% Mizar problem: t14_waybel18,waybel18,1645,49 
fof(t14_waybel18,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m2_cantor_1(a_1_0_waybel18(A),k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc1_funct_1,cc1_monoid_0,cc1_relset_1,cc1_waybel18,cc2_funct_1,commutativity_k2_tarski,commutativity_k3_xboole_0,commutativity_k5_subset_1,d10_xboole_0,d13_pralg_1,d1_enumset1,d1_tarski,d2_funcop_1,d2_tarski,d2_waybel18,d3_pboole,d3_tarski,d3_waybel18,d3_xboole_0,d4_cantor_1,d4_xboole_0,d5_cantor_1,d5_card_3,d5_funct_1,d5_pre_topc,d9_waybel18,dt_g1_pre_topc,dt_k12_pralg_1,dt_k1_enumset1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cantor_1,dt_k2_funcop_1,dt_k2_funct_7,dt_k2_pre_circ,dt_k2_relat_1,dt_k2_tarski,dt_k2_waybel18,dt_k2_zfmisc_1,dt_k3_waybel18,dt_k3_xboole_0,dt_k4_card_3,dt_k4_waybel18,dt_k4_xboole_0,dt_k5_subset_1,dt_k8_setfam_1,dt_k9_waybel18,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_cantor_1,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_cantor_1,existence_m1_pboole,existence_m1_subset_1,existence_m2_cantor_1,fc1_funcop_1,fc1_struct_0,fc1_subset_1,fc1_waybel18,fc1_xboole_0,fc2_funcop_1,fc2_subset_1,fc2_waybel18,fc3_card_3,fc3_funcop_1,fc3_subset_1,fc4_subset_1,fc5_card_3,fc5_waybel18,fc6_funct_1,fc6_waybel18,fc7_waybel18,fc8_waybel18,fc9_funcop_1,fc9_waybel18,fraenkel_a_1_0_waybel18,free_g1_pre_topc,idempotence_k3_xboole_0,idempotence_k5_subset_1,rc1_funct_1,rc1_monoid_0,rc1_pre_topc,rc1_subset_1,rc1_waybel18,rc1_xboole_0,rc2_funct_1,rc2_pre_topc,rc2_subset_1,rc2_waybel18,rc2_xboole_0,rc3_funct_1,rc3_struct_0,rc5_funct_1,rc5_struct_0,redefinition_k2_pre_circ,redefinition_k4_waybel18,redefinition_k5_subset_1,reflexivity_r1_tarski,spc0_boole,spc1_boole,t12_zfmisc_1,t13_finset_1,t13_funcop_1,t17_xboole_1,t1_subset,t1_xboole_1,t23_yellow_9,t2_boole,t2_subset,t2_tarski,t32_funct_7,t33_funct_7,t34_funct_7,t37_card_3,t37_funct_7,t3_boole,t3_mssubfam,t3_subset,t3_waybel18,t4_boole,t4_subset,t58_setfam_1,t59_setfam_1,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(waybel18,t14_waybel18)]).

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_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_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_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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

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

fof(d13_pralg_1,axiom,(
    ! [A,B] : 
      ( ( v2_pralg_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k12_pralg_1(A,B)
          <=> ! [D] : ~ ( r2_hidden(D,A)
                & ! [E] : 
                    ( l1_struct_0(E)
                   => ~ ( E = k1_funct_1(B,D)
                        & k1_funct_1(C,D) = u1_struct_0(E) ) ) ) ) ) ) ),
    file(pralg_1,d13_pralg_1),
    []).

fof(d1_enumset1,axiom,(
    ! [A,B,C,D] : 
      ( D = k1_enumset1(A,B,C)
    <=> ! [E] : 
          ( r2_hidden(E,D)
        <=> ~ ( E != A
              & E != B
              & E != C ) ) ) ),
    file(enumset1,d1_enumset1),
    []).

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

fof(d2_funcop_1,axiom,(
    ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ),
    file(funcop_1,d2_funcop_1),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

fof(d2_waybel18,axiom,(
    ! [A,B] : 
      ( ( v1_waybel18(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B)))))
         => ( C = k2_waybel18(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))
               => ( r2_hidden(D,C)
                <=> ? [E,F] : 
                      ( l1_pre_topc(F)
                      & ? [G] : 
                          ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(F)))
                          & r2_hidden(E,A)
                          & v3_pre_topc(G,F)
                          & F = k1_funct_1(B,E)
                          & D = k4_card_3(k2_funct_7(k12_pralg_1(A,B),E,G)) ) ) ) ) ) ) ) ),
    file(waybel18,d2_waybel18),
    []).

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(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_cantor_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k2_cantor_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A)))
                      & r1_tarski(E,B)
                      & v1_finset_1(E)
                      & D = k8_setfam_1(A,E) ) ) ) ) ) ) ),
    file(cantor_1,d4_cantor_1),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_cantor_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( m2_cantor_1(B,A)
          <=> ( r1_tarski(B,u1_pre_topc(A))
              & ? [C] : 
                  ( m1_cantor_1(C,A)
                  & r1_tarski(C,k2_cantor_1(u1_struct_0(A),B)) ) ) ) ) ) ),
    file(cantor_1,d5_cantor_1),
    []).

fof(d5_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    []).

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(d5_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> r2_hidden(B,u1_pre_topc(A)) ) ) ) ),
    file(pre_topc,d5_pre_topc),
    []).

fof(d9_waybel18,axiom,(
    ! [A] : 
      ( ( v1_pre_topc(A)
        & l1_pre_topc(A) )
     => ( A = k9_waybel18
      <=> ( u1_struct_0(A) = k2_tarski(0,1)
          & u1_pre_topc(A) = k1_enumset1(k1_xboole_0,k1_tarski(1),k2_tarski(0,1)) ) ) ) ),
    file(waybel18,d9_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_enumset1,axiom,(
    $true ),
    file(enumset1,k1_enumset1),
    []).

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_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_cantor_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k2_cantor_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ),
    file(cantor_1,k2_cantor_1),
    []).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    []).

fof(dt_k2_funct_7,axiom,(
    ! [A,B,C] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_7(A,B,C))
        & v1_funct_1(k2_funct_7(A,B,C)) ) ) ),
    file(funct_7,k2_funct_7),
    []).

fof(dt_k2_pre_circ,axiom,(
    ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ),
    file(pre_circ,k2_pre_circ),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_k8_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k8_setfam_1),
    []).

fof(dt_k9_waybel18,axiom,
    ( v1_pre_topc(k9_waybel18)
    & l1_pre_topc(k9_waybel18) ),
    file(waybel18,k9_waybel18),
    []).

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_cantor_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_cantor_1(B,A)
         => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ),
    file(cantor_1,m1_cantor_1),
    []).

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_cantor_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : m1_cantor_1(B,A) ) ),
    file(cantor_1,m1_cantor_1),
    []).

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(fc1_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

fof(fc2_funcop_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

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_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_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

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(fc5_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k4_card_3(A))
        & v1_fraenkel(k4_card_3(A)) ) ) ),
    file(card_3,fc5_card_3),
    []).

fof(fc5_waybel18,axiom,
    ( ~ v3_struct_0(k9_waybel18)
    & v1_pre_topc(k9_waybel18)
    & v2_pre_topc(k9_waybel18) ),
    file(waybel18,fc5_waybel18),
    []).

fof(fc6_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => v1_setfam_1(k2_relat_1(A)) ) ),
    file(funct_1,fc6_funct_1),
    []).

fof(fc6_waybel18,axiom,
    ( ~ v3_struct_0(k9_waybel18)
    & v1_pre_topc(k9_waybel18)
    & v2_pre_topc(k9_waybel18)
    & v2_t_0topsp(k9_waybel18) ),
    file(waybel18,fc6_waybel18),
    []).

fof(fc7_waybel18,axiom,
    ( ~ v3_struct_0(k9_waybel18)
    & v1_pre_topc(k9_waybel18)
    & v2_pre_topc(k9_waybel18)
    & v2_t_0topsp(k9_waybel18)
    & v2_waybel18(k9_waybel18) ),
    file(waybel18,fc7_waybel18),
    []).

fof(fc8_waybel18,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_struct_0(B) )
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v4_waybel_3(k2_funcop_1(A,B)) ) ) ),
    file(waybel18,fc8_waybel18),
    []).

fof(fc9_funcop_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    []).

fof(fc9_waybel18,axiom,(
    ! [A,B] : 
      ( l1_pre_topc(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v2_pralg_1(k2_funcop_1(A,B))
        & v1_waybel18(k2_funcop_1(A,B)) ) ) ),
    file(waybel18,fc9_waybel18),
    []).

fof(fraenkel_a_1_0_waybel18,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( r2_hidden(A,a_1_0_waybel18(B))
      <=> ? [C] : 
            ( m1_subset_1(C,B)
            & A = k4_card_3(k2_funct_7(k12_pralg_1(B,k2_pre_circ(B,k9_waybel18)),C,k1_tarski(1))) ) ) ) ),
    file(waybel18,a_1_0_waybel18),
    []).

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(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

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

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

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_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_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_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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(redefinition_k2_pre_circ,axiom,(
    ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ),
    file(pre_circ,k2_pre_circ),
    []).

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_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

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

fof(t12_zfmisc_1,axiom,(
    ! [A,B] : r1_tarski(k1_tarski(A),k2_tarski(A,B)) ),
    file(zfmisc_1,t12_zfmisc_1),
    []).

fof(t13_finset_1,axiom,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    []).

fof(t13_funcop_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    []).

fof(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    []).

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t23_yellow_9,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( m2_cantor_1(B,A)
          <=> m1_cantor_1(k2_cantor_1(u1_struct_0(A),B),A) ) ) ) ),
    file(yellow_9,t23_yellow_9),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t32_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_relat_1(k2_funct_7(A,C,B)) = k1_relat_1(A) ) ),
    file(funct_7,t32_funct_7),
    []).

fof(t33_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( r2_hidden(C,k1_relat_1(A))
         => k1_funct_1(k2_funct_7(A,C,B),C) = B ) ) ),
    file(funct_7,t33_funct_7),
    []).

fof(t34_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D] : 
          ( C != D
         => k1_funct_1(k2_funct_7(A,C,B),D) = k1_funct_1(A,D) ) ) ),
    file(funct_7,t34_funct_7),
    []).

fof(t37_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k4_card_3(A) = k1_xboole_0
      <=> r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ),
    file(card_3,t37_card_3),
    []).

fof(t37_funct_7,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : k2_funct_7(A,B,k1_funct_1(A,B)) = A ) ),
    file(funct_7,t37_funct_7),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

fof(t3_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( r2_hidden(k1_xboole_0,B)
       => k8_setfam_1(A,B) = k1_xboole_0 ) ) ),
    file(mssubfam,t3_mssubfam),
    []).

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

fof(t3_waybel18,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( m1_cantor_1(B,A)
          <=> m1_cantor_1(k4_xboole_0(B,k1_tarski(k1_xboole_0)),A) ) ) ) ),
    file(waybel18,t3_waybel18),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t58_setfam_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( r2_hidden(B,A)
       => ( r2_hidden(B,k8_setfam_1(A,C))
        <=> ! [D] : 
              ( r2_hidden(D,C)
             => r2_hidden(B,D) ) ) ) ) ),
    file(setfam_1,t58_setfam_1),
    []).

fof(t59_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( r1_tarski(B,C)
           => r1_tarski(k8_setfam_1(A,C),k8_setfam_1(A,B)) ) ) ) ),
    file(setfam_1,t59_setfam_1),
    []).

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),
    []).