% Mizar problem: t12_yellow_1,yellow_1,507,29 
fof(t12_yellow_1,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ! [B,C] : 
            ( ( r2_hidden(B,A)
              & r2_hidden(C,A) )
           => r2_hidden(k3_xboole_0(B,C),A) )
       => v2_lattice3(k2_yellow_1(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc1_relset_1,cc2_lattice3,commutativity_k2_struct_0,commutativity_k2_tarski,commutativity_k3_xboole_0,d1_yellow_1,d2_tarski,d8_lattice3,dt_g1_orders_2,dt_k11_lattice3,dt_k1_wellord2,dt_k1_xboole_0,dt_k1_yellow_1,dt_k1_zfmisc_1,dt_k2_struct_0,dt_k2_tarski,dt_k2_yellow_1,dt_k2_zfmisc_1,dt_k3_xboole_0,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_orders_2,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_orders_2,fc3_orders_2,fc3_subset_1,fc4_subset_1,fc5_yellow_1,fc6_yellow_1,free_g1_orders_2,idempotence_k3_xboole_0,rc1_orders_2,rc1_subset_1,rc1_xboole_0,rc2_orders_2,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,redefinition_k1_yellow_1,redefinition_k2_struct_0,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,t16_yellow_0,t17_xboole_1,t19_xboole_1,t1_subset,t21_yellow_0,t2_boole,t2_subset,t3_subset,t3_yellow_1,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t8_yellow_0,t9_yellow_1]),
    [file(yellow_1,t12_yellow_1)]).

fof(abstractness_v1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_orders_2(A)
       => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ),
    file(orders_2,v1_orders_2),
    []).

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_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc2_lattice3),
    []).

fof(commutativity_k2_struct_0,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k2_struct_0(A,B,C) = k2_struct_0(A,C,B) ) ),
    file(struct_0,k2_struct_0),
    []).

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

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d1_yellow_1,axiom,(
    ! [A] : k2_yellow_1(A) = g1_orders_2(A,k1_yellow_1(A)) ),
    file(yellow_1,d1_yellow_1),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

fof(d8_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r1_lattice3(A,B,C)
          <=> ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_hidden(D,B)
                 => r1_orders_2(A,C,D) ) ) ) ) ) ),
    file(lattice3,d8_lattice3),
    []).

fof(dt_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ( v1_orders_2(g1_orders_2(A,B))
        & l1_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(dt_k11_lattice3,axiom,(
    ! [A,B,C] : 
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k11_lattice3(A,B,C),u1_struct_0(A)) ) ),
    file(lattice3,k11_lattice3),
    []).

fof(dt_k1_wellord2,axiom,(
    ! [A] : v1_relat_1(k1_wellord2(A)) ),
    file(wellord2,k1_wellord2),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_yellow_1,axiom,(
    ! [A] : 
      ( v1_relat_2(k1_yellow_1(A))
      & v4_relat_2(k1_yellow_1(A))
      & v8_relat_2(k1_yellow_1(A))
      & v1_partfun1(k1_yellow_1(A),A,A)
      & m2_relset_1(k1_yellow_1(A),A,A) ) ),
    file(yellow_1,k1_yellow_1),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_struct_0,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(struct_0,k2_struct_0),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_yellow_1,axiom,(
    ! [A] : 
      ( v1_orders_2(k2_yellow_1(A))
      & l1_orders_2(k2_yellow_1(A)) ) ),
    file(yellow_1,k2_yellow_1),
    []).

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

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

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_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(orders_2,u1_orders_2),
    []).

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

fof(existence_l1_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

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_orders_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,A) )
     => ( ~ v3_struct_0(g1_orders_2(A,B))
        & v1_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,fc1_orders_2),
    []).

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

fof(fc2_orders_2,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(u1_orders_2(A))
        & v1_relat_2(u1_orders_2(A))
        & v4_relat_2(u1_orders_2(A))
        & v8_relat_2(u1_orders_2(A))
        & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(orders_2,fc2_orders_2),
    []).

fof(fc3_orders_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m1_relset_1(B,A,A) )
     => ( v1_orders_2(g1_orders_2(A,B))
        & v2_orders_2(g1_orders_2(A,B))
        & v3_orders_2(g1_orders_2(A,B))
        & v4_orders_2(g1_orders_2(A,B)) ) ) ),
    file(orders_2,fc3_orders_2),
    []).

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(fc5_yellow_1,axiom,(
    ! [A] : 
      ( v1_orders_2(k2_yellow_1(A))
      & v2_orders_2(k2_yellow_1(A))
      & v3_orders_2(k2_yellow_1(A))
      & v4_orders_2(k2_yellow_1(A)) ) ),
    file(yellow_1,fc5_yellow_1),
    []).

fof(fc6_yellow_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v3_struct_0(k2_yellow_1(A))
        & v1_orders_2(k2_yellow_1(A))
        & v2_orders_2(k2_yellow_1(A))
        & v3_orders_2(k2_yellow_1(A))
        & v4_orders_2(k2_yellow_1(A)) ) ) ),
    file(yellow_1,fc6_yellow_1),
    []).

fof(free_g1_orders_2,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,A)
     => ! [C,D] : 
          ( g1_orders_2(A,B) = g1_orders_2(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(orders_2,g1_orders_2),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(rc1_orders_2,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & v1_orders_2(A) ) ),
    file(orders_2,rc1_orders_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_orders_2,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A) ) ),
    file(orders_2,rc2_orders_2),
    []).

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(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(redefinition_k1_yellow_1,axiom,(
    ! [A] : k1_yellow_1(A) = k1_wellord2(A) ),
    file(yellow_1,k1_yellow_1),
    []).

fof(redefinition_k2_struct_0,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k2_struct_0(A,B,C) = k2_tarski(B,C) ) ),
    file(struct_0,k2_struct_0),
    []).

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(redefinition_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_orders_2(A,B,C)
      <=> r1_orders_2(A,B,C) ) ) ),
    file(orders_2,r3_orders_2),
    []).

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

fof(reflexivity_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_orders_2(A,B,B) ) ),
    file(orders_2,r3_orders_2),
    []).

fof(t16_yellow_0,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( r2_yellow_0(A,B)
        <=> ? [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
              & r1_lattice3(A,B,C)
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_lattice3(A,B,D)
                   => r1_orders_2(A,D,C) ) ) ) ) ) ),
    file(yellow_0,t16_yellow_0),
    []).

fof(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    []).

fof(t19_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(A,k3_xboole_0(B,C)) ) ),
    file(xboole_1,t19_xboole_1),
    []).

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

fof(t21_yellow_0,axiom,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_lattice3(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ),
    file(yellow_0,t21_yellow_0),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t3_yellow_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
             => ( r3_orders_2(k2_yellow_1(A),B,C)
              <=> r1_tarski(B,C) ) ) ) ) ),
    file(yellow_1,t3_yellow_1),
    []).

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),
    []).

fof(t8_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_lattice3(A,k2_tarski(C,D),B)
                     => ( r1_orders_2(A,B,C)
                        & r1_orders_2(A,B,D) ) )
                    & ( ( r1_orders_2(A,B,C)
                        & r1_orders_2(A,B,D) )
                     => r1_lattice3(A,k2_tarski(C,D),B) )
                    & ( r2_lattice3(A,k2_tarski(C,D),B)
                     => ( r1_orders_2(A,C,B)
                        & r1_orders_2(A,D,B) ) )
                    & ( ( r1_orders_2(A,C,B)
                        & r1_orders_2(A,D,B) )
                     => r2_lattice3(A,k2_tarski(C,D),B) ) ) ) ) ) ) ),
    file(yellow_0,t8_yellow_0),
    []).

fof(t9_yellow_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
             => ( r2_hidden(k3_xboole_0(B,C),A)
               => k11_lattice3(k2_yellow_1(A),B,C) = k3_xboole_0(B,C) ) ) ) ) ),
    file(yellow_1,t9_yellow_1),
    []).