% Mizar problem: t20_conlat_2,conlat_2,2778,50 
fof(t20_conlat_2,conjecture,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & v4_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] : 
          ( ( v6_conlat_1(B,A)
            & ~ v7_conlat_1(B,A)
            & v9_conlat_1(B,A)
            & l3_conlat_1(B,A) )
         => k9_conlat_2(k7_conlat_2(A),k9_conlat_2(A,B)) = B ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v4_conlat_1,abstractness_v6_conlat_1,antisymmetry_r2_hidden,cc1_relset_1,cc2_conlat_1,d7_conlat_2,d8_conlat_2,dt_g2_conlat_1,dt_g3_conlat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k4_relat_1,dt_k6_relset_1,dt_k7_conlat_2,dt_k8_conlat_2,dt_k9_conlat_2,dt_l1_conlat_1,dt_l2_conlat_1,dt_l3_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,dt_u4_conlat_1,dt_u5_conlat_1,existence_l1_conlat_1,existence_l2_conlat_1,existence_l3_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,free_g2_conlat_1,free_g3_conlat_1,involutiveness_k4_relat_1,involutiveness_k6_relset_1,rc10_conlat_1,rc11_conlat_1,rc12_conlat_1,rc13_conlat_1,rc14_conlat_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc5_conlat_1,rc7_conlat_1,rc8_conlat_1,rc9_conlat_1,redefinition_k6_relset_1,redefinition_k9_conlat_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(conlat_2,t20_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(abstractness_v6_conlat_1,axiom,(
    ! [A,B] : 
      ( ( l1_conlat_1(A)
        & l3_conlat_1(B,A) )
     => ( v6_conlat_1(B,A)
       => B = g3_conlat_1(A,u4_conlat_1(A,B),u5_conlat_1(A,B)) ) ) ),
    file(conlat_1,v6_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(cc2_conlat_1,axiom,(
    ! [A] : 
      ( ( v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ! [B] : 
          ( l3_conlat_1(B,A)
         => v8_conlat_1(B,A) ) ) ),
    file(conlat_1,cc2_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(d8_conlat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ! [B] : 
          ( l3_conlat_1(B,A)
         => ! [C] : 
              ( ( v6_conlat_1(C,k7_conlat_2(A))
                & l3_conlat_1(C,k7_conlat_2(A)) )
             => ( C = k8_conlat_2(A,B)
              <=> ( u4_conlat_1(k7_conlat_2(A),C) = u5_conlat_1(A,B)
                  & u5_conlat_1(k7_conlat_2(A),C) = u4_conlat_1(A,B) ) ) ) ) ) ),
    file(conlat_2,d8_conlat_2),
    []).

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_g3_conlat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_conlat_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
        & m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) )
     => ( v6_conlat_1(g3_conlat_1(A,B,C),A)
        & l3_conlat_1(g3_conlat_1(A,B,C),A) ) ) ),
    file(conlat_1,g3_conlat_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_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    []).

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_conlat_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & l3_conlat_1(B,A) )
     => ( v6_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A))
        & l3_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) ) ) ),
    file(conlat_2,k8_conlat_2),
    []).

fof(dt_k9_conlat_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & ~ v7_conlat_1(B,A)
        & v9_conlat_1(B,A)
        & l3_conlat_1(B,A) )
     => ( v6_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
        & ~ v7_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
        & v9_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
        & l3_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A)) ) ) ),
    file(conlat_2,k9_conlat_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_l3_conlat_1,axiom,(
    $true ),
    file(conlat_1,l3_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(dt_u4_conlat_1,axiom,(
    ! [A,B] : 
      ( ( l1_conlat_1(A)
        & l3_conlat_1(B,A) )
     => m1_subset_1(u4_conlat_1(A,B),k1_zfmisc_1(u1_conlat_1(A))) ) ),
    file(conlat_1,u4_conlat_1),
    []).

fof(dt_u5_conlat_1,axiom,(
    ! [A,B] : 
      ( ( l1_conlat_1(A)
        & l3_conlat_1(B,A) )
     => m1_subset_1(u5_conlat_1(A,B),k1_zfmisc_1(u2_conlat_1(A))) ) ),
    file(conlat_1,u5_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_l3_conlat_1,axiom,(
    ! [A] : 
      ( l1_conlat_1(A)
     => ? [B] : l3_conlat_1(B,A) ) ),
    file(conlat_1,l3_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(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(free_g3_conlat_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_conlat_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A)))
        & m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) )
     => ! [D,E,F] : 
          ( g3_conlat_1(A,B,C) = g3_conlat_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(conlat_1,g3_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(rc10_conlat_1,axiom,(
    ! [A] : 
      ( l1_conlat_1(A)
     => ? [B] : 
          ( l3_conlat_1(B,A)
          & v6_conlat_1(B,A) ) ) ),
    file(conlat_1,rc10_conlat_1),
    []).

fof(rc11_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ? [B] : 
          ( l3_conlat_1(B,A)
          & v6_conlat_1(B,A)
          & ~ v7_conlat_1(B,A) ) ) ),
    file(conlat_1,rc11_conlat_1),
    []).

fof(rc12_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l1_conlat_1(A) )
     => ? [B] : 
          ( l3_conlat_1(B,A)
          & v6_conlat_1(B,A)
          & v8_conlat_1(B,A) ) ) ),
    file(conlat_1,rc12_conlat_1),
    []).

fof(rc13_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ? [B] : 
          ( l3_conlat_1(B,A)
          & ~ v7_conlat_1(B,A)
          & v9_conlat_1(B,A) ) ) ),
    file(conlat_1,rc13_conlat_1),
    []).

fof(rc14_conlat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A) )
     => ? [B] : 
          ( l3_conlat_1(B,A)
          & v6_conlat_1(B,A)
          & ~ v7_conlat_1(B,A)
          & v9_conlat_1(B,A) ) ) ),
    file(conlat_1,rc14_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(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_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_k9_conlat_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_conlat_1(A)
        & l2_conlat_1(A)
        & ~ v7_conlat_1(B,A)
        & v9_conlat_1(B,A)
        & l3_conlat_1(B,A) )
     => k9_conlat_2(A,B) = k8_conlat_2(A,B) ) ),
    file(conlat_2,k9_conlat_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(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),
    []).