% Mizar problem: t25_fin_topo,fin_topo,958,25 
fof(t25_fin_topo,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_fin_topo(A,k3_subset_1(u1_struct_0(A),B)) = k4_fin_topo(A,B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_1,cc1_relset_1,d1_fin_topo,d6_fin_topo,dt_k1_fin_topo,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_subset_1,dt_k4_fin_topo,dt_k8_funct_2,dt_l1_fin_topo,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_fin_topo,dt_u1_struct_0,existence_l1_fin_topo,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_struct_0,fc1_subset_1,fc2_finseq_1,fc4_subset_1,fraenkel_a_2_0_fin_topo,involutiveness_k3_subset_1,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_struct_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,symmetry_r1_xboole_0,t10_fin_topo,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(fin_topo,t25_fin_topo)]).

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_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(d1_fin_topo,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_fin_topo(A,B) = k8_funct_2(u1_struct_0(A),k1_zfmisc_1(u1_struct_0(A)),u1_fin_topo(A),B) ) ) ),
    file(fin_topo,d1_fin_topo),
    []).

fof(d6_fin_topo,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_fin_topo(A,B) = a_2_0_fin_topo(A,B) ) ) ),
    file(fin_topo,d6_fin_topo),
    []).

fof(dt_k1_fin_topo,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k1_fin_topo(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(fin_topo,k1_fin_topo),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_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_k4_fin_topo,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_fin_topo(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(fin_topo,k4_fin_topo),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_l1_fin_topo,axiom,(
    ! [A] : 
      ( l1_fin_topo(A)
     => l1_struct_0(A) ) ),
    file(fin_topo,l1_fin_topo),
    []).

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

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_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_u1_fin_topo,axiom,(
    ! [A] : 
      ( l1_fin_topo(A)
     => ( v1_funct_1(u1_fin_topo(A))
        & v1_funct_2(u1_fin_topo(A),u1_struct_0(A),k1_zfmisc_1(u1_struct_0(A)))
        & m2_relset_1(u1_fin_topo(A),u1_struct_0(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(fin_topo,u1_fin_topo),
    []).

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

fof(existence_l1_fin_topo,axiom,(
    ? [A] : l1_fin_topo(A) ),
    file(fin_topo,l1_fin_topo),
    []).

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

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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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(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(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(fraenkel_a_2_0_fin_topo,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & l1_fin_topo(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_fin_topo(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_struct_0(B))
            & A = D
            & ~ r1_xboole_0(k1_fin_topo(B,D),C)
            & ~ r1_xboole_0(k1_fin_topo(B,D),k3_subset_1(u1_struct_0(B),C)) ) ) ) ),
    file(fin_topo,a_2_0_fin_topo),
    []).

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

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(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(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_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

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(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_fin_topo,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_fin_topo(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r2_hidden(B,k4_fin_topo(A,C))
              <=> ( ~ r1_xboole_0(k1_fin_topo(A,B),C)
                  & ~ r1_xboole_0(k1_fin_topo(A,B),k3_subset_1(u1_struct_0(A),C)) ) ) ) ) ) ),
    file(fin_topo,t10_fin_topo),
    []).

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

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

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_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),
    []).