% Mizar problem: t21_circcmb2,circcmb2,1963,59 
fof(t21_circcmb2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] : 
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] : 
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] : 
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] : 
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( ( ! [I] : 
                                              ( m1_subset_1(I,k4_card_3(u4_msualg_1(A,D)))
                                             => v1_circuit2(k9_facirc_1(A,D,I,G),A,D) )
                                          & ! [I] : 
                                              ( m1_subset_1(I,k4_card_3(u4_msualg_1(B,E)))
                                             => v1_circuit2(k9_facirc_1(B,E,I,H),B,E) ) )
                                       => ! [I] : 
                                            ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                           => v1_circuit2(k9_facirc_1(C,F,I,k1_nat_1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_msualg_1,abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc1_facirc_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_facirc_1,cc2_funct_1,cc3_facirc_1,cc4_facirc_1,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,d3_circcomb,dt_g1_msualg_1,dt_g3_msualg_1,dt_k13_finseq_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_msafree2,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_circcomb,dt_k3_finseq_2,dt_k3_msafree2,dt_k4_card_3,dt_k4_circcomb,dt_k4_msafree2,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k6_pboole,dt_k7_pboole,dt_k7_relat_1,dt_k9_facirc_1,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_m3_pboole,dt_u1_msualg_1,dt_u1_struct_0,dt_u2_msualg_1,dt_u3_msualg_1,dt_u4_msualg_1,dt_u5_msualg_1,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_finseq_2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,fc10_relat_1,fc12_relat_1,fc13_relat_1,fc1_funct_1,fc1_ordinal2,fc1_struct_0,fc3_card_3,fc3_circcomb,fc4_circcomb,fc4_funct_1,fc4_relat_1,fc9_relat_1,free_g1_msualg_1,free_g3_msualg_1,rc1_circcomb,rc1_facirc_1,rc1_fraenkel,rc1_funct_1,rc1_relat_1,rc2_facirc_1,rc2_funct_1,rc2_relat_1,rc3_facirc_1,rc3_funct_1,rc3_relat_1,rc3_struct_0,rc4_funct_1,rc5_struct_0,redefinition_k1_nat_1,redefinition_k3_finseq_2,redefinition_k4_msafree2,redefinition_k5_numbers,redefinition_k7_pboole,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_circcomb,reflexivity_r1_partfun1,reflexivity_r1_tarski,symmetry_r1_circcomb,symmetry_r1_partfun1,symmetry_r1_xboole_0,t1_subset,t20_circcmb2,t2_subset,t33_circcomb,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(circcmb2,t21_circcmb2)]).

fof(abstractness_v1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_msualg_1(A)
       => A = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ),
    file(msualg_1,v1_msualg_1),
    []).

fof(abstractness_v4_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ( v4_msualg_1(B,A)
       => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ),
    file(msualg_1,v4_msualg_1),
    []).

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

fof(cc1_facirc_1,axiom,(
    ! [A] : 
      ( v1_facirc_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(facirc_1,cc1_facirc_1),
    []).

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

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_facirc_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v1_facirc_1(A) ) ) ),
    file(facirc_1,cc2_facirc_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(cc3_facirc_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ~ v2_facirc_1(A) ) ),
    file(facirc_1,cc3_facirc_1),
    []).

fof(cc4_facirc_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & ~ v2_facirc_1(A) )
     => ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A)
        & ~ v2_facirc_1(A) ) ) ),
    file(facirc_1,cc4_facirc_1),
    []).

fof(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(d3_circcomb,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( l3_msualg_1(D,B)
                 => ( r2_circcomb(A,B,C,D)
                  <=> ( r1_circcomb(A,B)
                      & r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D))
                      & r1_partfun1(u5_msualg_1(A,C),u5_msualg_1(B,D)) ) ) ) ) ) ) ),
    file(circcomb,d3_circcomb),
    []).

fof(dt_g1_msualg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ( v1_msualg_1(g1_msualg_1(A,B,C,D))
        & l1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ),
    file(msualg_1,g1_msualg_1),
    []).

fof(dt_g3_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A))
        & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
     => ( v4_msualg_1(g3_msualg_1(A,B,C),A)
        & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ),
    file(msualg_1,g3_msualg_1),
    []).

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

fof(dt_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

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

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_msafree2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => m1_subset_1(k2_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(msafree2,k2_msafree2),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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

fof(dt_k3_circcomb,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ( ~ v3_struct_0(k3_circcomb(A,B))
        & v1_msualg_1(k3_circcomb(A,B))
        & l1_msualg_1(k3_circcomb(A,B)) ) ) ),
    file(circcomb,k3_circcomb),
    []).

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_k3_msafree2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => m1_subset_1(k3_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(msafree2,k3_msafree2),
    []).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

fof(dt_k4_circcomb,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & v5_msualg_1(D,B)
        & l3_msualg_1(D,B) )
     => ( v4_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
        & v5_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B))
        & l3_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) ) ) ),
    file(circcomb,k4_circcomb),
    []).

fof(dt_k4_msafree2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ( ~ v1_xboole_0(k4_msafree2(A))
        & m1_subset_1(k4_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(msafree2,k4_msafree2),
    []).

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_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_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ),
    file(pboole,k6_pboole),
    []).

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_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    []).

fof(dt_k9_facirc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & v4_msafree2(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B)))
        & m1_subset_1(D,k5_numbers) )
     => m1_subset_1(k9_facirc_1(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) ),
    file(facirc_1,k9_facirc_1),
    []).

fof(dt_l1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => l1_struct_0(A) ) ),
    file(msualg_1,l1_msualg_1),
    []).

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

fof(dt_l2_msualg_1,axiom,(
    $true ),
    file(msualg_1,l2_msualg_1),
    []).

fof(dt_l3_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => l2_msualg_1(B,A) ) ) ),
    file(msualg_1,l3_msualg_1),
    []).

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

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_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_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    []).

fof(dt_u1_msualg_1,axiom,(
    $true ),
    file(msualg_1,u1_msualg_1),
    []).

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

fof(dt_u2_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_funct_1(u2_msualg_1(A))
        & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)))
        & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ),
    file(msualg_1,u2_msualg_1),
    []).

fof(dt_u3_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_funct_1(u3_msualg_1(A))
        & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A))
        & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ),
    file(msualg_1,u3_msualg_1),
    []).

fof(dt_u4_msualg_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A) )
     => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ),
    file(msualg_1,u4_msualg_1),
    []).

fof(dt_u5_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ),
    file(msualg_1,u5_msualg_1),
    []).

fof(existence_l1_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) ),
    file(msualg_1,l1_msualg_1),
    []).

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

fof(existence_l2_msualg_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l2_msualg_1(B,A) ) ),
    file(msualg_1,l2_msualg_1),
    []).

fof(existence_l3_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] : l3_msualg_1(B,A) ) ),
    file(msualg_1,l3_msualg_1),
    []).

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

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_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_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    []).

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(fc13_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) ),
    file(relat_1,fc13_relat_1),
    []).

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

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

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(fc3_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => v1_fraenkel(k4_card_3(A)) ) ),
    file(card_3,fc3_card_3),
    []).

fof(fc3_circcomb,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ( ~ v3_struct_0(k3_circcomb(A,B))
        & v1_msualg_1(k3_circcomb(A,B))
        & ~ v2_msualg_1(k3_circcomb(A,B)) ) ) ),
    file(circcomb,fc3_circcomb),
    []).

fof(fc4_circcomb,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ( ~ v3_struct_0(k3_circcomb(B,A))
        & v1_msualg_1(k3_circcomb(B,A))
        & ~ v2_msualg_1(k3_circcomb(B,A)) ) ) ),
    file(circcomb,fc4_circcomb),
    []).

fof(fc4_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_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(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(free_g1_msualg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ! [E,F,G,H] : 
          ( g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(msualg_1,g1_msualg_1),
    []).

fof(free_g3_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A))
        & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
     => ! [D,E,F] : 
          ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(msualg_1,g3_msualg_1),
    []).

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

fof(rc1_facirc_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_facirc_1(A) ) ),
    file(facirc_1,rc1_facirc_1),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

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(rc2_facirc_1,axiom,(
    ? [A] : ~ v1_facirc_1(A) ),
    file(facirc_1,rc2_facirc_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(rc3_facirc_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v2_facirc_1(A) ) ),
    file(facirc_1,rc3_facirc_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(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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(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_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

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

fof(redefinition_k4_msafree2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => k4_msafree2(A) = k3_msafree2(A) ) ),
    file(msafree2,k4_msafree2),
    []).

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

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_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(reflexivity_r1_circcomb,axiom,(
    ! [A,B] : 
      ( ( l1_msualg_1(A)
        & l1_msualg_1(B) )
     => r1_circcomb(A,A) ) ),
    file(circcomb,r1_circcomb),
    []).

fof(reflexivity_r1_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_partfun1(A,A) ) ),
    file(partfun1,r1_partfun1),
    []).

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

fof(symmetry_r1_circcomb,axiom,(
    ! [A,B] : 
      ( ( l1_msualg_1(A)
        & l1_msualg_1(B) )
     => ( r1_circcomb(A,B)
       => r1_circcomb(B,A) ) ) ),
    file(circcomb,r1_circcomb),
    []).

fof(symmetry_r1_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_partfun1(A,B)
       => r1_partfun1(B,A) ) ) ),
    file(partfun1,r1_partfun1),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

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

fof(t20_circcmb2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v2_msafree2(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & v2_msafree2(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & ~ v2_msualg_1(C)
                & v2_msafree2(C)
                & l1_msualg_1(C) )
             => ( ( r1_xboole_0(k2_msafree2(A),k4_msafree2(B))
                  & C = k3_circcomb(A,B) )
               => ! [D] : 
                    ( ( v5_msualg_1(D,A)
                      & v4_msafree2(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] : 
                        ( ( v5_msualg_1(E,B)
                          & v4_msafree2(E,B)
                          & l3_msualg_1(E,B) )
                       => ! [F] : 
                            ( ( v5_msualg_1(F,C)
                              & v4_msafree2(F,C)
                              & l3_msualg_1(F,C) )
                           => ( ( r2_circcomb(A,B,D,E)
                                & F = k4_circcomb(A,B,D,E) )
                             => ! [G] : 
                                  ( m2_subset_1(G,k1_numbers,k5_numbers)
                                 => ! [H] : 
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ! [I] : 
                                          ( m1_subset_1(I,k4_card_3(u4_msualg_1(C,F)))
                                         => ! [J] : 
                                              ( m1_subset_1(J,k4_card_3(u4_msualg_1(A,D)))
                                             => ! [K] : 
                                                  ( m1_subset_1(K,k4_card_3(u4_msualg_1(B,E)))
                                                 => ( ( J = k7_relat_1(I,u1_struct_0(A))
                                                      & v1_circuit2(k9_facirc_1(A,D,J,G),A,D)
                                                      & K = k7_relat_1(k9_facirc_1(C,F,I,G),u1_struct_0(B))
                                                      & v1_circuit2(k9_facirc_1(B,E,K,H),B,E) )
                                                   => v1_circuit2(k9_facirc_1(C,F,I,k1_nat_1(G,H)),C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(circcmb2,t20_circcmb2),
    []).

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

fof(t33_circcomb,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,B)
                    & l3_msualg_1(D,B) )
                 => ( r1_partfun1(u4_msualg_1(A,C),u4_msualg_1(B,D))
                   => ! [E] : 
                        ( m1_subset_1(E,k4_card_3(u4_msualg_1(k3_circcomb(A,B),k4_circcomb(A,B,C,D))))
                       => ( r2_hidden(k7_relat_1(E,u1_struct_0(A)),k4_card_3(u4_msualg_1(A,C)))
                          & r2_hidden(k7_relat_1(E,u1_struct_0(B)),k4_card_3(u4_msualg_1(B,D))) ) ) ) ) ) ) ) ),
    file(circcomb,t33_circcomb),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

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

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

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

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