% Mizar problem: t39_yellow14,yellow14,1343,8 
fof(t39_yellow14,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v4_waybel_3(B)
            & v1_waybel18(B)
            & m1_pboole(B,A) )
         => ( ! [C] : 
                ( m1_subset_1(C,A)
               => ( v1_urysohn1(k4_waybel18(A,B,C))
                  & v2_pre_topc(k4_waybel18(A,B,C)) ) )
           => v1_urysohn1(k3_waybel18(A,B)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc1_borsuk_3,cc1_funct_1,cc1_monoid_0,cc1_realset1,cc1_relat_1,cc1_waybel12,cc1_waybel18,cc2_funct_1,cc2_waybel12,d10_xboole_0,d1_tarski,d3_pboole,d3_tarski,d3_waybel18,dt_g1_pre_topc,dt_k12_pralg_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_waybel18,dt_k3_waybel18,dt_k4_card_3,dt_k4_waybel18,dt_k5_waybel18,dt_k6_pre_topc,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pboole,dt_m1_subset_1,dt_m2_cantor_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pboole,existence_m1_subset_1,existence_m2_cantor_1,fc12_relat_1,fc1_struct_0,fc1_tex_4,fc1_waybel12,fc1_waybel18,fc2_tex_4,fc2_waybel18,fc3_realset1,fc3_tex_4,fc4_relat_1,fc5_relat_1,fc5_yellow12,fc5_yellow_6,fc6_yellow12,fc7_relat_1,free_g1_pre_topc,rc1_funct_1,rc1_monoid_0,rc1_partfun1,rc1_pre_topc,rc1_realset1,rc1_relat_1,rc1_waybel12,rc1_waybel18,rc2_funct_1,rc2_pre_topc,rc2_realset1,rc2_relat_1,rc2_waybel12,rc2_waybel18,rc2_waybel_7,rc3_funct_1,rc3_relat_1,rc3_struct_0,rc3_waybel12,rc3_waybel_7,rc3_yellow_6,rc4_funct_1,rc4_waybel12,rc5_funct_1,rc5_struct_0,rc6_pre_topc,rc6_waybel12,rc7_pre_topc,rc7_waybel12,redefinition_k1_struct_0,redefinition_k4_waybel18,redefinition_k5_waybel18,reflexivity_r1_tarski,t18_card_3,t1_subset,t27_urysohn1,t2_subset,t30_yellow14,t3_subset,t48_pre_topc,t4_subset,t52_pre_topc,t5_subset,t6_boole,t7_boole,t8_boole,t9_funct_1]),
    [file(yellow14,t39_yellow14)]).

fof(abstractness_v1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( v1_pre_topc(A)
       => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ),
    file(pre_topc,v1_pre_topc),
    []).

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

fof(cc1_borsuk_3,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( v3_struct_0(A)
          & v2_pre_topc(A) )
       => ( v2_pre_topc(A)
          & v2_compts_1(A) ) ) ) ),
    file(borsuk_3,cc1_borsuk_3),
    []).

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

fof(cc1_monoid_0,axiom,(
    ! [A] : 
      ( ( v1_monoid_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(monoid_0,cc1_monoid_0),
    []).

fof(cc1_realset1,axiom,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

fof(cc1_waybel12,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)
            & v1_finset_1(B) ) ) ) ),
    file(waybel12,cc1_waybel12),
    []).

fof(cc1_waybel18,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_waybel18(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) ),
    file(waybel18,cc1_waybel18),
    []).

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_waybel12,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => v1_card_4(A) ) ),
    file(waybel12,cc2_waybel12),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d3_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d3_waybel18,axiom,(
    ! [A,B] : 
      ( ( v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_pre_topc(C)
            & v2_pre_topc(C)
            & l1_pre_topc(C) )
         => ( C = k3_waybel18(A,B)
          <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
              & m2_cantor_1(k2_waybel18(A,B),C) ) ) ) ) ),
    file(waybel18,d3_waybel18),
    []).

fof(dt_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v1_pre_topc(g1_pre_topc(A,B))
        & l1_pre_topc(g1_pre_topc(A,B)) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

fof(dt_k12_pralg_1,axiom,(
    ! [A,B] : 
      ( ( v2_pralg_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k12_pralg_1(A,B),A) ) ),
    file(pralg_1,k12_pralg_1),
    []).

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

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_waybel18,axiom,(
    ! [A,B] : 
      ( ( v1_waybel18(B)
        & m1_pboole(B,A) )
     => m1_subset_1(k2_waybel18(A,B),k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))) ) ),
    file(waybel18,k2_waybel18),
    []).

fof(dt_k3_waybel18,axiom,(
    ! [A,B] : 
      ( ( v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A) )
     => ( v1_pre_topc(k3_waybel18(A,B))
        & v2_pre_topc(k3_waybel18(A,B))
        & l1_pre_topc(k3_waybel18(A,B)) ) ) ),
    file(waybel18,k3_waybel18),
    []).

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

fof(dt_k4_waybel18,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(k4_waybel18(A,B,C))
        & l1_pre_topc(k4_waybel18(A,B,C)) ) ) ),
    file(waybel18,k4_waybel18),
    []).

fof(dt_k5_waybel18,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
        & m1_subset_1(D,A) )
     => m1_subset_1(k5_waybel18(A,B,C,D),u1_struct_0(k4_waybel18(A,B,D))) ) ),
    file(waybel18,k5_waybel18),
    []).

fof(dt_k6_pre_topc,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k6_pre_topc),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

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

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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_cantor_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m2_cantor_1(B,A)
         => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ),
    file(cantor_1,m2_cantor_1),
    []).

fof(dt_u1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ),
    file(pre_topc,u1_pre_topc),
    []).

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

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

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

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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

fof(existence_m2_cantor_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : m2_cantor_1(B,A) ) ),
    file(cantor_1,m2_cantor_1),
    []).

fof(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc1_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_tex_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k6_pre_topc(A,B))
        & v4_pre_topc(k6_pre_topc(A,B),A) ) ) ),
    file(tex_4,fc1_tex_4),
    []).

fof(fc1_waybel12,axiom,(
    ! [A] : 
      ( ( v3_struct_0(A)
        & l1_struct_0(A) )
     => ( v1_xboole_0(u1_struct_0(A))
        & v1_finset_1(u1_struct_0(A)) ) ) ),
    file(waybel12,fc1_waybel12),
    []).

fof(fc1_waybel18,axiom,(
    ! [A,B] : 
      ( ( v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k3_waybel18(A,B))
        & v1_pre_topc(k3_waybel18(A,B))
        & v2_pre_topc(k3_waybel18(A,B)) ) ) ),
    file(waybel18,fc1_waybel18),
    []).

fof(fc2_tex_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_xboole_0(k6_pre_topc(A,B))
        & v3_pre_topc(k6_pre_topc(A,B),A)
        & v4_pre_topc(k6_pre_topc(A,B),A)
        & v2_tops_1(k6_pre_topc(A,B),A)
        & v3_tops_1(k6_pre_topc(A,B),A)
        & v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A)))
        & v1_membered(k6_pre_topc(A,B))
        & v2_membered(k6_pre_topc(A,B))
        & v3_membered(k6_pre_topc(A,B))
        & v4_membered(k6_pre_topc(A,B))
        & v5_membered(k6_pre_topc(A,B)) ) ) ),
    file(tex_4,fc2_tex_4),
    []).

fof(fc2_waybel18,axiom,(
    ! [A,B] : 
      ( ( v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k3_waybel18(A,B))
        & v1_pre_topc(k3_waybel18(A,B))
        & v2_pre_topc(k3_waybel18(A,B))
        & v1_monoid_0(k3_waybel18(A,B)) ) ) ),
    file(waybel18,fc2_waybel18),
    []).

fof(fc3_realset1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    []).

fof(fc3_tex_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( ~ v1_xboole_0(k6_pre_topc(A,B))
        & v4_pre_topc(k6_pre_topc(A,B),A)
        & ~ v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(tex_4,fc3_tex_4),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

fof(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc5_yellow12,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_pre_topc(A) )
     => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ),
    file(yellow12,fc5_yellow12),
    []).

fof(fc5_yellow_6,axiom,(
    ! [A,B] : 
      ( ( v2_pralg_1(B)
        & v4_waybel_3(B)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k12_pralg_1(A,B))
        & v2_relat_1(k12_pralg_1(A,B))
        & v1_funct_1(k12_pralg_1(A,B)) ) ) ),
    file(yellow_6,fc5_yellow_6),
    []).

fof(fc6_yellow12,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
        & v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ),
    file(yellow12,fc6_yellow12),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(free_g1_pre_topc,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C,D] : 
          ( g1_pre_topc(A,B) = g1_pre_topc(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(pre_topc,g1_pre_topc),
    []).

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

fof(rc1_monoid_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & v1_monoid_0(A) ) ),
    file(monoid_0,rc1_monoid_0),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_pre_topc,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & v1_pre_topc(A) ) ),
    file(pre_topc,rc1_pre_topc),
    []).

fof(rc1_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

fof(rc1_waybel12,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & v3_struct_0(A) ) ),
    file(waybel12,rc1_waybel12),
    []).

fof(rc1_waybel18,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v1_waybel18(B) ) ),
    file(waybel18,rc1_waybel18),
    []).

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_pre_topc,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v1_pre_topc(A)
      & v2_pre_topc(A) ) ),
    file(pre_topc,rc2_pre_topc),
    []).

fof(rc2_realset1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

fof(rc2_waybel12,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc2_waybel12),
    []).

fof(rc2_waybel18,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v4_waybel_3(B)
      & v2_pralg_1(B)
      & v1_waybel18(B) ) ),
    file(waybel18,rc2_waybel18),
    []).

fof(rc2_waybel_7,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      & ~ v1_xboole_0(B)
      & v1_finset_1(B) ) ),
    file(waybel_7,rc2_waybel_7),
    []).

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(rc3_waybel12,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_card_4(B) ) ) ),
    file(waybel12,rc3_waybel12),
    []).

fof(rc3_waybel_7,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(waybel_7,rc3_waybel_7),
    []).

fof(rc3_yellow_6,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v4_waybel_3(B) ) ),
    file(yellow_6,rc3_yellow_6),
    []).

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_waybel12,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc4_waybel12),
    []).

fof(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

fof(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(rc6_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc6_pre_topc),
    []).

fof(rc6_waybel12,axiom,(
    ? [A] : 
      ( ~ v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc6_waybel12),
    []).

fof(rc7_pre_topc,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc7_pre_topc),
    []).

fof(rc7_waybel12,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
          & v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_card_4(B) ) ) ),
    file(waybel12,rc7_waybel12),
    []).

fof(redefinition_k1_struct_0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k1_struct_0(A,B) = k1_tarski(B) ) ),
    file(struct_0,k1_struct_0),
    []).

fof(redefinition_k4_waybel18,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k4_waybel18(A,B,C) = k1_funct_1(B,C) ) ),
    file(waybel18,k4_waybel18),
    []).

fof(redefinition_k5_waybel18,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v4_waybel_3(B)
        & v1_waybel18(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
        & m1_subset_1(D,A) )
     => k5_waybel18(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(waybel18,k5_waybel18),
    []).

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

fof(t18_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    []).

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

fof(t27_urysohn1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_urysohn1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => v4_pre_topc(k1_struct_0(A,B),A) ) ) ) ),
    file(urysohn1,t27_urysohn1),
    []).

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_yellow14,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v4_waybel_3(B)
            & v1_waybel18(B)
            & m1_pboole(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k3_waybel18(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k3_waybel18(A,B)))
                 => ( r2_hidden(C,k6_pre_topc(k3_waybel18(A,B),k1_struct_0(k3_waybel18(A,B),D)))
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => r2_hidden(k5_waybel18(A,B,C,E),k6_pre_topc(k4_waybel18(A,B,E),k1_struct_0(k4_waybel18(A,B,E),k5_waybel18(A,B,D,E)))) ) ) ) ) ) ) ),
    file(yellow14,t30_yellow14),
    []).

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

fof(t48_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => r1_tarski(B,k6_pre_topc(A,B)) ) ) ),
    file(pre_topc,t48_pre_topc),
    []).

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(t52_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v4_pre_topc(B,A)
             => k6_pre_topc(A,B) = B )
            & ( ( v2_pre_topc(A)
                & k6_pre_topc(A,B) = B )
             => v4_pre_topc(B,A) ) ) ) ) ),
    file(pre_topc,t52_pre_topc),
    []).

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),
    []).

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).