% Mizar problem: t34_robbins2,robbins2,442,27 
fof(t34_robbins2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_robbins2(A)
        & l2_robbins1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C)))),C)) = k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,C),C)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_robbins2,commutativity_k5_robbins1,dt_k1_lattices,dt_k3_robbins1,dt_k5_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,redefinition_k5_robbins1,t15_robbins2,t31_robbins2]),
    [file(robbins2,t34_robbins2)]).

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(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(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_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_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(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(t15_robbins2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_robbins2(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))
                 => k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,C,D)))),D)) = k3_robbins1(A,k1_lattices(A,C,D)) ) ) ) ) ),
    file(robbins2,t15_robbins2),
    []).

fof(t31_robbins2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C))),k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,C),C))) = k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C))) ) ) ) ),
    file(robbins2,t31_robbins2),
    []).