% Mizar problem: t48_waybel12,waybel12,1925,17 
fof(t48_waybel12,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ( v3_yellow_8(A)
          & v6_waybel_3(A) )
       => v1_yellow_8(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_finset_1,cc1_finsub_1,cc1_waybel12,cc1_yellow_8,cc2_finset_1,cc2_finsub_1,cc2_waybel12,cc4_yellow_8,commutativity_k1_finsub_1,commutativity_k2_xboole_0,commutativity_k3_finsub_1,commutativity_k3_xboole_0,commutativity_k5_subset_1,d10_setfam_1,d1_tops_2,d1_xboole_0,d2_waybel12,d3_pre_topc,d3_xboole_0,d4_yellow_8,d6_waybel12,d6_yellow_8,d7_xboole_0,dt_k1_finsub_1,dt_k1_setfam_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k2_xboole_0,dt_k3_finsub_1,dt_k3_subset_1,dt_k3_xboole_0,dt_k5_subset_1,dt_k6_pre_topc,dt_k6_setfam_1,dt_k8_setfam_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,fc10_finset_1,fc11_finset_1,fc1_finset_1,fc1_finsub_1,fc1_struct_0,fc1_waybel12,fc2_finseq_1,fc9_finset_1,idempotence_k1_finsub_1,idempotence_k2_xboole_0,idempotence_k3_finsub_1,idempotence_k3_xboole_0,idempotence_k5_subset_1,involutiveness_k3_subset_1,rc1_finseq_1,rc1_finset_1,rc1_waybel12,rc1_yellow_8,rc2_waybel12,rc2_waybel_7,rc2_yellow_8,rc3_finseq_1,rc3_finset_1,rc3_struct_0,rc3_waybel12,rc3_waybel_7,rc4_finset_1,rc4_waybel12,rc5_struct_0,rc6_finseq_1,rc6_waybel12,rc7_finseq_1,rc7_waybel12,rc8_finseq_1,redefinition_k1_finsub_1,redefinition_k1_struct_0,redefinition_k3_finsub_1,redefinition_k5_subset_1,redefinition_k6_setfam_1,reflexivity_r1_tarski,symmetry_r1_xboole_0,t10_yellow_6,t16_tops_3,t16_xboole_1,t1_boole,t1_subset,t25_yellow_8,t2_boole,t2_subset,t30_tops_1,t37_zfmisc_1,t38_tops_1,t3_subset,t43_subset_1,t47_waybel12,t49_pre_topc,t4_subset,t52_pre_topc,t58_setfam_1,t5_subset,t6_boole,t7_boole,t80_tops_1,t8_boole]),
    [file(waybel12,t48_waybel12)]).

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

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_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_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_yellow_8,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_yellow_8(B,A)
           => ~ v1_xboole_0(B) ) ) ) ),
    file(yellow_8,cc1_yellow_8),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    []).

fof(cc2_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

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

fof(cc4_yellow_8,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_yellow_8(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A) ) ) ) ),
    file(yellow_8,cc4_yellow_8),
    []).

fof(commutativity_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,C) = k1_finsub_1(A,C,B) ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k3_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k3_finsub_1(A,B,C) = k3_finsub_1(A,C,B) ) ),
    file(finsub_1,k3_finsub_1),
    []).

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_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( B != k1_xboole_0
         => k8_setfam_1(A,B) = k6_setfam_1(A,B) )
        & ( B = k1_xboole_0
         => k8_setfam_1(A,B) = A ) ) ) ),
    file(setfam_1,d10_setfam_1),
    []).

fof(d1_tops_2,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_tops_2(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v3_pre_topc(C,A) ) ) ) ) ) ),
    file(tops_2,d1_tops_2),
    []).

fof(d1_xboole_0,axiom,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    []).

fof(d2_waybel12,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( v1_waybel12(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v1_tops_1(C,A) ) ) ) ) ) ),
    file(waybel12,d2_waybel12),
    []).

fof(d3_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => k2_pre_topc(A) = u1_struct_0(A) ) ),
    file(pre_topc,d3_pre_topc),
    []).

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_yellow_8,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_yellow_8(B,A)
          <=> ( ~ v1_xboole_0(B)
              & v4_pre_topc(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v4_pre_topc(C,A)
                          & v4_pre_topc(D,A)
                          & B = k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),C,D)
                          & C != B
                          & D != B ) ) ) ) ) ) ) ),
    file(yellow_8,d4_yellow_8),
    []).

fof(d6_waybel12,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v1_yellow_8(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
           => ~ ( v1_card_4(B)
                & ! [C] : 
                    ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                   => ( r2_hidden(C,B)
                     => ( v3_pre_topc(C,A)
                        & v1_tops_1(C,A) ) ) )
                & ! [C] : 
                    ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                   => ~ ( C = k8_setfam_1(u1_struct_0(A),B)
                        & v1_tops_1(C,A) ) ) ) ) ) ) ),
    file(waybel12,d6_waybel12),
    []).

fof(d6_yellow_8,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v3_yellow_8(A)
      <=> ! [B] : 
            ( ( v2_yellow_8(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & r1_yellow_8(A,B,C)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_yellow_8(A,B,D)
                     => C = D ) ) ) ) ) ) ),
    file(yellow_8,d6_yellow_8),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

fof(dt_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k1_finsub_1(A,B,C),A) ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_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_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k3_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k3_finsub_1(A,B,C),A) ) ),
    file(finsub_1,k3_finsub_1),
    []).

fof(dt_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ),
    file(subset_1,k3_subset_1),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_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_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_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_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_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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

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_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc1_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    []).

fof(fc1_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_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_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(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(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

fof(idempotence_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,B) = B ) ),
    file(finsub_1,k1_finsub_1),
    []).

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

fof(idempotence_k3_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k3_finsub_1(A,B,B) = B ) ),
    file(finsub_1,k3_finsub_1),
    []).

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(involutiveness_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,k3_subset_1(A,B)) = B ) ),
    file(subset_1,k3_subset_1),
    []).

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_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

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

fof(rc1_yellow_8,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)
          & v2_yellow_8(B,A) ) ) ),
    file(yellow_8,rc1_yellow_8),
    []).

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

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(rc2_yellow_8,axiom,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v3_yellow_8(A) ) ),
    file(yellow_8,rc2_yellow_8),
    []).

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_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_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(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

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

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_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_waybel12,axiom,(
    ? [A] : 
      ( ~ v1_finset_1(A)
      & v1_card_4(A) ) ),
    file(waybel12,rc6_waybel12),
    []).

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_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(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_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(finsub_1,k1_finsub_1),
    []).

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_k3_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k3_finsub_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(finsub_1,k3_finsub_1),
    []).

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(redefinition_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_1),
    []).

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

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(t10_yellow_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ~ r2_hidden(C,B)
              <=> r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) ) ) ) ) ),
    file(yellow_6,t10_yellow_6),
    []).

fof(t16_tops_3,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v1_tops_1(k2_pre_topc(A),A) ) ),
    file(tops_3,t16_tops_3),
    []).

fof(t16_xboole_1,axiom,(
    ! [A,B,C] : k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C)) ),
    file(xboole_1,t16_xboole_1),
    []).

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

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

fof(t25_yellow_8,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)))
         => ( v4_pre_topc(B,A)
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r1_yellow_8(A,B,C)
                 => B = k6_pre_topc(A,k1_struct_0(A,C)) ) ) ) ) ) ),
    file(yellow_8,t25_yellow_8),
    []).

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(t30_tops_1,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_pre_topc(B,A)
          <=> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ),
    file(tops_1,t30_tops_1),
    []).

fof(t37_zfmisc_1,axiom,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    []).

fof(t38_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v3_pre_topc(B,A)
                  & v3_pre_topc(C,A) )
               => v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ),
    file(tops_1,t38_tops_1),
    []).

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

fof(t43_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_xboole_0(B,C)
          <=> r1_tarski(B,k3_subset_1(A,C)) ) ) ) ),
    file(subset_1,t43_subset_1),
    []).

fof(t47_waybel12,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( v6_waybel_3(A)
       => ! [B] : 
            ( ( v1_card_4(B)
              & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
           => ( ( v1_waybel12(B,A)
                & v1_tops_2(B,A) )
             => ( v1_xboole_0(B)
                | ! [C] : 
                    ( ( ~ v1_xboole_0(C)
                      & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
                   => ~ ( v3_pre_topc(C,A)
                        & ! [D] : 
                            ( ( v2_yellow_8(D,A)
                              & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                           => ? [E] : 
                                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                                & r2_hidden(E,B)
                                & r1_xboole_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),D,C),E) ) ) ) ) ) ) ) ) ) ),
    file(waybel12,t47_waybel12),
    []).

fof(t49_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => r1_tarski(k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ) ),
    file(pre_topc,t49_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(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(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(t80_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_tops_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( C != k1_xboole_0
                    & v3_pre_topc(C,A)
                    & r1_xboole_0(B,C) ) ) ) ) ) ),
    file(tops_1,t80_tops_1),
    []).

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