% Mizar problem: t23_graph_4,graph_4,1604,39 
fof(t23_graph_4,conjecture,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,u1_graph_1(A))
         => ! [C] : 
              ( ( v8_graph_1(C,A)
                & m2_graph_1(C,A) )
             => ~ ( r3_graph_4(A,B,C)
                  & ! [D] : 
                      ( m1_graph_2(D,u2_graph_1(A),C)
                     => ! [E] : 
                          ( m1_graph_2(E,u1_graph_1(A),B)
                         => ! [F] : 
                              ( ( v8_graph_1(F,A)
                                & v3_graph_2(F,A)
                                & m2_graph_1(F,A) )
                             => ! [G] : 
                                  ( m2_finseq_1(G,u1_graph_1(A))
                                 => ~ ( k15_finseq_1(D) = F
                                      & k15_finseq_1(E) = G
                                      & r3_graph_4(A,G,F)
                                      & k1_funct_1(B,1) = k1_funct_1(G,1)
                                      & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(G,k3_finseq_1(G)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_funct_1,cc1_graph_2,cc1_membered,cc1_nat_1,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_graph_2,cc2_membered,cc2_nat_1,cc3_membered,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,connectedness_r1_xreal_0,dt_k14_finseq_1,dt_k15_finseq_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k7_relat_1,dt_l1_graph_1,dt_m1_finseq_1,dt_m1_graph_1,dt_m1_graph_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_graph_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_graph_1,dt_u2_graph_1,existence_l1_graph_1,existence_m1_finseq_1,existence_m1_graph_1,existence_m1_graph_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_graph_1,existence_m2_relset_1,existence_m2_subset_1,fc10_finseq_1,fc11_finseq_1,fc17_finseq_1,fc1_graph_2,fc2_finseq_1,fc2_membered,fc4_funct_1,fc5_membered,fc6_membered,rc1_finseq_1,rc1_funct_1,rc1_graph_4,rc1_membered,rc1_nat_1,rc2_finseq_1,rc2_funct_1,rc2_graph_2,rc2_graph_4,rc2_nat_1,rc3_finseq_1,rc3_funct_1,rc3_graph_2,rc3_graph_4,rc3_nat_1,rc4_finseq_1,rc4_funct_1,rc4_graph_2,rc5_finseq_1,rc5_graph_1,rc6_finseq_1,rc6_graph_1,rc7_finseq_1,rc7_graph_1,rc8_finseq_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_graph_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s5_nat_1__e4_31_1_2__graph_4,spc1_boole,spc1_numerals,t1_real,t1_subset,t21_graph_4,t22_graph_4,t24_graph_2,t28_graph_2,t29_graph_2,t2_real,t2_subset,t30_graph_2,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(graph_4,t23_graph_4)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    []).

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

fof(cc1_graph_2,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] : 
          ( m1_graph_1(B,A)
         => ( v1_xboole_0(B)
           => v2_funct_1(B) ) ) ) ),
    file(graph_2,cc1_graph_2),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc1_nat_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) ) ) ),
    file(nat_1,cc1_nat_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(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

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_graph_2,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] : 
          ( m1_graph_1(B,A)
         => ( v1_xboole_0(B)
           => v8_graph_1(B,A) ) ) ) ),
    file(graph_2,cc2_graph_2),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc2_nat_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)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(dt_k14_finseq_1,axiom,(
    ! [A] : m2_finseq_1(k14_finseq_1(A),k5_numbers) ),
    file(finseq_1,k14_finseq_1),
    []).

fof(dt_k15_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => ( v1_relat_1(k15_finseq_1(A))
        & v1_funct_1(k15_finseq_1(A)) ) ) ),
    file(finseq_1,k15_finseq_1),
    []).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    []).

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_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_l1_graph_1,axiom,(
    $true ),
    file(graph_1,l1_graph_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_graph_1,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] : 
          ( m1_graph_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) ) ) ) ),
    file(graph_1,m1_graph_1),
    []).

fof(dt_m1_graph_2,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ! [C] : 
          ( m1_graph_2(C,A,B)
         => ( v1_relat_1(C)
            & v1_funct_1(C)
            & v2_finseq_1(C) ) ) ) ),
    file(graph_2,m1_graph_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_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_graph_1,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] : 
          ( m2_graph_1(B,A)
         => m2_finseq_1(B,u2_graph_1(A)) ) ) ),
    file(graph_1,m2_graph_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_u1_graph_1,axiom,(
    $true ),
    file(graph_1,u1_graph_1),
    []).

fof(dt_u2_graph_1,axiom,(
    $true ),
    file(graph_1,u2_graph_1),
    []).

fof(existence_l1_graph_1,axiom,(
    ? [A] : l1_graph_1(A) ),
    file(graph_1,l1_graph_1),
    []).

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

fof(existence_m1_graph_1,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : m1_graph_1(B,A) ) ),
    file(graph_1,m1_graph_1),
    []).

fof(existence_m1_graph_2,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ? [C] : m1_graph_2(C,A,B) ) ),
    file(graph_2,m1_graph_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_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_graph_1,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : m2_graph_1(B,A) ) ),
    file(graph_1,m2_graph_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(fc10_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => ( v1_relat_1(k15_finseq_1(A))
        & v1_funct_1(k15_finseq_1(A))
        & v1_finset_1(k15_finseq_1(A))
        & v1_finseq_1(k15_finseq_1(A)) ) ) ),
    file(finseq_1,fc10_finseq_1),
    []).

fof(fc11_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    []).

fof(fc17_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    []).

fof(fc1_graph_2,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ~ v1_xboole_0(u1_graph_1(A)) ) ),
    file(graph_2,fc1_graph_2),
    []).

fof(fc2_finseq_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

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(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(rc1_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    []).

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

fof(rc1_graph_4,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v8_graph_1(B,A)
          & v1_membered(B)
          & v2_membered(B)
          & v3_membered(B)
          & v4_membered(B)
          & v5_membered(B) ) ) ),
    file(graph_4,rc1_graph_4),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,k5_numbers,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc2_finseq_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_graph_2,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_finseq_1(B) ) ) ),
    file(graph_2,rc2_graph_2),
    []).

fof(rc2_graph_4,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v8_graph_1(B,A)
          & v1_graph_4(B,A) ) ) ),
    file(graph_4,rc2_graph_4),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

fof(rc3_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_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_graph_2,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v3_graph_2(B,A) ) ) ),
    file(graph_2,rc3_graph_2),
    []).

fof(rc3_graph_4,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v8_graph_1(B,A)
          & v3_graph_2(B,A) ) ) ),
    file(graph_4,rc3_graph_4),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

fof(rc4_finseq_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_1(B,A)
      & v1_xboole_0(B)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_finset_1(B)
      & v1_finseq_1(B) ) ),
    file(finseq_1,rc4_finseq_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_graph_2,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v3_graph_2(B,A) ) ) ),
    file(graph_2,rc4_graph_2),
    []).

fof(rc5_finseq_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_finseq_1(A) ) ),
    file(finseq_1,rc5_finseq_1),
    []).

fof(rc5_graph_1,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v8_graph_1(B,A) ) ) ),
    file(graph_1,rc5_graph_1),
    []).

fof(rc6_finseq_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    []).

fof(rc6_graph_1,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B) ) ) ),
    file(graph_1,rc6_graph_1),
    []).

fof(rc7_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    []).

fof(rc7_graph_1,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ? [B] : 
          ( m1_graph_1(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v2_funct_1(B)
          & v1_finset_1(B)
          & v1_finseq_1(B)
          & v8_graph_1(B,A) ) ) ),
    file(graph_1,rc7_graph_1),
    []).

fof(rc8_finseq_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    []).

fof(redefinition_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    []).

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_graph_1,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] : 
          ( m2_graph_1(B,A)
        <=> m1_graph_1(B,A) ) ) ),
    file(graph_1,m2_graph_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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(s5_nat_1__e4_31_1_2__graph_4,axiom,(
    ! [A,B,C] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A)
        & m2_finseq_1(B,u1_graph_1(A))
        & v8_graph_1(C,A)
        & m2_graph_1(C,A) )
     => ( ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & ? [E] : 
                ( m1_graph_2(E,u2_graph_1(A),C)
                & ? [F] : 
                    ( m1_graph_2(F,u1_graph_1(A),B)
                    & ? [G] : 
                        ( v8_graph_1(G,A)
                        & m2_graph_1(G,A)
                        & ? [H] : 
                            ( m2_finseq_1(H,u1_graph_1(A))
                            & k15_finseq_1(E) = G
                            & k15_finseq_1(F) = H
                            & r3_graph_4(A,H,G)
                            & k1_funct_1(B,1) = k1_funct_1(H,1)
                            & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(H,k3_finseq_1(H))
                            & k3_finseq_1(G) = D
                            & ~ v1_graph_4(G,A) ) ) ) ) )
       => ? [D] : 
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & ? [I] : 
                ( m1_graph_2(I,u2_graph_1(A),C)
                & ? [J] : 
                    ( m1_graph_2(J,u1_graph_1(A),B)
                    & ? [K] : 
                        ( v8_graph_1(K,A)
                        & m2_graph_1(K,A)
                        & ? [L] : 
                            ( m2_finseq_1(L,u1_graph_1(A))
                            & k15_finseq_1(I) = K
                            & k15_finseq_1(J) = L
                            & r3_graph_4(A,L,K)
                            & k1_funct_1(B,1) = k1_funct_1(L,1)
                            & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(L,k3_finseq_1(L))
                            & k3_finseq_1(K) = D
                            & ~ v1_graph_4(K,A) ) ) ) )
            & ! [M] : 
                ( m2_subset_1(M,k1_numbers,k5_numbers)
               => ( ? [N] : 
                      ( m1_graph_2(N,u2_graph_1(A),C)
                      & ? [O] : 
                          ( m1_graph_2(O,u1_graph_1(A),B)
                          & ? [P] : 
                              ( v8_graph_1(P,A)
                              & m2_graph_1(P,A)
                              & ? [Q] : 
                                  ( m2_finseq_1(Q,u1_graph_1(A))
                                  & k15_finseq_1(N) = P
                                  & k15_finseq_1(O) = Q
                                  & r3_graph_4(A,Q,P)
                                  & k1_funct_1(B,1) = k1_funct_1(Q,1)
                                  & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(Q,k3_finseq_1(Q))
                                  & k3_finseq_1(P) = M
                                  & ~ v1_graph_4(P,A) ) ) ) )
                 => r1_xreal_0(D,M) ) ) ) ) ) ),
    file(graph_4,s5_nat_1__e4_31_1_2__graph_4),
    []).

fof(spc1_boole,axiom,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(t1_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    []).

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

fof(t21_graph_4,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] : 
          ( ( v8_graph_1(B,A)
            & v1_graph_4(B,A)
            & m2_graph_1(B,A) )
         => ( v8_graph_1(B,A)
            & v3_graph_2(B,A)
            & m2_graph_1(B,A) ) ) ) ),
    file(graph_4,t21_graph_4),
    []).

fof(t22_graph_4,axiom,(
    ! [A] : 
      ( ( v2_graph_1(A)
        & l1_graph_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,u1_graph_1(A))
         => ! [C] : 
              ( ( v8_graph_1(C,A)
                & m2_graph_1(C,A) )
             => ~ ( ~ v1_graph_4(C,A)
                  & r3_graph_4(A,B,C)
                  & ! [D] : 
                      ( m1_graph_2(D,u2_graph_1(A),C)
                     => ! [E] : 
                          ( m1_graph_2(E,u1_graph_1(A),B)
                         => ! [F] : 
                              ( ( v8_graph_1(F,A)
                                & m2_graph_1(F,A) )
                             => ! [G] : 
                                  ( m2_finseq_1(G,u1_graph_1(A))
                                 => ~ ( ~ r1_xreal_0(k3_finseq_1(C),k3_finseq_1(F))
                                      & r3_graph_4(A,G,F)
                                      & ~ r1_xreal_0(k3_finseq_1(B),k3_finseq_1(G))
                                      & k1_funct_1(B,1) = k1_funct_1(G,1)
                                      & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(G,k3_finseq_1(G))
                                      & k15_finseq_1(D) = F
                                      & k15_finseq_1(E) = G ) ) ) ) ) ) ) ) ) ),
    file(graph_4,t22_graph_4),
    []).

fof(t24_graph_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_finseq_1(A) )
     => ( ( v1_relat_1(A)
          & v1_funct_1(A)
          & v1_finseq_1(A) )
       => k15_finseq_1(A) = A ) ) ),
    file(graph_2,t24_graph_2),
    []).

fof(t28_graph_2,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => m1_graph_2(B,A,B) ) ),
    file(graph_2,t28_graph_2),
    []).

fof(t29_graph_2,axiom,(
    ! [A,B,C] : 
      ( m2_finseq_1(C,A)
     => ! [D] : 
          ( m1_graph_2(D,A,C)
         => m1_graph_2(k7_relat_1(D,B),A,C) ) ) ),
    file(graph_2,t29_graph_2),
    []).

fof(t2_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    []).

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

fof(t30_graph_2,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ! [C] : 
          ( m2_finseq_1(C,A)
         => ! [D] : 
              ( m2_finseq_1(D,A)
             => ! [E] : 
                  ( m1_graph_2(E,A,B)
                 => ! [F] : 
                      ( m1_graph_2(F,A,B)
                     => ! [G] : 
                          ( m1_graph_2(G,A,C)
                         => ( ( k15_finseq_1(E) = C
                              & k15_finseq_1(G) = D
                              & F = k7_relat_1(E,k2_relat_1(k7_relat_1(k14_finseq_1(k1_relat_1(E)),k1_relat_1(G)))) )
                           => k15_finseq_1(F) = D ) ) ) ) ) ) ) ),
    file(graph_2,t30_graph_2),
    []).

fof(t3_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    []).

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

fof(t4_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    []).

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_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    []).

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_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    []).

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

fof(t7_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    []).

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

fof(t8_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    []).