% Mizar problem: t22_cat_5,cat_5,1841,32 
fof(t22_cat_5,conjecture,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( ( v2_cat_1(C)
                & v3_cat_5(C)
                & l1_cat_1(C) )
             => ! [D] : 
                  ( m2_cat_1(D,A,B)
                 => ! [E] : 
                      ( m2_cat_1(E,A,C)
                     => ( D = E
                       => k7_cat_5(A,B,D) = k7_cat_5(A,C,E) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_cat_1,antisymmetry_r2_hidden,cc1_cat_5,cc1_funct_1,cc1_relset_1,cc2_cat_5,cc2_funct_1,commutativity_k2_xboole_0,d21_cat_1,d2_xboole_0,d5_cat_2,d5_cat_5,dt_g1_cat_1,dt_k14_cat_1,dt_k15_cat_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k5_relat_1,dt_k6_partfun1,dt_k6_relat_1,dt_k7_cat_5,dt_k8_cat_2,dt_l1_cat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_cat_1,dt_m2_relset_1,dt_m3_cat_2,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_relset_1,existence_m1_subset_1,existence_m2_cat_1,existence_m2_relset_1,existence_m3_cat_2,fc1_funct_1,fc1_subset_1,fc1_xboole_0,fc2_funct_1,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,free_g1_cat_1,idempotence_k2_xboole_0,rc1_cat_1,rc1_cat_2,rc1_cat_5,rc1_funct_1,rc1_subset_1,rc1_xboole_0,rc2_cat_1,rc2_cat_5,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_cat_1,rc3_cat_5,rc3_funct_1,rc4_cat_5,redefinition_k14_cat_1,redefinition_k6_partfun1,redefinition_m2_relset_1,reflexivity_r1_tarski,t12_cat_5,t12_relset_1,t1_boole,t1_subset,t20_cat_5,t21_cat_5,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t79_relat_1,t7_boole,t7_xboole_1,t8_boole,t9_cat_5]),
    [file(cat_5,t22_cat_5)]).

fof(abstractness_v1_cat_1,axiom,(
    ! [A] : 
      ( l1_cat_1(A)
     => ( v1_cat_1(A)
       => A = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ) ),
    file(cat_1,v1_cat_1),
    []).

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

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

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_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_cat_5,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_cat_2(B,A)
         => v3_cat_5(B) ) ) ),
    file(cat_5,cc2_cat_5),
    []).

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

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(d21_cat_1,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => k15_cat_1(A) = k6_partfun1(u2_cat_1(A)) ) ),
    file(cat_1,d21_cat_1),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d5_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_cat_2(B,A)
         => k8_cat_2(A,B) = k15_cat_1(B) ) ) ),
    file(cat_2,d5_cat_2),
    []).

fof(d5_cat_5,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v2_cat_5(A)
      <=> ! [B] : 
            ( m1_subset_1(B,A)
           => ( v2_cat_1(B)
              & l1_cat_1(B) ) ) ) ) ),
    file(cat_5,d5_cat_5),
    []).

fof(dt_g1_cat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B) )
     => ( v1_cat_1(g1_cat_1(A,B,C,D,E,F))
        & l1_cat_1(g1_cat_1(A,B,C,D,E,F)) ) ) ),
    file(cat_1,g1_cat_1),
    []).

fof(dt_k14_cat_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,B,C) )
     => m2_cat_1(k14_cat_1(A,B,C,D,E),A,C) ) ),
    file(cat_1,k14_cat_1),
    []).

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

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_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_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k6_partfun1,axiom,(
    ! [A] : 
      ( v1_partfun1(k6_partfun1(A),A,A)
      & m2_relset_1(k6_partfun1(A),A,A) ) ),
    file(partfun1,k6_partfun1),
    []).

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

fof(dt_k7_cat_5,axiom,(
    ! [A,B,C] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => ( v1_cat_1(k7_cat_5(A,B,C))
        & m3_cat_2(k7_cat_5(A,B,C),B) ) ) ),
    file(cat_5,k7_cat_5),
    []).

fof(dt_k8_cat_2,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m3_cat_2(B,A) )
     => m2_cat_1(k8_cat_2(A,B),B,A) ) ),
    file(cat_2,k8_cat_2),
    []).

fof(dt_l1_cat_1,axiom,(
    $true ),
    file(cat_1,l1_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_cat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ! [C] : 
          ( m2_cat_1(C,A,B)
         => ( v1_funct_1(C)
            & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
            & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) ) ) ) ),
    file(cat_1,m2_cat_1),
    []).

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

fof(dt_m3_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_cat_2(B,A)
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) ),
    file(cat_2,m3_cat_2),
    []).

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

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

fof(existence_m2_cat_1,axiom,(
    ! [A,B] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B) )
     => ? [C] : m2_cat_1(C,A,B) ) ),
    file(cat_1,m2_cat_1),
    []).

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

fof(existence_m3_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ? [B] : m3_cat_2(B,A) ) ),
    file(cat_2,m3_cat_2),
    []).

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

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

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

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

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

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(free_g1_cat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B) )
     => ! [G,H,I,J,K,L] : 
          ( g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L)
         => ( A = G
            & B = H
            & C = I
            & D = J
            & E = K
            & F = L ) ) ) ),
    file(cat_1,g1_cat_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(rc1_cat_2,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ? [B] : 
          ( m3_cat_2(B,A)
          & v1_cat_1(B)
          & v2_cat_1(B) ) ) ),
    file(cat_2,rc1_cat_2),
    []).

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

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

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

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

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

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

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

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

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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

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

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

fof(rc4_cat_5,axiom,(
    ? [A] : 
      ( l1_cat_1(A)
      & v1_cat_1(A)
      & v2_cat_1(A)
      & v1_cat_5(A)
      & v3_cat_5(A)
      & v4_cat_5(A) ) ),
    file(cat_5,rc4_cat_5),
    []).

fof(redefinition_k14_cat_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m2_cat_1(E,B,C) )
     => k14_cat_1(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(cat_1,k14_cat_1),
    []).

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

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(t12_cat_5,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ( v2_cat_1(B)
            & l1_cat_1(B) ) ) ) ),
    file(cat_5,t12_cat_5),
    []).

fof(t12_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

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

fof(t20_cat_5,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v2_cat_5(A) )
     => ? [B] : 
          ( v1_cat_1(B)
          & v2_cat_1(B)
          & v3_cat_5(B)
          & v4_cat_5(B)
          & l1_cat_1(B)
          & u1_cat_1(B) = A ) ) ),
    file(cat_5,t20_cat_5),
    []).

fof(t21_cat_5,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & v4_cat_5(B)
            & l1_cat_1(B) )
         => ( r1_tarski(u1_cat_1(A),u1_cat_1(B))
           => m3_cat_2(A,B) ) ) ) ),
    file(cat_5,t21_cat_5),
    []).

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

fof(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(t79_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k5_relat_1(B,k6_relat_1(A)) = B ) ) ),
    file(relat_1,t79_relat_1),
    []).

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

fof(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

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

fof(t9_cat_5,axiom,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] : 
              ( m3_cat_2(C,B)
             => ! [D] : 
                  ( m2_cat_1(D,A,C)
                 => ! [E] : 
                      ( m2_cat_1(E,A,B)
                     => ( D = E
                       => k7_cat_5(A,C,D) = k7_cat_5(A,B,E) ) ) ) ) ) ) ),
    file(cat_5,t9_cat_5),
    []).