% Mizar problem: t19_isocat_2,isocat_2,701,27 
fof(t19_isocat_2,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] : 
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] : 
                      ( m1_subset_1(E,u2_cat_1(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_cat_1(B))
                         => k5_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),k4_isocat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,E,k10_cat_1(B,F))) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relset_1,commutativity_k2_tarski,d2_isocat_2,d3_isocat_2,d5_cat_1,d5_nattra_1,d5_tarski,d7_nattra_1,dt_k10_cat_1,dt_k10_cat_2,dt_k11_cat_2,dt_k13_cat_1,dt_k13_cat_2,dt_k14_cat_2,dt_k15_funct_3,dt_k1_cat_2,dt_k1_domain_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cat_1,dt_k2_cat_2,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k3_funct_4,dt_k3_funct_5,dt_k3_isocat_2,dt_k3_nattra_1,dt_k4_isocat_2,dt_k4_tarski,dt_k5_cat_1,dt_k5_nattra_1,dt_k5_relat_1,dt_k6_cat_1,dt_k7_funct_2,dt_k8_funct_2,dt_k9_cat_1,dt_k9_cat_2,dt_l1_cat_1,dt_m1_cat_1,dt_m1_fraenkel,dt_m1_nattra_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_cat_1,dt_m2_fraenkel,dt_m2_nattra_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_cat_1,existence_m1_fraenkel,existence_m1_nattra_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_cat_1,existence_m2_fraenkel,existence_m2_nattra_1,existence_m2_relset_1,fc1_subset_1,fc1_xboole_0,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,redefinition_k10_cat_1,redefinition_k10_cat_2,redefinition_k13_cat_2,redefinition_k1_cat_2,redefinition_k1_domain_1,redefinition_k1_fraenkel,redefinition_k2_cat_2,redefinition_k7_funct_2,redefinition_k8_funct_2,redefinition_k9_cat_2,redefinition_m2_fraenkel,redefinition_m2_relset_1,reflexivity_r1_nattra_1,reflexivity_r1_tarski,reflexivity_r2_nattra_1,t18_isocat_2,t1_subset,t21_funct_2,t2_subset,t33_cat_2,t3_cat_2,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(isocat_2,t19_isocat_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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d2_isocat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] : 
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] : 
                      ( m1_subset_1(E,u2_cat_1(A))
                     => k3_isocat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),E) ) ) ) ) ) ),
    file(isocat_2,d2_isocat_2),
    []).

fof(d3_isocat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] : 
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] : 
                      ( m1_subset_1(E,u2_cat_1(A))
                     => k4_isocat_2(A,B,C,D,E) = k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,E)) ) ) ) ) ) ),
    file(isocat_2,d3_isocat_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(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_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)
                 => ( r2_nattra_1(A,B,C,D)
                  <=> ( 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))
                             => ! [G] : 
                                  ( m1_subset_1(G,u1_cat_1(A))
                                 => ( k6_cat_1(A,F,G) != k1_xboole_0
                                   => ! [H] : 
                                        ( m1_cat_1(H,A,F,G)
                                       => k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k3_nattra_1(A,B,C,F,G,H),k5_nattra_1(A,B,C,D,E,G)) = k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,F),k3_nattra_1(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(nattra_1,d7_nattra_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_k10_cat_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & m1_relset_1(D,k2_zfmisc_1(B,B),B) )
     => ( v1_funct_1(k10_cat_2(A,B,C,D))
        & m2_relset_1(k10_cat_2(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) ) ) ),
    file(cat_2,k10_cat_2),
    []).

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_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_k14_cat_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,k11_cat_2(A,B),C)
        & m1_subset_1(E,u1_cat_1(A)) )
     => m2_cat_1(k14_cat_2(A,B,C,D,E),B,C) ) ),
    file(cat_2,k14_cat_2),
    []).

fof(dt_k15_funct_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k15_funct_3(A,B))
        & v1_funct_1(k15_funct_3(A,B)) ) ) ),
    file(funct_3,k15_funct_3),
    []).

fof(dt_k1_cat_2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(C)
        & m1_fraenkel(D,B,C)
        & v1_funct_1(E)
        & v1_funct_2(E,A,D)
        & m1_relset_1(E,A,D)
        & m1_subset_1(F,A) )
     => m2_fraenkel(k1_cat_2(A,B,C,D,E,F),B,C,D) ) ),
    file(cat_2,k1_cat_2),
    []).

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_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

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_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_cat_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v1_funct_1(k2_cat_2(A,B,C,D))
        & v1_funct_2(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C))
        & m2_relset_1(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) ) ) ),
    file(cat_2,k2_cat_2),
    []).

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_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k3_funct_4(A,B))
        & v1_funct_1(k3_funct_4(A,B)) ) ) ),
    file(funct_4,k3_funct_4),
    []).

fof(dt_k3_funct_5,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_5(A))
        & v1_funct_1(k3_funct_5(A)) ) ) ),
    file(funct_5,k3_funct_5),
    []).

fof(dt_k3_isocat_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,k11_cat_2(A,B),C)
        & m1_subset_1(E,u2_cat_1(A)) )
     => ( v1_funct_1(k3_isocat_2(A,B,C,D,E))
        & v1_funct_2(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C))
        & m2_relset_1(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C)) ) ) ),
    file(isocat_2,k3_isocat_2),
    []).

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_k4_isocat_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,k11_cat_2(A,B),C)
        & m1_subset_1(E,u2_cat_1(A)) )
     => m2_nattra_1(k4_isocat_2(A,B,C,D,E),B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))) ) ),
    file(isocat_2,k4_isocat_2),
    []).

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

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_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_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_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

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_cat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A))
        & m1_subset_1(D,u1_cat_1(A))
        & m1_cat_1(E,A,B,C)
        & m1_cat_1(F,A,C,D) )
     => m1_cat_1(k9_cat_1(A,B,C,D,E,F),A,B,D) ) ),
    file(cat_1,k9_cat_1),
    []).

fof(dt_k9_cat_2,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,C)
        & m1_relset_1(E,A,C)
        & v1_funct_1(F)
        & v1_funct_2(F,B,D)
        & m1_relset_1(F,B,D) )
     => ( v1_funct_1(k9_cat_2(A,B,C,D,E,F))
        & v1_funct_2(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))
        & m2_relset_1(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) ) ) ),
    file(cat_2,k9_cat_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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

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_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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_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_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

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_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_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_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(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_k10_cat_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & m1_relset_1(D,k2_zfmisc_1(B,B),B) )
     => k10_cat_2(A,B,C,D) = k3_funct_4(C,D) ) ),
    file(cat_2,k10_cat_2),
    []).

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_cat_2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(C)
        & m1_fraenkel(D,B,C)
        & v1_funct_1(E)
        & v1_funct_2(E,A,D)
        & m1_relset_1(E,A,D)
        & m1_subset_1(F,A) )
     => k1_cat_2(A,B,C,D,E,F) = k1_funct_1(E,F) ) ),
    file(cat_2,k1_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_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k2_cat_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => k2_cat_2(A,B,C,D) = k3_funct_5(D) ) ),
    file(cat_2,k2_cat_2),
    []).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

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_k9_cat_2,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,C)
        & m1_relset_1(E,A,C)
        & v1_funct_1(F)
        & v1_funct_2(F,B,D)
        & m1_relset_1(F,B,D) )
     => k9_cat_2(A,B,C,D,E,F) = k15_funct_3(E,F) ) ),
    file(cat_2,k9_cat_2),
    []).

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_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_r2_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) )
     => r2_nattra_1(A,B,C,C) ) ),
    file(nattra_1,r2_nattra_1),
    []).

fof(t18_isocat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] : 
                  ( m2_cat_1(D,k11_cat_2(A,B),C)
                 => ! [E] : 
                      ( m1_subset_1(E,u2_cat_1(A))
                     => r2_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))) ) ) ) ) ) ),
    file(isocat_2,t18_isocat_2),
    []).

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

fof(t21_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_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    []).

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

fof(t33_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( u1_cat_1(k11_cat_2(A,B)) = k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B))
            & u2_cat_1(k11_cat_2(A,B)) = k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B))
            & u3_cat_1(k11_cat_2(A,B)) = k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B))
            & u4_cat_1(k11_cat_2(A,B)) = k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B))
            & u5_cat_1(k11_cat_2(A,B)) = k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B))
            & u6_cat_1(k11_cat_2(A,B)) = k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B)) ) ) ) ),
    file(cat_2,t33_cat_2),
    []).

fof(t3_cat_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),k2_cat_2(A,B,C,F),D),E) ) ) ) ) ) ) ),
    file(cat_2,t3_cat_2),
    []).

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),
    []).