% Mizar problem: t43_cat_4,cat_4,985,36 
fof(t43_cat_4,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_cat_1(A))
                         => ! [G] : 
                              ( m1_cat_1(G,A,B,C)
                             => ! [H] : 
                                  ( m1_cat_1(H,A,D,E)
                                 => ! [I] : 
                                      ( m1_cat_1(I,A,F,B)
                                     => ! [J] : 
                                          ( m1_cat_1(J,A,F,D)
                                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                              & k6_cat_1(A,D,E) != k1_xboole_0
                                              & k6_cat_1(A,F,B) != k1_xboole_0
                                              & k6_cat_1(A,F,D) != k1_xboole_0
                                              & k9_cat_1(A,F,k2_cat_4(A,B,D),k2_cat_4(A,C,E),k9_cat_4(A,B,D,F,I,J),k18_cat_4(A,B,C,D,E,G,H)) != k9_cat_4(A,C,E,F,k9_cat_1(A,F,B,C,I,G),k9_cat_1(A,F,D,E,J,H)) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,d11_cat_4,d20_cat_4,d2_cat_1,d3_cat_1,d5_cat_4,d6_cat_1,d6_cat_4,d7_cat_4,dt_k18_cat_4,dt_k1_domain_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cat_1,dt_k2_cat_4,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k3_cat_4,dt_k4_cat_4,dt_k4_tarski,dt_k6_cat_1,dt_k7_cat_4,dt_k8_cat_4,dt_k8_funct_2,dt_k9_cat_1,dt_k9_cat_4,dt_l1_cat_1,dt_l1_cat_4,dt_m1_cat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_cat_1,dt_u2_cat_1,dt_u2_cat_4,dt_u3_cat_1,dt_u3_cat_4,dt_u4_cat_1,dt_u4_cat_4,existence_l1_cat_1,existence_l1_cat_4,existence_m1_cat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc12_relat_1,fc14_finset_1,fc1_subset_1,fc4_relat_1,fc4_subset_1,fraenkel_a_3_0_cat_1,rc1_finset_1,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_finset_1,rc3_funct_1,rc3_relat_1,rc4_finset_1,rc4_funct_1,redefinition_k1_domain_1,redefinition_k7_cat_4,redefinition_k8_cat_4,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t21_cat_4,t25_cat_4,t27_cat_4,t2_subset,t2_tarski,t3_subset,t4_subset,t52_cat_1,t54_cat_1,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(cat_4,t43_cat_4)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

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

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_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_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(d11_cat_4,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_cat_1(E,A,D,B)
                     => ! [F] : 
                          ( m1_cat_1(F,A,D,C)
                         => ~ ( k6_cat_1(A,D,B) != k1_xboole_0
                              & k6_cat_1(A,D,C) != k1_xboole_0
                              & ~ ! [G] : 
                                    ( m1_cat_1(G,A,D,k2_cat_4(A,B,C))
                                   => ( G = k9_cat_4(A,B,C,D,E,F)
                                    <=> ( k9_cat_1(A,D,k2_cat_4(A,B,C),B,G,k7_cat_4(A,B,C)) = E
                                        & k9_cat_1(A,D,k2_cat_4(A,B,C),C,G,k8_cat_4(A,B,C)) = F ) ) ) ) ) ) ) ) ) ) ),
    file(cat_4,d11_cat_4),
    []).

fof(d20_cat_4,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] : 
                              ( m1_cat_1(G,A,D,E)
                             => k18_cat_4(A,B,C,D,E,F,G) = k9_cat_4(A,C,E,k2_cat_4(A,B,D),k9_cat_1(A,k2_cat_4(A,B,D),B,C,k7_cat_4(A,B,D),F),k9_cat_1(A,k2_cat_4(A,B,D),D,E,k8_cat_4(A,B,D),G)) ) ) ) ) ) ) ) ),
    file(cat_4,d20_cat_4),
    []).

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_4,axiom,(
    ! [A] : 
      ( l1_cat_4(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => k2_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u2_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ),
    file(cat_4,d5_cat_4),
    []).

fof(d6_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => k6_cat_1(A,B,C) = a_3_0_cat_1(A,B,C) ) ) ) ),
    file(cat_1,d6_cat_1),
    []).

fof(d6_cat_4,axiom,(
    ! [A] : 
      ( l1_cat_4(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => k3_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u3_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ),
    file(cat_4,d6_cat_4),
    []).

fof(d7_cat_4,axiom,(
    ! [A] : 
      ( l1_cat_4(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => k4_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u4_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ),
    file(cat_4,d7_cat_4),
    []).

fof(dt_k18_cat_4,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(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_subset_1(E,u1_cat_1(A))
        & m1_cat_1(F,A,B,C)
        & m1_cat_1(G,A,D,E) )
     => m1_cat_1(k18_cat_4(A,B,C,D,E,F,G),A,k2_cat_4(A,B,D),k2_cat_4(A,C,E)) ) ),
    file(cat_4,k18_cat_4),
    []).

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_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_4,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k2_cat_4(A,B,C),u1_cat_1(A)) ) ),
    file(cat_4,k2_cat_4),
    []).

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_cat_4,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k3_cat_4(A,B,C),u2_cat_1(A)) ) ),
    file(cat_4,k3_cat_4),
    []).

fof(dt_k4_cat_4,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k4_cat_4(A,B,C),u2_cat_1(A)) ) ),
    file(cat_4,k4_cat_4),
    []).

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

fof(dt_k6_cat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_cat_1(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))) ) ),
    file(cat_1,k6_cat_1),
    []).

fof(dt_k7_cat_4,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_cat_1(k7_cat_4(A,B,C),A,k2_cat_4(A,B,C),B) ) ),
    file(cat_4,k7_cat_4),
    []).

fof(dt_k8_cat_4,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => m1_cat_1(k8_cat_4(A,B,C),A,k2_cat_4(A,B,C),C) ) ),
    file(cat_4,k8_cat_4),
    []).

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_4,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(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,D,B)
        & m1_cat_1(F,A,D,C) )
     => m1_cat_1(k9_cat_4(A,B,C,D,E,F),A,D,k2_cat_4(A,B,C)) ) ),
    file(cat_4,k9_cat_4),
    []).

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

fof(dt_l1_cat_4,axiom,(
    ! [A] : 
      ( l1_cat_4(A)
     => l1_cat_1(A) ) ),
    file(cat_4,l1_cat_4),
    []).

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_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u1_cat_1(A)) ) ),
    file(cat_1,u1_cat_1),
    []).

fof(dt_u2_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ~ v1_xboole_0(u2_cat_1(A)) ) ),
    file(cat_1,u2_cat_1),
    []).

fof(dt_u2_cat_4,axiom,(
    ! [A] : 
      ( l1_cat_4(A)
     => ( v1_funct_1(u2_cat_4(A))
        & v1_funct_2(u2_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A))
        & m2_relset_1(u2_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A)) ) ) ),
    file(cat_4,u2_cat_4),
    []).

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_u3_cat_4,axiom,(
    ! [A] : 
      ( l1_cat_4(A)
     => ( v1_funct_1(u3_cat_4(A))
        & v1_funct_2(u3_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
        & m2_relset_1(u3_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) ),
    file(cat_4,u3_cat_4),
    []).

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_u4_cat_4,axiom,(
    ! [A] : 
      ( l1_cat_4(A)
     => ( v1_funct_1(u4_cat_4(A))
        & v1_funct_2(u4_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
        & m2_relset_1(u4_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) ),
    file(cat_4,u4_cat_4),
    []).

fof(existence_l1_cat_1,axiom,(
    ? [A] : l1_cat_1(A) ),
    file(cat_1,l1_cat_1),
    []).

fof(existence_l1_cat_4,axiom,(
    ? [A] : l1_cat_4(A) ),
    file(cat_4,l1_cat_4),
    []).

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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

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

fof(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(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    []).

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

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

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fraenkel_a_3_0_cat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_cat_1(B)
        & m1_subset_1(C,u1_cat_1(B))
        & m1_subset_1(D,u1_cat_1(B)) )
     => ( r2_hidden(A,a_3_0_cat_1(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u2_cat_1(B))
            & A = E
            & k2_cat_1(B,E) = C
            & k3_cat_1(B,E) = D ) ) ) ),
    file(cat_1,a_3_0_cat_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

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

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

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

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

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

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

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

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

fof(redefinition_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k7_cat_4,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => k7_cat_4(A,B,C) = k3_cat_4(A,B,C) ) ),
    file(cat_4,k7_cat_4),
    []).

fof(redefinition_k8_cat_4,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A)
        & m1_subset_1(B,u1_cat_1(A))
        & m1_subset_1(C,u1_cat_1(A)) )
     => k8_cat_4(A,B,C) = k4_cat_4(A,B,C) ) ),
    file(cat_4,k8_cat_4),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

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

fof(t21_cat_4,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k6_cat_1(A,k2_cat_4(A,B,C),B) != k1_xboole_0
                & k6_cat_1(A,k2_cat_4(A,B,C),C) != k1_xboole_0 ) ) ) ) ),
    file(cat_4,t21_cat_4),
    []).

fof(t25_cat_4,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,B,D) != k1_xboole_0
                      & k6_cat_1(A,B,k2_cat_4(A,C,D)) = k1_xboole_0 ) ) ) ) ) ),
    file(cat_4,t25_cat_4),
    []).

fof(t27_cat_4,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_4(A)
        & l1_cat_4(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] : 
                              ( m1_cat_1(G,A,B,D)
                             => ! [H] : 
                                  ( m1_cat_1(H,A,E,B)
                                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                      & k6_cat_1(A,B,D) != k1_xboole_0
                                      & k6_cat_1(A,E,B) != k1_xboole_0
                                      & k9_cat_4(A,C,D,E,k9_cat_1(A,E,B,C,H,F),k9_cat_1(A,E,B,D,H,G)) != k9_cat_1(A,E,B,k2_cat_4(A,C,D),H,k9_cat_4(A,C,D,B,F,G)) ) ) ) ) ) ) ) ) ) ),
    file(cat_4,t27_cat_4),
    []).

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(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(t52_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,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,C,D) != k1_xboole_0
                      & k6_cat_1(A,B,D) = k1_xboole_0 ) ) ) ) ) ),
    file(cat_1,t52_cat_1),
    []).

fof(t54_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,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] : 
                              ( m1_cat_1(G,A,C,D)
                             => ! [H] : 
                                  ( m1_cat_1(H,A,D,E)
                                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                      & k6_cat_1(A,C,D) != k1_xboole_0
                                      & k6_cat_1(A,D,E) != k1_xboole_0
                                      & k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H)) != k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) ) ) ) ) ) ) ) ) ) ),
    file(cat_1,t54_cat_1),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(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),
    []).