t53_ens_1),
    []).

fof(t55_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)) ) ) ),
    file(cat_1,t55_cat_1),
    []).

fof(t56_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,B,B) != k1_xboole_0 ) ) ),
    file(cat_1,t56_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(t6_yoneda_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_oppcat_1(B,A,k12_nattra_1(A,k1_yoneda_1(A)))
         => ( ( v2_funct_1(k12_cat_1(A,k12_nattra_1(A,k1_yoneda_1(A)),B))
              & v1_yoneda_1(B,A,k12_nattra_1(A,k1_yoneda_1(A))) )
           => v2_funct_1(B) ) ) ) ),
    file(yoneda_1,t6_yoneda_1),
    []).

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

fof(t7_yoneda_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => v1_yoneda_1(k4_yoneda_1(A),A,k12_nattra_1(A,k1_yoneda_1(A))) ) ),
    file(yoneda_1,t7_yoneda_1),
    []).

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),
    []).