% Mizar problem: t18_conlat_2,conlat_2,2628,50 
fof(t18_conlat_2,conjecture,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
         => k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B) = k1_funct_1(k2_conlat_1(k7_conlat_2(A)),B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v4_conlat_1,antisymmetry_r2_hidden,cc1_funct_2,cc1_relset_1,cc5_funct_2,cc6_funct_2,commutativity_k2_tarski,d10_xboole_0,d3_tarski,d5_conlat_1,d5_tarski,d6_conlat_1,d7_conlat_1,d7_conlat_2,d7_relat_1,dt_g2_conlat_1,dt_k1_conlat_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_conlat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_relat_1,dt_k4_tarski,dt_k6_relset_1,dt_k7_conlat_2,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,dt_u3_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,fc2_subset_1,fc3_subset_1,fc4_subset_1,fraenkel_a_2_0_conlat_1,fraenkel_a_2_17_conlat_2,fraenkel_a_2_1_conlat_1,fraenkel_a_2_2_conlat_2,free_g2_conlat_1,involutiveness_k4_relat_1,involutiveness_k6_relset_1,rc1_funct_2,rc1_subset_1,rc1_xboole_0,rc2_partfun1,rc2_subset_1,rc2_xboole_0,rc5_conlat_1,rc7_conlat_1,rc8_conlat_1,rc9_conlat_1,redefinition_k1_domain_1,redefinition_k6_relset_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_2,t18_conlat_2)]).

fof(abstractness_v4_conlat_1,axiom,(
    ! [A] : 
      ( l2_conlat_1(A)
     => ( v4_conlat_1(A)
       => A = g2_conlat_1(u1_conlat_1(A),u2_conlat_1(A),u3_conlat_1(A)) ) ) ),
    file(conlat_1,v4_conlat_1),
    []).

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

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(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

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

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

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

fof(d5_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_conlat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_conlat_1(A))
             => ( r1_conlat_1(A,B,C)
              <=> r2_hidden(k4_tarski(B,C),u3_conlat_1(A)) ) ) ) ) ),
    file(conlat_1,d5_conlat_1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_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(d7_conlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => k7_conlat_2(A) = g2_conlat_1(u2_conlat_1(A),u1_conlat_1(A),k6_relset_1(u1_conlat_1(A),u2_conlat_1(A),u3_conlat_1(A))) ) ),
    file(conlat_2,d7_conlat_2),
    []).

fof(d7_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( B = k4_relat_1(A)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),B)
              <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ),
    file(relat_1,d7_relat_1),
    []).

fof(dt_g2_conlat_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( v4_conlat_1(g2_conlat_1(A,B,C))
        & l2_conlat_1(g2_conlat_1(A,B,C)) ) ) ),
    file(conlat_1,g2_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_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_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_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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k6_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m2_relset_1(k6_relset_1(A,B,C),B,A) ) ),
    file(relset_1,k6_relset_1),
    []).

fof(dt_k7_conlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ( ~ v3_conlat_1(k7_conlat_2(A))
        & v4_conlat_1(k7_conlat_2(A))
        & l2_conlat_1(k7_conlat_2(A)) ) ) ),
    file(conlat_2,k7_conlat_2),
    []).

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(dt_u3_conlat_1,axiom,(
    ! [A] : 
      ( l2_conlat_1(A)
     => m2_relset_1(u3_conlat_1(A),u1_conlat_1(A),u2_conlat_1(A)) ) ),
    file(conlat_1,u3_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(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_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(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_17_conlat_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_conlat_1(B)
        & l2_conlat_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(k7_conlat_2(B)))) )
     => ( r2_hidden(A,a_2_17_conlat_2(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,u1_conlat_1(k7_conlat_2(B)))
            & A = D
            & ! [E] : 
                ( m1_subset_1(E,u2_conlat_1(k7_conlat_2(B)))
               => ( r2_hidden(E,C)
                 => r1_conlat_1(k7_conlat_2(B),D,E) ) ) ) ) ) ),
    file(conlat_2,a_2_17_conlat_2),
    []).

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_2_conlat_2,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_2_conlat_2(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_2,a_2_2_conlat_2),
    []).

fof(free_g2_conlat_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ! [D,E,F] : 
          ( g2_conlat_1(A,B,C) = g2_conlat_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(conlat_1,g2_conlat_1),
    []).

fof(involutiveness_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) ),
    file(relat_1,k4_relat_1),
    []).

fof(involutiveness_k6_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k6_relset_1(A,B,k6_relset_1(A,B,C)) = C ) ),
    file(relset_1,k6_relset_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

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_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

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(rc5_conlat_1,axiom,(
    ? [A] : 
      ( l2_conlat_1(A)
      & v4_conlat_1(A) ) ),
    file(conlat_1,rc5_conlat_1),
    []).

fof(rc7_conlat_1,axiom,(
    ? [A] : 
      ( l2_conlat_1(A)
      & ~ v3_conlat_1(A)
      & v4_conlat_1(A) ) ),
    file(conlat_1,rc7_conlat_1),
    []).

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_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k6_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k6_relset_1(A,B,C) = k4_relat_1(C) ) ),
    file(relset_1,k6_relset_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),
    []).