% Mizar problem: t46_isomichi,isomichi,1081,52 
fof(t46_isomichi,conjecture,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( ~ v3_isomichi(B,A)
              & ~ v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_xboole_0,cc10_isomichi,cc1_isomichi,cc2_isomichi,cc3_isomichi,cc4_isomichi,cc5_isomichi,cc6_isomichi,cc7_isomichi,cc8_isomichi,cc9_isomichi,d6_isomichi,d7_isomichi,d8_isomichi,dt_k1_tops_1,dt_k1_zfmisc_1,dt_k6_pre_topc,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,fc2_tops_1,fc6_isomichi,fc6_tops_1,fc7_isomichi,irreflexivity_r2_xboole_0,rc1_tops_1,rc2_isomichi,rc2_tops_1,rc3_isomichi,reflexivity_r1_tarski,reflexivity_r3_xboole_0,symmetry_r3_xboole_0,t3_subset,t45_isomichi]),
    [file(isomichi,t46_isomichi)]).

fof(antisymmetry_r2_xboole_0,axiom,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
     => ~ r2_xboole_0(B,A) ) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(cc10_isomichi,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)
              & v4_tops_1(B,A) )
           => ( v4_pre_topc(B,A)
              & v5_tops_1(B,A) ) ) ) ) ),
    file(isomichi,cc10_isomichi),
    []).

fof(cc1_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
           => ( v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc1_isomichi),
    []).

fof(cc2_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v1_isomichi(B,A)
              & v2_isomichi(B,A) )
           => v4_tops_1(B,A) ) ) ) ),
    file(isomichi,cc2_isomichi),
    []).

fof(cc3_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
           => v1_decomp_1(B,A) ) ) ) ),
    file(isomichi,cc3_isomichi),
    []).

fof(cc4_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_decomp_1(B,A)
           => v2_isomichi(B,A) ) ) ) ),
    file(isomichi,cc4_isomichi),
    []).

fof(cc5_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
           => v3_pre_topc(B,A) ) ) ) ),
    file(isomichi,cc5_isomichi),
    []).

fof(cc6_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => v4_pre_topc(B,A) ) ) ) ),
    file(isomichi,cc6_isomichi),
    []).

fof(cc7_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
           => ( v3_pre_topc(B,A)
              & v4_tops_1(B,A)
              & v1_decomp_1(B,A)
              & v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc7_isomichi),
    []).

fof(cc8_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v4_tops_1(B,A) )
           => ( v3_pre_topc(B,A)
              & v6_tops_1(B,A) ) ) ) ) ),
    file(isomichi,cc8_isomichi),
    []).

fof(cc9_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => ( v4_pre_topc(B,A)
              & v4_tops_1(B,A)
              & v1_decomp_1(B,A)
              & v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc9_isomichi),
    []).

fof(d6_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_isomichi(B,A)
          <=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ),
    file(isomichi,d6_isomichi),
    []).

fof(d7_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_isomichi(B,A)
          <=> r2_xboole_0(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) ),
    file(isomichi,d7_isomichi),
    []).

fof(d8_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_isomichi(B,A)
          <=> ~ r3_xboole_0(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) ),
    file(isomichi,d8_isomichi),
    []).

fof(dt_k1_tops_1,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(tops_1,k1_tops_1),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_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_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(fc2_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k6_pre_topc(A,B),A) ) ),
    file(tops_1,fc2_tops_1),
    []).

fof(fc6_isomichi,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_pre_topc(k1_tops_1(A,k6_pre_topc(A,B)),A)
        & v6_tops_1(k1_tops_1(A,k6_pre_topc(A,B)),A) ) ) ),
    file(isomichi,fc6_isomichi),
    []).

fof(fc6_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_pre_topc(k1_tops_1(A,B),A) ) ),
    file(tops_1,fc6_tops_1),
    []).

fof(fc7_isomichi,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v4_pre_topc(k6_pre_topc(A,k1_tops_1(A,B)),A)
        & v5_tops_1(k6_pre_topc(A,k1_tops_1(A,B)),A) ) ) ),
    file(isomichi,fc7_isomichi),
    []).

fof(irreflexivity_r2_xboole_0,axiom,(
    ! [A,B] : ~ r2_xboole_0(A,A) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(rc1_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A) ) ) ),
    file(tops_1,rc1_tops_1),
    []).

fof(rc2_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_tops_1(B,A)
          & v1_isomichi(B,A)
          & v2_isomichi(B,A) ) ) ),
    file(isomichi,rc2_isomichi),
    []).

fof(rc2_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(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(B,A) ) ) ),
    file(tops_1,rc2_tops_1),
    []).

fof(rc3_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v5_tops_1(B,A)
          & v6_tops_1(B,A) ) ) ),
    file(isomichi,rc3_isomichi),
    []).

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

fof(reflexivity_r3_xboole_0,axiom,(
    ! [A,B] : r3_xboole_0(A,A) ),
    file(xboole_0,r3_xboole_0),
    []).

fof(symmetry_r3_xboole_0,axiom,(
    ! [A,B] : 
      ( r3_xboole_0(A,B)
     => r3_xboole_0(B,A) ) ),
    file(xboole_0,r3_xboole_0),
    []).

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

fof(t45_isomichi,axiom,(
    ! [A,B] : ~ ( r3_xboole_0(A,B)
      & ~ r1_tarski(A,B)
      & ~ r2_xboole_0(B,A) ) ),
    file(isomichi,t45_isomichi),
    []).