% Mizar problem: t15_index_1,index_1,1007,72 
fof(t15_index_1,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( m5_index_1(k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
            & m5_index_1(k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))),u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,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,d2_funcop_1,d5_tarski,d7_index_1,d8_index_1,dt_k10_cat_1,dt_k10_index_1,dt_k11_index_1,dt_k12_index_1,dt_k13_index_1,dt_k14_cat_1,dt_k14_index_1,dt_k15_cat_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_oppcat_1,dt_k1_partfun1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cat_1,dt_k2_funcop_1,dt_k2_funct_4,dt_k2_index_1,dt_k2_mcart_1,dt_k2_pre_circ,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_cat_1,dt_k4_cat_1,dt_k4_tarski,dt_k5_cat_1,dt_k5_relat_1,dt_k7_pboole,dt_k9_index_1,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_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_m5_index_1,fc10_relat_1,fc12_relat_1,fc1_circcomb,fc1_funcop_1,fc1_funct_1,fc1_index_1,fc2_funcop_1,fc2_pboole,fc3_funcop_1,fc3_index_1,fc4_relat_1,fc7_funcop_1,fc8_funcop_1,fc9_funcop_1,fc9_relat_1,l32_index_1,l33_index_1,rc1_circcomb,rc1_funcop_1,rc1_funct_1,rc1_index_1,rc1_pboole,rc1_relat_1,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_index_1,rc4_pboole,rc5_funct_1,redefinition_k10_cat_1,redefinition_k10_index_1,redefinition_k11_index_1,redefinition_k12_index_1,redefinition_k13_index_1,redefinition_k14_cat_1,redefinition_k14_index_1,redefinition_k1_oppcat_1,redefinition_k1_partfun1,redefinition_k2_index_1,redefinition_k2_pre_circ,redefinition_k7_pboole,redefinition_k9_index_1,redefinition_m2_relset_1,redefinition_r4_nattra_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r4_nattra_1,reflexivity_r6_pboole,symmetry_r4_nattra_1,symmetry_r6_pboole,t13_funcop_1,t1_subset,t2_subset,t3_subset,t4_isocat_1,t4_subset,t5_subset,t6_boole,t6_index_1,t7_boole,t7_index_1,t7_mcart_1,t8_boole]),
    [file(index_1,t15_index_1)]).

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

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

fof(cc1_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(d2_funcop_1,axiom,(
    ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ),
    file(funcop_1,d2_funcop_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_index_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_index_1(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( ( v1_index_1(C)
                & m1_pboole(C,A) )
             => ! [D] : 
                  ( ( v1_funcop_1(D)
                    & m1_pboole(D,A) )
                 => ( m2_index_1(D,A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => m2_cat_1(k1_funct_1(D,E),k2_index_1(A,B,E),k2_index_1(A,C,E)) ) ) ) ) ) ) ),
    file(index_1,d7_index_1),
    []).

fof(d8_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] : 
                      ( ( v2_index_1(E,A,B)
                        & m1_index_1(E,A,B) )
                     => ( m3_index_1(E,A,B,C,D)
                      <=> m2_index_1(k9_index_1(A,B,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,d8_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_k11_index_1,axiom,(
    ! [A,B,C] : 
      ( ( v3_index_1(C,A,B)
        & m1_index_1(C,A,B) )
     => ( v1_funcop_1(k11_index_1(A,B,C))
        & m1_pboole(k11_index_1(A,B,C),B) ) ) ),
    file(index_1,k11_index_1),
    []).

fof(dt_k12_index_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_index_1(C)
        & m1_pboole(C,A)
        & v1_funcop_1(D)
        & m1_pboole(D,B) )
     => ( v2_index_1(k12_index_1(A,B,C,D),A,B)
        & v3_index_1(k12_index_1(A,B,C,D),A,B)
        & m1_index_1(k12_index_1(A,B,C,D),A,B) ) ) ),
    file(index_1,k12_index_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_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_oppcat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v1_funct_1(k1_oppcat_1(A,B,C,D))
        & m2_relset_1(k1_oppcat_1(A,B,C,D),k2_zfmisc_1(B,A),C) ) ) ),
    file(oppcat_1,k1_oppcat_1),
    []).

fof(dt_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F))
        & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ),
    file(partfun1,k1_partfun1),
    []).

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_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

fof(dt_k2_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_4(A))
        & v1_funct_1(k2_funct_4(A)) ) ) ),
    file(funct_4,k2_funct_4),
    []).

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_pre_circ,axiom,(
    ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ),
    file(pre_circ,k2_pre_circ),
    []).

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_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_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_k9_index_1,axiom,(
    ! [A,B,C] : 
      ( m1_index_1(C,A,B)
     => m1_pboole(k9_index_1(A,B,C),B) ) ),
    file(index_1,k9_index_1),
    []).

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

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

fof(dt_m1_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_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_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_circcomb,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_funcop_1(k2_funcop_1(A,B)) ) ) ),
    file(circcomb,fc1_circcomb),
    []).

fof(fc1_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_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_index_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_index_1(k2_funcop_1(A,B)) ) ) ),
    file(index_1,fc1_index_1),
    []).

fof(fc2_funcop_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_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_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    []).

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(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(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_funcop_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_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(l32_index_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => m2_cat_1(k1_funct_1(k11_index_1(u1_cat_1(A),u2_cat_1(A),k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B)))),C),k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))))),C),k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))))),C)) ) ) ) ),
    file(index_1,l32_index_1),
    []).

fof(l33_index_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => m2_cat_1(k1_funct_1(k11_index_1(u1_cat_1(A),u2_cat_1(A),k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B)))),C),k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))))),C),k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))))),C)) ) ) ) ),
    file(index_1,l33_index_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_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_index_1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_index_1(C,A,B)
      & v2_index_1(C,A,B)
      & v3_index_1(C,A,B) ) ),
    file(index_1,rc4_index_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_k11_index_1,axiom,(
    ! [A,B,C] : 
      ( ( v3_index_1(C,A,B)
        & m1_index_1(C,A,B) )
     => k11_index_1(A,B,C) = k2_mcart_1(C) ) ),
    file(index_1,k11_index_1),
    []).

fof(redefinition_k12_index_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_index_1(C)
        & m1_pboole(C,A)
        & v1_funcop_1(D)
        & m1_pboole(D,B) )
     => k12_index_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(index_1,k12_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_oppcat_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => k1_oppcat_1(A,B,C,D) = k2_funct_4(D) ) ),
    file(oppcat_1,k1_oppcat_1),
    []).

fof(redefinition_k1_partfun1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( v1_funct_1(E)
        & m1_relset_1(E,A,B)
        & v1_funct_1(F)
        & m1_relset_1(F,C,D) )
     => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ),
    file(partfun1,k1_partfun1),
    []).

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_k2_pre_circ,axiom,(
    ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ),
    file(pre_circ,k2_pre_circ),
    []).

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_k9_index_1,axiom,(
    ! [A,B,C] : 
      ( m1_index_1(C,A,B)
     => k9_index_1(A,B,C) = k2_mcart_1(C) ) ),
    file(index_1,k9_index_1),
    []).

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(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

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(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

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(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

fof(t13_funcop_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    []).

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

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

fof(t6_index_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A))
         => ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
          <=> ( ! [C] : 
                  ( m1_subset_1(C,u1_cat_1(A))
                 => k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),k10_cat_1(A,C)) = k15_cat_1(k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C)) )
              & ! [C] : 
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( k2_cat_1(A,D) = k3_cat_1(A,C)
                       => k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),k4_cat_1(A,C,D)) = k1_partfun1(u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),C),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),D)) ) ) ) ) ) ) ) ),
    file(index_1,t6_index_1),
    []).

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

fof(t7_index_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A))
         => ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
          <=> ( ! [C] : 
                  ( m1_subset_1(C,u1_cat_1(A))
                 => k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),k10_cat_1(A,C)) = k15_cat_1(k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C)) )
              & ! [C] : 
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( k2_cat_1(A,D) = k3_cat_1(A,C)
                       => k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),k4_cat_1(A,C,D)) = k1_partfun1(u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),D),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),C)) ) ) ) ) ) ) ) ),
    file(index_1,t7_index_1),
    []).

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),
    []).