% Mizar problem: t8_conlat_1,conlat_1,798,69 
fof(t8_conlat_1,conjecture,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
         => k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B) = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relset_1,d3_tarski,d6_conlat_1,d7_conlat_1,dt_k1_conlat_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_conlat_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_conlat_1,dt_l2_conlat_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_conlat_1,dt_u2_conlat_1,existence_l1_conlat_1,existence_l2_conlat_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_conlat_1,fc1_subset_1,fc1_xboole_0,fc2_conlat_1,fc4_subset_1,fraenkel_a_2_0_conlat_1,fraenkel_a_2_1_conlat_1,fraenkel_a_2_6_conlat_1,fraenkel_a_2_7_conlat_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc8_conlat_1,rc9_conlat_1,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(conlat_1,t8_conlat_1)]).

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

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

fof(d6_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)))
            & m2_relset_1(B,k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A))) )
         => ( B = k1_conlat_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A)))
               => k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),B,C) = a_2_0_conlat_1(A,C) ) ) ) ) ),
    file(conlat_1,d6_conlat_1),
    []).

fof(d7_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)))
            & m2_relset_1(B,k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A))) )
         => ( B = k2_conlat_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A)))
               => k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),B,C) = a_2_1_conlat_1(A,C) ) ) ) ) ),
    file(conlat_1,d7_conlat_1),
    []).

fof(dt_k1_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( v1_funct_1(k1_conlat_1(A))
        & v1_funct_2(k1_conlat_1(A),k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)))
        & m2_relset_1(k1_conlat_1(A),k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A))) ) ) ),
    file(conlat_1,k1_conlat_1),
    []).

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_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( v1_funct_1(k2_conlat_1(A))
        & v1_funct_2(k2_conlat_1(A),k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)))
        & m2_relset_1(k2_conlat_1(A),k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A))) ) ) ),
    file(conlat_1,k2_conlat_1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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_conlat_1,axiom,(
    $true ),
    file(conlat_1,l1_conlat_1),
    []).

fof(dt_l2_conlat_1,axiom,(
    ! [A] : 
      ( l2_conlat_1(A)
     => l1_conlat_1(A) ) ),
    file(conlat_1,l2_conlat_1),
    []).

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_conlat_1,axiom,(
    $true ),
    file(conlat_1,u1_conlat_1),
    []).

fof(dt_u2_conlat_1,axiom,(
    $true ),
    file(conlat_1,u2_conlat_1),
    []).

fof(existence_l1_conlat_1,axiom,(
    ? [A] : l1_conlat_1(A) ),
    file(conlat_1,l1_conlat_1),
    []).

fof(existence_l2_conlat_1,axiom,(
    ? [A] : l2_conlat_1(A) ),
    file(conlat_1,l2_conlat_1),
    []).

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_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ~ v1_xboole_0(u2_conlat_1(A)) ) ),
    file(conlat_1,fc1_conlat_1),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

fof(fc2_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ~ v1_xboole_0(u1_conlat_1(A)) ) ),
    file(conlat_1,fc2_conlat_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_conlat_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(B))) )
     => ( r2_hidden(A,a_2_0_conlat_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u2_conlat_1(B))
            & A = D
            & ! [E] : 
                ( m1_subset_1(E,u1_conlat_1(B))
               => ( r2_hidden(E,C)
                 => r1_conlat_1(B,E,D) ) ) ) ) ) ),
    file(conlat_1,a_2_0_conlat_1),
    []).

fof(fraenkel_a_2_1_conlat_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(B))) )
     => ( r2_hidden(A,a_2_1_conlat_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_conlat_1(B))
            & A = D
            & ! [E] : 
                ( m1_subset_1(E,u2_conlat_1(B))
               => ( r2_hidden(E,C)
                 => r1_conlat_1(B,D,E) ) ) ) ) ) ),
    file(conlat_1,a_2_1_conlat_1),
    []).

fof(fraenkel_a_2_6_conlat_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(B))) )
     => ( r2_hidden(A,a_2_6_conlat_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u2_conlat_1(B))
            & A = D
            & ! [E] : 
                ( m1_subset_1(E,u1_conlat_1(B))
               => ( r2_hidden(E,a_2_1_conlat_1(B,C))
                 => r1_conlat_1(B,E,D) ) ) ) ) ) ),
    file(conlat_1,a_2_6_conlat_1),
    []).

fof(fraenkel_a_2_7_conlat_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(B))) )
     => ( r2_hidden(A,a_2_7_conlat_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_conlat_1(B))
            & A = D
            & ! [E] : 
                ( m1_subset_1(E,u2_conlat_1(B))
               => ( r2_hidden(E,a_2_6_conlat_1(B,C))
                 => r1_conlat_1(B,D,E) ) ) ) ) ) ),
    file(conlat_1,a_2_7_conlat_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(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

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

fof(rc8_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(conlat_1,rc8_conlat_1),
    []).

fof(rc9_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(conlat_1,rc9_conlat_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(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),
    []).