% Mizar problem: t17_index_1,index_1,1140,40 
fof(t17_index_1,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m2_cat_1(C,A,B)
             => m4_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k19_index_1(A,B,C)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_cat_5,cc1_funct_1,cc1_index_1,cc1_pboole,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_index_1,cc2_pboole,commutativity_k2_tarski,d13_mcart_1,d15_index_1,d1_funct_2,d2_cat_1,d3_cat_1,d5_tarski,d6_cat_5,d9_index_1,dt_k10_cat_1,dt_k10_index_1,dt_k12_cat_1,dt_k13_index_1,dt_k14_cat_1,dt_k14_index_1,dt_k15_cat_1,dt_k16_mcart_1,dt_k17_mcart_1,dt_k18_mcart_1,dt_k19_index_1,dt_k1_funct_1,dt_k1_index_1,dt_k1_mcart_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cat_1,dt_k2_index_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_relset_1,dt_k4_tarski,dt_k5_cat_1,dt_k5_cat_5,dt_k5_relat_1,dt_k7_pboole,dt_k8_cat_5,dt_k8_funct_2,dt_k9_cat_5,dt_l1_cat_1,dt_m1_cat_1,dt_m1_index_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_cat_1,dt_m2_index_1,dt_m2_relset_1,dt_m3_index_1,dt_m4_index_1,dt_m5_index_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_index_1,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_cat_1,existence_m2_index_1,existence_m2_relset_1,existence_m3_index_1,existence_m4_index_1,existence_m5_index_1,fc10_relat_1,fc12_relat_1,fc1_funct_1,fc2_pboole,fc3_index_1,fc4_relat_1,fc5_index_1,fc5_relat_1,fc7_funcop_1,fc7_relat_1,fc8_funcop_1,fc9_relat_1,rc1_circcomb,rc1_funcop_1,rc1_funct_1,rc1_index_1,rc1_pboole,rc1_relat_1,rc2_cat_5,rc2_funct_1,rc2_index_1,rc2_pboole,rc2_relat_1,rc3_funct_1,rc3_index_1,rc3_pboole,rc3_relat_1,rc4_funct_1,rc4_pboole,rc5_funct_1,redefinition_k10_cat_1,redefinition_k10_index_1,redefinition_k13_index_1,redefinition_k14_cat_1,redefinition_k14_index_1,redefinition_k1_index_1,redefinition_k2_index_1,redefinition_k4_cat_5,redefinition_k4_relset_1,redefinition_k5_cat_5,redefinition_k7_pboole,redefinition_k8_cat_5,redefinition_k8_funct_2,redefinition_k9_cat_5,redefinition_m2_relset_1,reflexivity_r1_tarski,t105_cat_1,t13_cat_5,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t7_funct_2,t7_mcart_1,t8_boole]),
    [file(index_1,t17_index_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_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_index_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(index_1,cc1_index_1),
    []).

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

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

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

fof(cc2_index_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(index_1,cc2_index_1),
    []).

fof(cc2_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d13_mcart_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k16_mcart_1(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k2_mcart_1(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(mcart_1,d13_mcart_1),
    []).

fof(d15_index_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m2_cat_1(C,A,B)
             => k19_index_1(A,B,C) = k4_tarski(k12_cat_1(A,B,C),k16_mcart_1(C)) ) ) ) ),
    file(index_1,d15_index_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(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_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(d9_index_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] : 
                      ( m3_index_1(E,A,B,C,D)
                     => ! [F] : 
                          ( ( v2_cat_1(F)
                            & v3_cat_5(F)
                            & l1_cat_1(F) )
                         => ( m4_index_1(F,A,B,C,D,E)
                          <=> ( ! [G] : 
                                  ( m1_subset_1(G,A)
                                 => m1_subset_1(k2_index_1(A,k10_index_1(A,B,E),G),u1_cat_1(F)) )
                              & ! [G] : 
                                  ( m1_subset_1(G,B)
                                 => m1_subset_1(k4_tarski(k4_tarski(k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,C,G)),k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,D,G))),k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,E)),k7_pboole(B,A,D,k10_index_1(A,B,E)),k14_index_1(A,B,C,D,E),G)),u2_cat_1(F)) ) ) ) ) ) ) ) ) ) ),
    file(index_1,d9_index_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_index_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_index_1(C,A,B)
        & m1_index_1(C,A,B) )
     => ( v1_index_1(k10_index_1(A,B,C))
        & m1_pboole(k10_index_1(A,B,C),A) ) ) ),
    file(index_1,k10_index_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_k13_index_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & v1_index_1(C)
        & m1_pboole(C,A)
        & m2_index_1(D,A,B,C)
        & m1_subset_1(E,A) )
     => m2_cat_1(k13_index_1(A,B,C,D,E),k2_index_1(A,B,E),k2_index_1(A,C,E)) ) ),
    file(index_1,k13_index_1),
    []).

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_k14_index_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ 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)
        & m3_index_1(E,A,B,C,D) )
     => m2_index_1(k14_index_1(A,B,C,D,E),B,k7_pboole(B,A,C,k10_index_1(A,B,E)),k7_pboole(B,A,D,k10_index_1(A,B,E))) ) ),
    file(index_1,k14_index_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_k16_mcart_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k16_mcart_1(A))
        & v1_funct_1(k16_mcart_1(A)) ) ) ),
    file(mcart_1,k16_mcart_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_index_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & v3_cat_5(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => m5_index_1(k19_index_1(A,B,C),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(index_1,k19_index_1),
    []).

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

fof(dt_k1_index_1,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(k1_index_1(A,B),k8_cat_5(A,B),k9_cat_5(A,B)) ) ),
    file(index_1,k1_index_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_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_index_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( v2_cat_1(k2_index_1(A,B,C))
        & l1_cat_1(k2_index_1(A,B,C)) ) ) ),
    file(index_1,k2_index_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_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_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_k7_pboole,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,B) )
     => m1_pboole(k7_pboole(A,B,C,D),A) ) ),
    file(pboole,k7_pboole),
    []).

fof(dt_k8_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)) )
     => ( v2_cat_1(k8_cat_5(A,B))
        & l1_cat_1(k8_cat_5(A,B)) ) ) ),
    file(cat_5,k8_cat_5),
    []).

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_5,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => ( v2_cat_1(k9_cat_5(A,B))
        & l1_cat_1(k9_cat_5(A,B)) ) ) ),
    file(cat_5,k9_cat_5),
    []).

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_index_1,axiom,(
    $true ),
    file(index_1,m1_index_1),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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_index_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & v1_index_1(C)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m2_index_1(D,A,B,C)
         => ( v1_funcop_1(D)
            & m1_pboole(D,A) ) ) ) ),
    file(index_1,m2_index_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_m3_index_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ 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) )
     => ! [E] : 
          ( m3_index_1(E,A,B,C,D)
         => ( v2_index_1(E,A,B)
            & m1_index_1(E,A,B) ) ) ) ),
    file(index_1,m3_index_1),
    []).

fof(dt_m4_index_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ 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)
        & m3_index_1(E,A,B,C,D) )
     => ! [F] : 
          ( m4_index_1(F,A,B,C,D,E)
         => ( v2_cat_1(F)
            & v3_cat_5(F)
            & l1_cat_1(F) ) ) ) ),
    file(index_1,m4_index_1),
    []).

fof(dt_m5_index_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] : 
          ( m5_index_1(G,A,B,C,D,E,F)
         => m3_index_1(G,A,B,C,D) ) ) ),
    file(index_1,m5_index_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_index_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_index_1(C,A,B) ),
    file(index_1,m1_index_1),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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_index_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & v1_index_1(C)
        & m1_pboole(C,A) )
     => ? [D] : m2_index_1(D,A,B,C) ) ),
    file(index_1,m2_index_1),
    []).

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

fof(existence_m3_index_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ 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) )
     => ? [E] : m3_index_1(E,A,B,C,D) ) ),
    file(index_1,m3_index_1),
    []).

fof(existence_m4_index_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ 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)
        & m3_index_1(E,A,B,C,D) )
     => ? [F] : m4_index_1(F,A,B,C,D,E) ) ),
    file(index_1,m4_index_1),
    []).

fof(existence_m5_index_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] : m5_index_1(G,A,B,C,D,E,F) ) ),
    file(index_1,m5_index_1),
    []).

fof(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    []).

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

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

fof(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

fof(fc3_index_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_index_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B))
        & v1_index_1(k5_relat_1(A,B)) ) ) ),
    file(index_1,fc3_index_1),
    []).

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

fof(fc5_index_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & v3_cat_5(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => ( v1_relat_1(k12_cat_1(A,B,C))
        & 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))
        & v1_index_1(k12_cat_1(A,B,C)) ) ) ),
    file(index_1,fc5_index_1),
    []).

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

fof(fc7_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    []).

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

fof(fc8_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(B,A))
        & v1_funct_1(k5_relat_1(B,A))
        & v1_funcop_1(k5_relat_1(B,A)) ) ) ),
    file(funcop_1,fc8_funcop_1),
    []).

fof(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    []).

fof(rc1_circcomb,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(circcomb,rc1_circcomb),
    []).

fof(rc1_funcop_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    []).

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

fof(rc1_index_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & ~ v3_relat_1(B)
          & v1_funct_1(B) ) ) ),
    file(index_1,rc1_index_1),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_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_index_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_index_1(A) ) ),
    file(index_1,rc2_index_1),
    []).

fof(rc2_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

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

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

fof(rc3_index_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_index_1(B) ) ),
    file(index_1,rc3_index_1),
    []).

fof(rc3_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

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

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

fof(rc4_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) ),
    file(pboole,rc4_pboole),
    []).

fof(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_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_k10_index_1,axiom,(
    ! [A,B,C] : 
      ( ( v2_index_1(C,A,B)
        & m1_index_1(C,A,B) )
     => k10_index_1(A,B,C) = k1_mcart_1(C) ) ),
    file(index_1,k10_index_1),
    []).

fof(redefinition_k13_index_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & v1_index_1(C)
        & m1_pboole(C,A)
        & m2_index_1(D,A,B,C)
        & m1_subset_1(E,A) )
     => k13_index_1(A,B,C,D,E) = k1_funct_1(D,E) ) ),
    file(index_1,k13_index_1),
    []).

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_k14_index_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ 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)
        & m3_index_1(E,A,B,C,D) )
     => k14_index_1(A,B,C,D,E) = k2_mcart_1(E) ) ),
    file(index_1,k14_index_1),
    []).

fof(redefinition_k1_index_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k1_index_1(A,B) = k2_mcart_1(B) ) ),
    file(index_1,k1_index_1),
    []).

fof(redefinition_k2_index_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k2_index_1(A,B,C) = k1_funct_1(B,C) ) ),
    file(index_1,k2_index_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_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_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_k7_pboole,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,B) )
     => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(pboole,k7_pboole),
    []).

fof(redefinition_k8_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)) )
     => k8_cat_5(A,B) = k17_mcart_1(B) ) ),
    file(cat_5,k8_cat_5),
    []).

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_5,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k9_cat_5(A,B) = k18_mcart_1(B) ) ),
    file(cat_5,k9_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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t105_cat_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,u2_cat_1(A))
                 => ( k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))
                    & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) ) ) ) ) ) ),
    file(cat_1,t105_cat_1),
    []).

fof(t13_cat_5,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ( k2_cat_1(A,B) = k4_cat_5(A,B)
            & k3_cat_1(A,B) = k5_cat_5(A,B) ) ) ) ),
    file(cat_5,t13_cat_5),
    []).

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

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

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(t7_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) ),
    file(funct_2,t7_funct_2),
    []).

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