% Mizar problem: t22_unialg_3,unialg_3,747,70 
fof(t22_unialg_3,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_unialg_1(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = u1_struct_0(A)
               => k8_unialg_2(A,k7_unialg_2(A,C),B) = k7_unialg_2(A,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v3_unialg_1,antisymmetry_r2_hidden,cc1_arytm_3,cc1_relset_1,cc1_unialg_3,cc2_arytm_3,cc3_arytm_3,commutativity_k2_xboole_0,d11_unialg_2,d3_unialg_2,dt_g1_unialg_1,dt_k13_finseq_1,dt_k1_numbers,dt_k1_unialg_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_unialg_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_finseq_2,dt_k4_partfun1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_unialg_2,dt_k7_unialg_2,dt_k8_unialg_2,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m1_unialg_2,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_m2_unialg_2,dt_m3_unialg_2,dt_u1_struct_0,dt_u1_unialg_1,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m1_unialg_2,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,existence_m2_unialg_2,existence_m3_unialg_2,fc1_struct_0,fc1_subset_1,fc1_unialg_2,fc1_xboole_0,fc2_xboole_0,fc3_xboole_0,fc4_subset_1,fraenkel_a_1_0_unialg_2,free_g1_unialg_1,idempotence_k2_xboole_0,rc1_arytm_3,rc1_subset_1,rc1_unialg_2,rc1_xboole_0,rc2_subset_1,rc2_unialg_2,rc2_xboole_0,rc3_struct_0,rc5_struct_0,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m2_unialg_2,reflexivity_r1_tarski,spc0_boole,t12_xboole_1,t1_boole,t1_numerals,t1_subset,t23_unialg_2,t2_subset,t2_tarski,t3_subset,t3_unialg_3,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(unialg_3,t22_unialg_3)]).

fof(abstractness_v3_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => ( v3_unialg_1(A)
       => A = g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) ) ) ),
    file(unialg_1,v3_unialg_1),
    []).

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

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

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(cc1_unialg_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => v2_unialg_2(B) ) ) ),
    file(unialg_3,cc1_unialg_3),
    []).

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

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(d11_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k6_unialg_2(A) = a_1_0_unialg_2(A) ) ),
    file(unialg_2,d11_unialg_2),
    []).

fof(d3_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k1_unialg_2(A) = k2_relat_1(u1_unialg_1(A)) ) ),
    file(unialg_2,d3_unialg_2),
    []).

fof(dt_g1_unialg_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
     => ( v3_unialg_1(g1_unialg_1(A,B))
        & l1_unialg_1(g1_unialg_1(A,B)) ) ) ),
    file(unialg_1,g1_unialg_1),
    []).

fof(dt_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m1_unialg_2(k1_unialg_2(A),u1_struct_0(A)) ) ),
    file(unialg_2,k1_unialg_2),
    []).

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_unialg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(B)
        & v1_unialg_1(B,A)
        & m1_relset_1(B,k13_finseq_1(A),A) )
     => m2_subset_1(k2_unialg_1(A,B),k1_numbers,k5_numbers) ) ),
    file(unialg_1,k2_unialg_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_k3_finseq_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k3_finseq_2(A))
      & m1_finseq_2(k3_finseq_2(A),A) ) ),
    file(finseq_2,k3_finseq_2),
    []).

fof(dt_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k6_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(unialg_2,k6_unialg_2),
    []).

fof(dt_k7_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_unialg_1(k7_unialg_2(A,B))
        & m3_unialg_2(k7_unialg_2(A,B),A) ) ) ),
    file(unialg_2,k7_unialg_2),
    []).

fof(dt_k8_unialg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & m3_unialg_2(B,A)
        & m3_unialg_2(C,A) )
     => ( v3_unialg_1(k8_unialg_2(A,B,C))
        & m3_unialg_2(k8_unialg_2(A,B,C),A) ) ) ),
    file(unialg_2,k8_unialg_2),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => l1_struct_0(A) ) ),
    file(unialg_1,l1_unialg_1),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    []).

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_m1_unialg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_unialg_2(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(unialg_2,m1_unialg_2),
    []).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_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_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(dt_m2_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ! [C] : 
          ( m2_unialg_2(C,A,B)
         => ( ~ v1_xboole_0(C)
            & v1_funct_1(C)
            & v1_unialg_1(C,A)
            & v2_unialg_1(C,A)
            & m2_relset_1(C,k3_finseq_2(A),A) ) ) ) ),
    file(unialg_2,m2_unialg_2),
    []).

fof(dt_m3_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) ) ) ) ),
    file(unialg_2,m3_unialg_2),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => m2_finseq_1(u1_unialg_1(A),k4_partfun1(k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))) ) ),
    file(unialg_1,u1_unialg_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l1_unialg_1,axiom,(
    ? [A] : l1_unialg_1(A) ),
    file(unialg_1,l1_unialg_1),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    []).

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_m1_unialg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_unialg_2(B,A) ) ),
    file(unialg_2,m1_unialg_2),
    []).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(existence_m2_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ? [C] : m2_unialg_2(C,A,B) ) ),
    file(unialg_2,m2_unialg_2),
    []).

fof(existence_m3_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : m3_unialg_2(B,A) ) ),
    file(unialg_2,m3_unialg_2),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

fof(fc1_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ~ v1_xboole_0(k6_unialg_2(A)) ) ),
    file(unialg_2,fc1_unialg_2),
    []).

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

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(fraenkel_a_1_0_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v6_unialg_1(B)
        & v7_unialg_1(B)
        & v8_unialg_1(B)
        & l1_unialg_1(B) )
     => ( r2_hidden(A,a_1_0_unialg_2(B))
      <=> ? [C] : 
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ? [D] : 
                ( m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B))
                & k2_unialg_1(u1_struct_0(B),D) = 0
                & r2_hidden(C,k2_relat_1(D)) ) ) ) ) ),
    file(unialg_2,a_1_0_unialg_2),
    []).

fof(free_g1_unialg_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
     => ! [C,D] : 
          ( g1_unialg_1(A,B) = g1_unialg_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(unialg_1,g1_unialg_1),
    []).

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

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

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_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ? [B] : 
          ( m3_unialg_2(B,A)
          & ~ v3_struct_0(B)
          & v3_unialg_1(B)
          & v6_unialg_1(B)
          & v7_unialg_1(B)
          & v8_unialg_1(B) ) ) ),
    file(unialg_2,rc1_unialg_2),
    []).

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

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_unialg_2,axiom,(
    ? [A] : 
      ( l1_unialg_1(A)
      & ~ v3_struct_0(A)
      & v3_unialg_1(A)
      & v6_unialg_1(A)
      & v7_unialg_1(A)
      & v8_unialg_1(A)
      & v2_unialg_2(A) ) ),
    file(unialg_2,rc2_unialg_2),
    []).

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

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k3_finseq_2,axiom,(
    ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ),
    file(finseq_2,k3_finseq_2),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_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_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(redefinition_m2_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ! [C] : 
          ( m2_unialg_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(unialg_2,m2_unialg_2),
    []).

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

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(t12_xboole_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    []).

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

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

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

fof(t23_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( D = k2_xboole_0(C,u1_struct_0(B))
                   => ( ( C = k1_xboole_0
                        & k6_unialg_2(A) = k1_xboole_0 )
                      | k8_unialg_2(A,k7_unialg_2(A,C),B) = k7_unialg_2(A,D) ) ) ) ) ) ) ),
    file(unialg_2,t23_unialg_2),
    []).

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(t3_unialg_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) ) ),
    file(unialg_3,t3_unialg_3),
    []).

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