% Mizar problem: t4_lattice7,lattice7,305,33 
fof(t4_lattice7,conjecture,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v5_orders_2(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_hidden(C,B)
                      & r2_hidden(D,B) )
                   => ( C = D
                    <=> k1_lattice7(A,C) = k1_lattice7(A,D) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_lattice3,cc1_membered,cc1_waybel11,cc1_yellow_0,cc20_membered,cc2_arytm_3,cc2_lattice3,cc2_membered,cc3_arytm_3,cc3_membered,cc3_waybel11,cc3_yellow_0,cc4_membered,cc4_yellow11,cc4_yellow_0,cc5_yellow11,cc5_yellow_0,cc6_membered,cc9_membered,connectedness_r1_xreal_0,d10_orders_2,dt_k1_lattice7,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_numbers,dt_k5_ordinal2,dt_l1_orders_2,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_subset_1,existence_m2_subset_1,fc1_struct_0,fc1_subset_1,fc1_yellow13,fc2_membered,fc5_membered,fc6_membered,irreflexivity_r2_orders_2,rc1_arytm_3,rc1_lattice7,rc1_membered,rc1_subset_1,rc1_yellow11,rc2_subset_1,rc2_yellow_0,rc3_orders_2,rc3_struct_0,rc5_struct_0,redefinition_k5_numbers,redefinition_m2_subset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r3_orders_2,t1_subset,t2_subset,t38_orders_2,t3_lattice7,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(lattice7,t4_lattice7)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_lattice3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_lattice3(A)
       => ~ v3_struct_0(A) ) ) ),
    file(lattice3,cc1_lattice3),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc1_waybel11,axiom,(
    ! [A] : 
      ( ( v6_group_1(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => v1_finset_1(B) ) ) ),
    file(waybel11,cc1_waybel11),
    []).

fof(cc1_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v3_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v1_lattice3(A)
          & v2_lattice3(A) ) ) ) ),
    file(yellow_0,cc1_yellow_0),
    []).

fof(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

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

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc3_waybel11,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_finset_1(B)
            & v1_waybel11(B,A) ) ) ) ),
    file(waybel11,cc3_waybel11),
    []).

fof(cc3_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v3_lattice3(A) )
       => ( ~ v3_struct_0(A)
          & v3_yellow_0(A) ) ) ) ),
    file(yellow_0,cc3_yellow_0),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc4_yellow11,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_lattice3(A)
          & v6_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v2_lattice3(A)
          & v1_yellow_0(A) ) ) ) ),
    file(yellow11,cc4_yellow11),
    []).

fof(cc4_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_yellow_0(A)
       => ( v1_yellow_0(A)
          & v2_yellow_0(A) ) ) ) ),
    file(yellow_0,cc4_yellow_0),
    []).

fof(cc5_yellow11,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v6_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A) ) ) ) ),
    file(yellow11,cc5_yellow11),
    []).

fof(cc5_yellow_0,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( v1_yellow_0(A)
          & v2_yellow_0(A) )
       => v3_yellow_0(A) ) ) ),
    file(yellow_0,cc5_yellow_0),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(cc9_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d10_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_orders_2(A,B,C)
              <=> ( r1_orders_2(A,B,C)
                  & B != C ) ) ) ) ) ),
    file(orders_2,d10_orders_2),
    []).

fof(dt_k1_lattice7,axiom,(
    ! [A,B] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v6_group_1(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m2_subset_1(k1_lattice7(A,B),k1_numbers,k5_numbers) ) ),
    file(lattice7,k1_lattice7),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_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(fc1_yellow13,axiom,(
    ! [A] : 
      ( ( v6_group_1(A)
        & l1_struct_0(A) )
     => v1_finset_1(u1_struct_0(A)) ) ),
    file(yellow13,fc1_yellow13),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc5_membered,axiom,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(irreflexivity_r2_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ~ r2_orders_2(A,B,B) ) ),
    file(orders_2,r2_orders_2),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_lattice7,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v5_orders_2(B,A) ) ) ),
    file(lattice7,rc1_lattice7),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

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_yellow11,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v6_group_1(A) ) ),
    file(yellow11,rc1_yellow11),
    []).

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_yellow_0,axiom,(
    ? [A] : 
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A) ) ),
    file(yellow_0,rc2_yellow_0),
    []).

fof(rc3_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v5_orders_2(B,A) ) ) ),
    file(orders_2,rc3_orders_2),
    []).

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_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_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_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

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(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(t38_orders_2,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ~ ( ? [D] : 
                        ( v5_orders_2(D,A)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                        & r2_hidden(B,D)
                        & r2_hidden(C,D) )
                    & ~ r1_orders_2(A,B,C)
                    & ~ r1_orders_2(A,C,B) )
                & ~ ( ( r1_orders_2(A,B,C)
                      | r1_orders_2(A,C,B) )
                    & ! [D] : 
                        ( ( v5_orders_2(D,A)
                          & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                       => ~ ( r2_hidden(B,D)
                            & r2_hidden(C,D) ) ) ) ) ) ) ) ),
    file(orders_2,t38_orders_2),
    []).

fof(t3_lattice7,axiom,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v6_group_1(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v5_orders_2(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_hidden(C,B)
                      & r2_hidden(D,B) )
                   => ( r2_orders_2(A,C,D)
                    <=> ~ r1_xreal_0(k1_lattice7(A,D),k1_lattice7(A,C)) ) ) ) ) ) ) ),
    file(lattice7,t3_lattice7),
    []).

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),
    []).