% Mizar problem: t30_robbins3,robbins3,1676,23 
fof(t30_robbins3,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_robbins1(A) )
     => ( ( v17_lattices(A)
          & v7_robbins1(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v9_robbins1(A)
          & v8_robbins3(A)
          & v9_robbins3(A)
          & l3_robbins1(A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_2,cc1_lattices,cc1_relset_1,cc1_robbins1,cc1_robbins3,cc1_sheffer1,cc2_lattices,cc2_robbins1,cc2_sheffer1,cc3_lattices,cc4_lattices,cc4_robbins1,cc5_funct_2,cc5_lattices,cc5_robbins1,cc6_funct_2,cc6_lattices,cc6_robbins1,cc7_lattices,cc7_robbins1,cc8_robbins1,cc9_robbins1,commutativity_k3_lattices,commutativity_k4_lattices,commutativity_k5_robbins1,commutativity_k5_robbins3,d1_lattices,d23_robbins1,d2_lattices,d6_robbins3,d7_robbins3,dt_k1_binop_1,dt_k1_lattices,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_lattices,dt_k2_zfmisc_1,dt_k3_lattices,dt_k3_robbins1,dt_k4_lattices,dt_k5_robbins1,dt_k5_robbins3,dt_l1_lattices,dt_l1_robbins1,dt_l1_struct_0,dt_l2_lattices,dt_l2_robbins1,dt_l3_lattices,dt_l3_robbins1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_lattices,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_robbins1,existence_l1_struct_0,existence_l2_lattices,existence_l2_robbins1,existence_l3_lattices,existence_l3_robbins1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_struct_0,rc11_robbins3,rc1_funct_2,rc1_sheffer1,rc2_partfun1,rc3_struct_0,rc5_struct_0,redefinition_k2_binop_1,redefinition_k3_lattices,redefinition_k4_lattices,redefinition_k5_robbins1,redefinition_k5_robbins3,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t34_robbins1,t3_robbins1,t3_subset,t4_robbins1,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(robbins3,t30_robbins3)]).

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_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) ) ) ) ),
    file(lattices,cc1_lattices),
    []).

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(cc1_robbins1,axiom,(
    ! [A] : 
      ( l2_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v5_robbins1(A)
          & v6_robbins1(A) )
       => ( ~ v3_struct_0(A)
          & v14_lattices(A) ) ) ) ),
    file(robbins1,cc1_robbins1),
    []).

fof(cc1_robbins3,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v1_robbins3(A)
          & v2_robbins3(A) ) ) ) ),
    file(robbins3,cc1_robbins3),
    []).

fof(cc1_sheffer1,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v6_lattices(A)
          & v11_lattices(A)
          & v1_sheffer1(A)
          & v2_sheffer1(A)
          & v3_sheffer1(A)
          & v4_sheffer1(A) ) ) ) ),
    file(sheffer1,cc1_sheffer1),
    []).

fof(cc2_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v10_lattices(A) ) ) ) ),
    file(lattices,cc2_lattices),
    []).

fof(cc2_robbins1,axiom,(
    ! [A] : 
      ( l2_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v5_robbins1(A) )
       => ( ~ v3_struct_0(A)
          & v6_robbins1(A) ) ) ) ),
    file(robbins1,cc2_robbins1),
    []).

fof(cc2_sheffer1,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v6_lattices(A)
          & v11_lattices(A)
          & v1_sheffer1(A)
          & v2_sheffer1(A)
          & v3_sheffer1(A)
          & v4_sheffer1(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & v12_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A)
          & v17_lattices(A) ) ) ) ),
    file(sheffer1,cc2_sheffer1),
    []).

fof(cc3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v15_lattices(A) ) ) ) ),
    file(lattices,cc3_lattices),
    []).

fof(cc4_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v15_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) ) ) ) ),
    file(lattices,cc4_lattices),
    []).

fof(cc4_robbins1,axiom,(
    ! [A] : 
      ( l2_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v4_robbins1(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v14_lattices(A)
          & v5_robbins1(A)
          & v6_robbins1(A) ) ) ) ),
    file(robbins1,cc4_robbins1),
    []).

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(cc5_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v17_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) ) ) ) ),
    file(lattices,cc5_lattices),
    []).

fof(cc5_robbins1,axiom,(
    ! [A] : 
      ( l3_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v9_robbins1(A) )
       => ( ~ v3_struct_0(A)
          & v6_lattices(A) ) ) ) ),
    file(robbins1,cc5_robbins1),
    []).

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(cc6_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v17_lattices(A) ) ) ) ),
    file(lattices,cc6_lattices),
    []).

fof(cc6_robbins1,axiom,(
    ! [A] : 
      ( l3_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & v7_robbins1(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v14_lattices(A)
          & v5_robbins1(A)
          & v6_robbins1(A)
          & v7_robbins1(A) ) ) ) ),
    file(robbins1,cc6_robbins1),
    []).

fof(cc7_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v12_lattices(A) ) ) ) ),
    file(lattices,cc7_lattices),
    []).

fof(cc7_robbins1,axiom,(
    ! [A] : 
      ( l3_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v5_robbins1(A)
          & v9_robbins1(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & v12_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A)
          & v17_lattices(A)
          & v9_robbins1(A) ) ) ) ),
    file(robbins1,cc7_robbins1),
    []).

fof(cc8_robbins1,axiom,(
    ! [A] : 
      ( l3_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v4_robbins1(A)
          & v9_robbins1(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & v12_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A)
          & v17_lattices(A) ) ) ) ),
    file(robbins1,cc8_robbins1),
    []).

fof(cc9_robbins1,axiom,(
    ! [A] : 
      ( l3_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & v7_robbins1(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A)
          & v6_lattices(A)
          & v7_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_lattices(A)
          & v14_lattices(A)
          & v4_robbins1(A)
          & v5_robbins1(A)
          & v6_robbins1(A)
          & v7_robbins1(A) ) ) ) ),
    file(robbins1,cc9_robbins1),
    []).

fof(commutativity_k3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_lattices(A,B,C) = k3_lattices(A,C,B) ) ),
    file(lattices,k3_lattices),
    []).

fof(commutativity_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_lattices(A,B,C) = k4_lattices(A,C,B) ) ),
    file(lattices,k4_lattices),
    []).

fof(commutativity_k5_robbins1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_robbins1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k5_robbins1(A,B,C) = k5_robbins1(A,C,B) ) ),
    file(robbins1,k5_robbins1),
    []).

fof(commutativity_k5_robbins3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k5_robbins3(A,B,C) = k5_robbins3(A,C,B) ) ),
    file(robbins3,k5_robbins3),
    []).

fof(d1_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) ) ) ) ),
    file(lattices,d1_lattices),
    []).

fof(d23_robbins1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_robbins1(A) )
     => ( v9_robbins1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_lattices(A,B,C) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),k3_robbins1(A,C))) ) ) ) ) ),
    file(robbins1,d23_robbins1),
    []).

fof(d2_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) ) ) ) ),
    file(lattices,d2_lattices),
    []).

fof(d6_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_robbins1(A) )
     => ( v8_robbins3(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => k3_robbins1(A,k3_robbins1(A,B)) = B ) ) ) ),
    file(robbins3,d6_robbins3),
    []).

fof(d7_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_robbins1(A) )
     => ( v9_robbins3(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_lattices(A,B,k3_robbins1(A,B)) = k1_lattices(A,C,k3_robbins1(A,C)) ) ) ) ) ),
    file(robbins3,d7_robbins3),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k1_lattices),
    []).

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_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(dt_k2_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k2_lattices),
    []).

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

fof(dt_k3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k3_lattices),
    []).

fof(dt_k3_robbins1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_robbins1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k3_robbins1(A,B),u1_struct_0(A)) ) ),
    file(robbins1,k3_robbins1),
    []).

fof(dt_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)) ) ),
    file(lattices,k4_lattices),
    []).

fof(dt_k5_robbins1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_robbins1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k5_robbins1(A,B,C),u1_struct_0(A)) ) ),
    file(robbins1,k5_robbins1),
    []).

fof(dt_k5_robbins3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k5_robbins3(A,B,C),u1_struct_0(A)) ) ),
    file(robbins3,k5_robbins3),
    []).

fof(dt_l1_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l1_lattices),
    []).

fof(dt_l1_robbins1,axiom,(
    ! [A] : 
      ( l1_robbins1(A)
     => l1_struct_0(A) ) ),
    file(robbins1,l1_robbins1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => l1_struct_0(A) ) ),
    file(lattices,l2_lattices),
    []).

fof(dt_l2_robbins1,axiom,(
    ! [A] : 
      ( l2_robbins1(A)
     => ( l2_lattices(A)
        & l1_robbins1(A) ) ) ),
    file(robbins1,l2_robbins1),
    []).

fof(dt_l3_lattices,axiom,(
    ! [A] : 
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ) ),
    file(lattices,l3_lattices),
    []).

fof(dt_l3_robbins1,axiom,(
    ! [A] : 
      ( l3_robbins1(A)
     => ( l2_robbins1(A)
        & l3_lattices(A) ) ) ),
    file(robbins1,l3_robbins1),
    []).

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_lattices,axiom,(
    ! [A] : 
      ( l1_lattices(A)
     => ( v1_funct_1(u1_lattices(A))
        & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u1_lattices),
    []).

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

fof(dt_u2_lattices,axiom,(
    ! [A] : 
      ( l2_lattices(A)
     => ( v1_funct_1(u2_lattices(A))
        & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(lattices,u2_lattices),
    []).

fof(existence_l1_lattices,axiom,(
    ? [A] : l1_lattices(A) ),
    file(lattices,l1_lattices),
    []).

fof(existence_l1_robbins1,axiom,(
    ? [A] : l1_robbins1(A) ),
    file(robbins1,l1_robbins1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_lattices,axiom,(
    ? [A] : l2_lattices(A) ),
    file(lattices,l2_lattices),
    []).

fof(existence_l2_robbins1,axiom,(
    ? [A] : l2_robbins1(A) ),
    file(robbins1,l2_robbins1),
    []).

fof(existence_l3_lattices,axiom,(
    ? [A] : l3_lattices(A) ),
    file(lattices,l3_lattices),
    []).

fof(existence_l3_robbins1,axiom,(
    ? [A] : l3_robbins1(A) ),
    file(robbins1,l3_robbins1),
    []).

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_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(rc11_robbins3,axiom,(
    ? [A] : 
      ( l3_robbins1(A)
      & ~ v3_struct_0(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A)
      & v9_robbins1(A)
      & v1_robbins3(A)
      & v2_robbins3(A)
      & v8_robbins3(A)
      & v9_robbins3(A) ) ),
    file(robbins3,rc11_robbins3),
    []).

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_sheffer1,axiom,(
    ? [A] : 
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A)
      & v11_lattices(A)
      & v12_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A)
      & v15_lattices(A)
      & v16_lattices(A)
      & v17_lattices(A)
      & v6_robbins1(A)
      & v1_sheffer1(A)
      & v2_sheffer1(A)
      & v3_sheffer1(A)
      & v4_sheffer1(A) ) ),
    file(sheffer1,rc1_sheffer1),
    []).

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(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_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(redefinition_k3_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_lattices(A,B,C) = k1_lattices(A,B,C) ) ),
    file(lattices,k3_lattices),
    []).

fof(redefinition_k4_lattices,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l1_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_lattices(A,B,C) = k2_lattices(A,B,C) ) ),
    file(lattices,k4_lattices),
    []).

fof(redefinition_k5_robbins1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_robbins1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k5_robbins1(A,B,C) = k1_lattices(A,B,C) ) ),
    file(robbins1,k5_robbins1),
    []).

fof(redefinition_k5_robbins3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l2_lattices(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k5_robbins3(A,B,C) = k1_lattices(A,B,C) ) ),
    file(robbins3,k5_robbins3),
    []).

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(t34_robbins1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_lattices(A)
        & v15_lattices(A)
        & v7_robbins1(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_lattices(A,B,C) = k3_robbins1(A,k3_lattices(A,k3_robbins1(A,B),k3_robbins1(A,C))) ) ) ) ),
    file(robbins1,t34_robbins1),
    []).

fof(t3_robbins1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v5_lattices(A)
        & v5_robbins1(A)
        & l2_robbins1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_robbins1(A,k3_robbins1(A,B)) = B ) ) ),
    file(robbins1,t3_robbins1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_robbins1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v5_lattices(A)
        & v5_robbins1(A)
        & l2_robbins1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_robbins1(A,B,k3_robbins1(A,B)) = k5_robbins1(A,C,k3_robbins1(A,C)) ) ) ) ),
    file(robbins1,t4_robbins1),
    []).

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),
    []).