% Mizar problem: t59_robbins2,robbins2,729,26 
fof(t59_robbins2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_robbins1(A) )
     => ( ( v4_lattices(A)
          & v5_lattices(A)
          & v4_robbins1(A) )
       => v1_robbins2(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_robbins1,cc1_robbins2,cc2_robbins1,cc2_robbins2,cc3_robbins2,cc4_robbins1,commutativity_k5_robbins1,commutativity_k6_robbins1,d1_robbins2,d4_lattices,d5_lattices,dt_k1_lattices,dt_k3_robbins1,dt_k4_robbins1,dt_k5_robbins1,dt_k6_robbins1,dt_l1_robbins1,dt_l1_struct_0,dt_l2_lattices,dt_l2_robbins1,dt_m1_subset_1,dt_u1_struct_0,existence_l1_robbins1,existence_l1_struct_0,existence_l2_lattices,existence_l2_robbins1,existence_m1_subset_1,rc1_robbins2,redefinition_k5_robbins1,redefinition_k6_robbins1,t13_robbins1,t17_robbins1,t18_robbins1,t22_robbins1,t31_robbins1,t32_robbins1,t3_robbins1,t58_robbins2,t8_robbins1]),
    [file(robbins2,t59_robbins2)]).

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_robbins2,axiom,(
    ! [A] : 
      ( l2_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_robbins2(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A) ) ) ) ),
    file(robbins2,cc1_robbins2),
    []).

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_robbins2,axiom,(
    ! [A] : 
      ( l2_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_robbins2(A) )
       => ( ~ v3_struct_0(A)
          & v5_lattices(A) ) ) ) ),
    file(robbins2,cc2_robbins2),
    []).

fof(cc3_robbins2,axiom,(
    ! [A] : 
      ( l2_robbins1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_robbins2(A) )
       => ( ~ v3_struct_0(A)
          & v4_robbins1(A) ) ) ) ),
    file(robbins2,cc3_robbins2),
    []).

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(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_k6_robbins1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v5_lattices(A)
        & l2_robbins1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k6_robbins1(A,B,C) = k6_robbins1(A,C,B) ) ),
    file(robbins1,k6_robbins1),
    []).

fof(d1_robbins2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_robbins1(A) )
     => ( v1_robbins2(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))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),D)),k3_robbins1(A,k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,D),k3_robbins1(A,k1_lattices(A,D,E)))))))) = D ) ) ) ) ) ) ),
    file(robbins2,d1_robbins2),
    []).

fof(d4_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ( v4_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) = k1_lattices(A,C,B) ) ) ) ) ),
    file(lattices,d4_lattices),
    []).

fof(d5_lattices,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_lattices(A) )
     => ( v5_lattices(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))
                   => k1_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k1_lattices(A,B,C),D) ) ) ) ) ) ),
    file(lattices,d5_lattices),
    []).

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_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_robbins1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_robbins1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_robbins1(A,B,C),u1_struct_0(A)) ) ),
    file(robbins1,k4_robbins1),
    []).

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_k6_robbins1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v5_lattices(A)
        & l2_robbins1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_robbins1(A,B,C),u1_struct_0(A)) ) ),
    file(robbins1,k6_robbins1),
    []).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

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

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_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(rc1_robbins2,axiom,(
    ? [A] : 
      ( l2_robbins1(A)
      & ~ v3_struct_0(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v1_robbins2(A) ) ),
    file(robbins2,rc1_robbins2),
    []).

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_k6_robbins1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v5_lattices(A)
        & l2_robbins1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k6_robbins1(A,B,C) = k4_robbins1(A,B,C) ) ),
    file(robbins1,k6_robbins1),
    []).

fof(t13_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))
         => k5_robbins1(A,B,B) = B ) ) ),
    file(robbins1,t13_robbins1),
    []).

fof(t17_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))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_robbins1(A,B,k6_robbins1(A,C,D)) = k6_robbins1(A,k6_robbins1(A,B,C),D) ) ) ) ) ),
    file(robbins1,t17_robbins1),
    []).

fof(t18_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,C) = k3_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C))) ) ) ) ),
    file(robbins1,t18_robbins1),
    []).

fof(t22_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))
             => k6_robbins1(A,B,k5_robbins1(A,B,C)) = B ) ) ) ),
    file(robbins1,t22_robbins1),
    []).

fof(t31_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))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k6_robbins1(A,B,k5_robbins1(A,C,D)) = k5_robbins1(A,k6_robbins1(A,B,C),k6_robbins1(A,B,D)) ) ) ) ) ),
    file(robbins1,t31_robbins1),
    []).

fof(t32_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))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k5_robbins1(A,B,k6_robbins1(A,C,D)) = k6_robbins1(A,k5_robbins1(A,B,C),k5_robbins1(A,B,D)) ) ) ) ) ),
    file(robbins1,t32_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(t58_robbins2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_robbins1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( v4_lattices(A)
                  & v5_lattices(A)
                  & v5_robbins1(A) )
               => k4_robbins1(A,k1_lattices(A,C,B),k1_lattices(A,C,k3_robbins1(A,B))) = C ) ) ) ) ),
    file(robbins2,t58_robbins2),
    []).

fof(t8_robbins1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v5_lattices(A)
        & l2_robbins1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_robbins1(A,B,C) = k4_robbins1(A,C,B) ) ) ) ),
    file(robbins1,t8_robbins1),
    []).