% Mizar problem: t17_cat_5,cat_5,1577,38 
fof(t17_cat_5,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ~ ( ! [C] : 
                  ( m1_cat_5(C,A)
                 => ! [D] : 
                      ( m1_cat_5(D,A)
                     => ! [E] : 
                          ( m1_cat_5(E,A)
                         => ! [F] : 
                              ( m2_cat_1(F,C,D)
                             => ! [G] : 
                                  ( m2_cat_1(G,D,E)
                                 => ( ( r2_hidden(F,B)
                                      & r2_hidden(G,B) )
                                   => r2_hidden(k14_cat_1(C,D,E,F,G),B) ) ) ) ) ) )
              & ! [C] : 
                  ( m1_cat_5(C,A)
                 => r2_hidden(k15_cat_1(C),B) )
              & ! [C] : 
                  ( ( v1_cat_1(C)
                    & v2_cat_1(C)
                    & v3_cat_5(C)
                    & l1_cat_1(C) )
                 => ~ ( u1_cat_1(C) = A
                      & ! [D] : 
                          ( m1_cat_5(D,A)
                         => ! [E] : 
                              ( m1_cat_5(E,A)
                             => ! [F] : 
                                  ( m2_cat_1(F,D,E)
                                 => ( m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(D),u2_cat_1(E))),k1_domain_1(A,A,D,E),F),u2_cat_1(C))
                                  <=> r2_hidden(F,B) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_cat_1,antisymmetry_r2_hidden,cc1_cat_5,cc1_fraenkel,cc1_funct_1,cc1_realset1,cc1_relset_1,cc2_funct_1,commutativity_k2_tarski,d1_fraenkel,d21_cat_1,d2_cat_1,d3_cat_1,d5_cat_1,d5_tarski,d6_cat_5,dt_g1_cat_1,dt_k10_cat_1,dt_k10_cat_5,dt_k11_cat_5,dt_k14_cat_1,dt_k15_cat_1,dt_k17_mcart_1,dt_k18_mcart_1,dt_k19_mcart_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_mcart_1,dt_k2_cat_1,dt_k2_mcart_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k4_cat_1,dt_k4_cat_5,dt_k4_tarski,dt_k5_cat_1,dt_k5_cat_5,dt_k5_relat_1,dt_k6_partfun1,dt_k6_relat_1,dt_k7_relset_1,dt_k8_funct_2,dt_l1_cat_1,dt_m1_cat_1,dt_m1_cat_5,dt_m1_relset_1,dt_m1_subset_1,dt_m2_cat_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_cat_5,existence_m1_relset_1,existence_m1_subset_1,existence_m2_cat_1,existence_m2_relset_1,fc1_funct_1,fc1_subset_1,fc1_xboole_0,fc2_funct_1,fc2_subset_1,fc3_realset1,fc3_subset_1,fc4_subset_1,fraenkel_a_1_0_cat_5,free_g1_cat_1,rc1_cat_1,rc1_cat_5,rc1_fraenkel,rc1_funct_1,rc1_realset1,rc1_subset_1,rc1_xboole_0,rc2_cat_1,rc2_cat_5,rc2_funct_1,rc2_realset1,rc2_subset_1,rc2_xboole_0,rc3_cat_1,rc3_cat_5,rc3_funct_1,redefinition_k10_cat_1,redefinition_k11_cat_5,redefinition_k14_cat_1,redefinition_k1_domain_1,redefinition_k4_cat_5,redefinition_k5_cat_5,redefinition_k6_partfun1,redefinition_k7_relset_1,redefinition_k8_funct_2,redefinition_m1_cat_5,redefinition_m2_relset_1,redefinition_r4_nattra_1,reflexivity_r1_tarski,reflexivity_r4_nattra_1,s1_cat_5__e13_38__cat_5,symmetry_r4_nattra_1,t1_subset,t23_funct_2,t2_cat_5,t2_subset,t2_tarski,t33_zfmisc_1,t3_subset,t44_cat_1,t46_cat_1,t4_isocat_1,t4_subset,t55_relat_1,t5_subset,t6_boole,t7_boole,t7_mcart_1,t89_mcart_1,t8_boole]),
    [file(cat_5,t17_cat_5)]).

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_cat_5,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( ( v2_cat_1(A)
          & v3_cat_5(A) )
       => ( v2_cat_1(A)
          & v1_cat_5(A) ) ) ) ),
    file(cat_5,cc1_cat_5),
    []).

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

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

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

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(d1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,d1_fraenkel),
    []).

fof(d21_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k15_cat_1(A) = k6_partfun1(u2_cat_1(A)) ) ),
    file(cat_1,d21_cat_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(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_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d6_cat_5,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v3_cat_5(A)
      <=> ( v2_cat_5(u1_cat_1(A))
          & ! [B] : 
              ( m1_subset_1(B,u1_cat_1(A))
             => ! [C] : 
                  ( ( v2_cat_1(C)
                    & l1_cat_1(C) )
                 => ( B = C
                   => k10_cat_1(A,B) = k4_tarski(k4_tarski(C,C),k15_cat_1(C)) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] : 
                  ( ( v2_cat_1(C)
                    & l1_cat_1(C) )
                 => ! [D] : 
                      ( ( v2_cat_1(D)
                        & l1_cat_1(D) )
                     => ~ ( C = k2_cat_1(A,B)
                          & D = k3_cat_1(A,B)
                          & ! [E] : 
                              ( m2_cat_1(E,C,D)
                             => B != k4_tarski(k4_tarski(C,D),E) ) ) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u2_cat_1(A))
             => ! [C] : 
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ! [D] : 
                      ( ( v2_cat_1(D)
                        & l1_cat_1(D) )
                     => ! [E] : 
                          ( ( v2_cat_1(E)
                            & l1_cat_1(E) )
                         => ! [F] : 
                              ( ( v2_cat_1(F)
                                & l1_cat_1(F) )
                             => ! [G] : 
                                  ( m2_cat_1(G,D,E)
                                 => ! [H] : 
                                      ( m2_cat_1(H,E,F)
                                     => ( ( B = k4_tarski(k4_tarski(D,E),G)
                                          & C = k4_tarski(k4_tarski(E,F),H) )
                                       => k4_cat_1(A,B,C) = k4_tarski(k4_tarski(D,F),k14_cat_1(D,E,F,G,H)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(cat_5,d6_cat_5),
    []).

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_k10_cat_5,axiom,(
    ! [A] : 
      ( v2_cat_1(k10_cat_5(A))
      & l1_cat_1(k10_cat_5(A)) ) ),
    file(cat_5,k10_cat_5),
    []).

fof(dt_k11_cat_5,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m2_cat_1(k11_cat_5(A,B),k10_cat_5(k2_cat_1(A,B)),k10_cat_5(k3_cat_1(A,B))) ) ),
    file(cat_5,k11_cat_5),
    []).

fof(dt_k14_cat_1,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,A,B)
        & m2_cat_1(E,B,C) )
     => m2_cat_1(k14_cat_1(A,B,C,D,E),A,C) ) ),
    file(cat_1,k14_cat_1),
    []).

fof(dt_k15_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => m2_cat_1(k15_cat_1(A),A,A) ) ),
    file(cat_1,k15_cat_1),
    []).

fof(dt_k17_mcart_1,axiom,(
    $true ),
    file(mcart_1,k17_mcart_1),
    []).

fof(dt_k18_mcart_1,axiom,(
    $true ),
    file(mcart_1,k18_mcart_1),
    []).

fof(dt_k19_mcart_1,axiom,(
    $true ),
    file(mcart_1,k19_mcart_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_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_k20_mcart_1,axiom,(
    $true ),
    file(mcart_1,k20_mcart_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_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_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_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_cat_5,axiom,(
    ! [A,B] : 
      ( ( v1_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k4_cat_5(A,B),u1_cat_1(A)) ) ),
    file(cat_5,k4_cat_5),
    []).

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_cat_5,axiom,(
    ! [A,B] : 
      ( ( v1_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m1_subset_1(k5_cat_5(A,B),u1_cat_1(A)) ) ),
    file(cat_5,k5_cat_5),
    []).

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_partfun1,axiom,(
    ! [A] : 
      ( v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) ),
    file(partfun1,k6_partfun1),
    []).

fof(dt_k6_relat_1,axiom,(
    ! [A] : v1_relat_1(k6_relat_1(A)) ),
    file(relat_1,k6_relat_1),
    []).

fof(dt_k7_relset_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D) ) ),
    file(relset_1,k7_relset_1),
    []).

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

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

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

fof(dt_m1_cat_5,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ! [B] : 
          ( m1_cat_5(B,A)
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) ),
    file(cat_5,m1_cat_5),
    []).

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_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_cat_5,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ? [B] : m1_cat_5(B,A) ) ),
    file(cat_5,m1_cat_5),
    []).

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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_funct_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k6_relat_1(A))
      & v1_funct_1(k6_relat_1(A)) ) ),
    file(funct_1,fc2_funct_1),
    []).

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

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

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(fraenkel_a_1_0_cat_5,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_0_cat_5(B))
      <=> ? [C] : 
            ( m1_subset_1(C,B)
            & A = C
            & v1_relat_1(C)
            & v1_funct_1(C) ) ) ) ),
    file(cat_5,a_1_0_cat_5),
    []).

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_cat_1,axiom,(
    ? [A] : 
      ( l1_cat_1(A)
      & v1_cat_1(A) ) ),
    file(cat_1,rc1_cat_1),
    []).

fof(rc1_cat_5,axiom,(
    ? [A] : 
      ( l1_cat_1(A)
      & v1_cat_1(A)
      & v2_cat_1(A)
      & v1_cat_5(A) ) ),
    file(cat_5,rc1_cat_5),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

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_cat_1,axiom,(
    ? [A] : 
      ( l1_cat_1(A)
      & v2_cat_1(A) ) ),
    file(cat_1,rc2_cat_1),
    []).

fof(rc2_cat_5,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v2_cat_5(A) ) ),
    file(cat_5,rc2_cat_5),
    []).

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_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

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(rc3_cat_1,axiom,(
    ? [A] : 
      ( l1_cat_1(A)
      & v1_cat_1(A)
      & v2_cat_1(A) ) ),
    file(cat_1,rc3_cat_1),
    []).

fof(rc3_cat_5,axiom,(
    ? [A] : 
      ( l1_cat_1(A)
      & v1_cat_1(A)
      & v2_cat_1(A)
      & v1_cat_5(A)
      & v3_cat_5(A) ) ),
    file(cat_5,rc3_cat_5),
    []).

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_k11_cat_5,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k11_cat_5(A,B) = k2_mcart_1(B) ) ),
    file(cat_5,k11_cat_5),
    []).

fof(redefinition_k14_cat_1,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,A,B)
        & m2_cat_1(E,B,C) )
     => k14_cat_1(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(cat_1,k14_cat_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_k4_cat_5,axiom,(
    ! [A,B] : 
      ( ( v1_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k4_cat_5(A,B) = k17_mcart_1(B) ) ),
    file(cat_5,k4_cat_5),
    []).

fof(redefinition_k5_cat_5,axiom,(
    ! [A,B] : 
      ( ( v1_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k5_cat_5(A,B) = k18_mcart_1(B) ) ),
    file(cat_5,k5_cat_5),
    []).

fof(redefinition_k6_partfun1,axiom,(
    ! [A] : k6_partfun1(A) = k6_relat_1(A) ),
    file(partfun1,k6_partfun1),
    []).

fof(redefinition_k7_relset_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_relset_1(E,A,B)
        & m1_relset_1(F,C,D) )
     => k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(relset_1,k7_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_m1_cat_5,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ! [B] : 
          ( m1_cat_5(B,A)
        <=> m1_subset_1(B,A) ) ) ),
    file(cat_5,m1_cat_5),
    []).

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_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(s1_cat_5__e13_38__cat_5,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & ~ v1_xboole_0(B)
        & v2_cat_5(B) )
     => ( ( ! [C] : 
              ( m1_subset_1(C,B)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( m1_subset_1(F,A)
                         => ! [G] : 
                              ( m1_subset_1(G,A)
                             => ( ( m2_cat_1(F,C,D)
                                  & m2_cat_1(G,D,E) )
                               => ( r2_hidden(k5_relat_1(F,G),A)
                                  & m2_cat_1(k5_relat_1(F,G),C,E) ) ) ) ) ) ) )
          & ! [C] : 
              ( m1_subset_1(C,B)
             => ? [D] : 
                  ( m1_subset_1(D,A)
                  & m2_cat_1(D,C,C)
                  & ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( m1_subset_1(F,A)
                         => ( ( m2_cat_1(F,C,E)
                             => k5_relat_1(D,F) = F )
                            & ( m2_cat_1(F,E,C)
                             => k5_relat_1(F,D) = F ) ) ) ) ) )
          & ! [C] : 
              ( m1_subset_1(C,B)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ! [F] : 
                          ( m1_subset_1(F,B)
                         => ! [G] : 
                              ( m1_subset_1(G,A)
                             => ! [H] : 
                                  ( m1_subset_1(H,A)
                                 => ! [I] : 
                                      ( m1_subset_1(I,A)
                                     => ( ( m2_cat_1(G,C,D)
                                          & m2_cat_1(H,D,E)
                                          & m2_cat_1(I,E,F) )
                                       => k5_relat_1(k5_relat_1(G,H),I) = k5_relat_1(G,k5_relat_1(H,I)) ) ) ) ) ) ) ) ) )
       => ? [C] : 
            ( v1_cat_1(C)
            & v2_cat_1(C)
            & v1_cat_5(C)
            & l1_cat_1(C)
            & u1_cat_1(C) = B
            & ! [D] : 
                ( m1_subset_1(D,B)
               => ! [E] : 
                    ( m1_subset_1(E,B)
                   => ! [F] : 
                        ( m1_subset_1(F,A)
                       => ( m2_cat_1(F,D,E)
                         => m1_subset_1(k1_domain_1(k2_zfmisc_1(B,B),A,k1_domain_1(B,B,D,E),F),u2_cat_1(C)) ) ) ) )
            & ! [D] : 
                ( m1_subset_1(D,u2_cat_1(C))
               => ? [E] : 
                    ( m1_subset_1(E,B)
                    & ? [F] : 
                        ( m1_subset_1(F,B)
                        & ? [G] : 
                            ( m1_subset_1(G,A)
                            & D = k1_domain_1(k2_zfmisc_1(B,B),A,k1_domain_1(B,B,E,F),G)
                            & m2_cat_1(G,E,F) ) ) ) )
            & ! [D] : 
                ( m1_subset_1(D,u2_cat_1(C))
               => ! [E] : 
                    ( m1_subset_1(E,u2_cat_1(C))
                   => ! [F] : 
                        ( m1_subset_1(F,B)
                       => ! [G] : 
                            ( m1_subset_1(G,B)
                           => ! [H] : 
                                ( m1_subset_1(H,B)
                               => ! [I] : 
                                    ( m1_subset_1(I,A)
                                   => ! [J] : 
                                        ( m1_subset_1(J,A)
                                       => ( ( D = k1_domain_1(k2_zfmisc_1(B,B),A,k1_domain_1(B,B,F,G),I)
                                            & E = k1_domain_1(k2_zfmisc_1(B,B),A,k1_domain_1(B,B,G,H),J) )
                                         => k4_cat_1(C,D,E) = k4_tarski(k1_domain_1(B,B,F,H),k5_relat_1(I,J)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(cat_5,s1_cat_5__e13_38__cat_5),
    []).

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

fof(t23_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ),
    file(funct_2,t23_funct_2),
    []).

fof(t2_cat_5,axiom,(
    ! [A] : 
      ( ( v1_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ( k2_cat_1(A,B) = k17_mcart_1(B)
            & k3_cat_1(A,B) = k18_mcart_1(B)
            & B = k4_tarski(k1_domain_1(u1_cat_1(A),u1_cat_1(A),k2_cat_1(A,B),k3_cat_1(A,B)),k2_mcart_1(B)) ) ) ) ),
    file(cat_5,t2_cat_5),
    []).

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(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(t46_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,u2_cat_1(A))
             => ( k3_cat_1(A,C) = B
               => k4_cat_1(A,C,k5_cat_1(A,B)) = C ) ) ) ) ),
    file(cat_1,t46_cat_1),
    []).

fof(t4_isocat_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,B,A)
                 => ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k14_cat_1(A,A,B,k15_cat_1(A),C),C)
                    & r4_nattra_1(u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),k14_cat_1(B,A,A,D,k15_cat_1(A)),D) ) ) ) ) ) ),
    file(isocat_1,t4_isocat_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(t55_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ),
    file(relat_1,t55_relat_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(t7_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

fof(t89_mcart_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) = A
      & k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) = B
      & k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D
      & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E ) ),
    file(mcart_1,t89_mcart_1),
    []).

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