% Mizar problem: t29_robbins3,robbins3,1665,26 
fof(t29_robbins3,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v9_robbins1(A)
        & v8_robbins3(A)
        & v9_robbins3(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( ( v10_robbins3(B)
            & m3_robbins3(B,A) )
         => v21_oposet_1(B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[existence_l1_struct_0,dt_l1_struct_0,rc3_struct_0,existence_l1_lattices,existence_l1_orders_2,existence_l1_robbins1,existence_l1_robbins3,existence_l2_lattices,existence_l2_robbins3,dt_l1_lattices,dt_l1_orders_2,dt_l1_robbins1,dt_l1_robbins3,dt_l2_lattices,dt_l2_robbins3,rc5_robbins3,rc6_robbins3,rc8_robbins3,cc3_oposet_1,cc5_oposet_1,cc7_oposet_1,cc8_oposet_1,cc12_oposet_1,cc15_oposet_1,existence_l1_oposet_1,existence_l2_robbins1,existence_l3_lattices,existence_l3_robbins3,dt_l1_oposet_1,dt_l2_robbins1,dt_l3_lattices,dt_l3_robbins3,cc1_robbins3,rc7_robbins3,rc9_robbins3,rc11_robbins3,cc14_robbins3,cc16_robbins3,cc17_robbins3,cc18_robbins3,cc19_robbins3,cc20_robbins3,cc21_robbins3,cc23_robbins3,cc24_robbins3,cc25_robbins3,cc5_robbins1,cc1_lattices,cc2_lattices,cc13_oposet_1,cc14_oposet_1,cc20_oposet_1,existence_l3_robbins1,existence_l4_robbins3,existence_m3_robbins3,dt_l3_robbins1,dt_l4_robbins3,dt_m3_robbins3,cc15_robbins3,cc22_robbins3,cc26_robbins3,cc27_robbins3,t28_robbins3]),
    [file(robbins3,t29_robbins3)]).

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

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

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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

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

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

fof(existence_l1_robbins3,axiom,(
    ? [A] : l1_robbins3(A) ),
    file(robbins3,l1_robbins3),
    []).

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

fof(existence_l2_robbins3,axiom,(
    ? [A] : l2_robbins3(A) ),
    file(robbins3,l2_robbins3),
    []).

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

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

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

fof(dt_l1_robbins3,axiom,(
    ! [A] : 
      ( l1_robbins3(A)
     => ( l2_lattices(A)
        & l1_orders_2(A) ) ) ),
    file(robbins3,l1_robbins3),
    []).

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

fof(dt_l2_robbins3,axiom,(
    ! [A] : 
      ( l2_robbins3(A)
     => ( l1_lattices(A)
        & l1_orders_2(A) ) ) ),
    file(robbins3,l2_robbins3),
    []).

fof(rc5_robbins3,axiom,(
    ? [A] : 
      ( l1_robbins3(A)
      & ~ v3_struct_0(A) ) ),
    file(robbins3,rc5_robbins3),
    []).

fof(rc6_robbins3,axiom,(
    ? [A] : 
      ( l2_robbins3(A)
      & ~ v3_struct_0(A) ) ),
    file(robbins3,rc6_robbins3),
    []).

fof(rc8_robbins3,axiom,(
    ? [A] : 
      ( l3_robbins3(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A) ) ),
    file(robbins3,rc8_robbins3),
    []).

fof(cc3_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & v7_oposet_1(A) ) ) ) ),
    file(oposet_1,cc3_oposet_1),
    []).

fof(cc5_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & v9_oposet_1(A) ) ) ) ),
    file(oposet_1,cc5_oposet_1),
    []).

fof(cc7_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v7_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_orders_2(A)
          & v7_oposet_1(A) ) ) ) ),
    file(oposet_1,cc7_oposet_1),
    []).

fof(cc8_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v9_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v3_orders_2(A)
          & v9_oposet_1(A) ) ) ) ),
    file(oposet_1,cc8_oposet_1),
    []).

fof(cc12_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v13_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v14_oposet_1(A) ) ) ) ),
    file(oposet_1,cc12_oposet_1),
    []).

fof(cc15_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & v13_oposet_1(A)
          & v14_oposet_1(A) ) ) ) ),
    file(oposet_1,cc15_oposet_1),
    []).

fof(existence_l1_oposet_1,axiom,(
    ? [A] : l1_oposet_1(A) ),
    file(oposet_1,l1_oposet_1),
    []).

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_robbins3,axiom,(
    ? [A] : l3_robbins3(A) ),
    file(robbins3,l3_robbins3),
    []).

fof(dt_l1_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( l1_orders_2(A)
        & l1_robbins1(A) ) ) ),
    file(oposet_1,l1_oposet_1),
    []).

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_robbins3,axiom,(
    ! [A] : 
      ( l3_robbins3(A)
     => ( l2_robbins3(A)
        & l1_robbins3(A)
        & l3_lattices(A) ) ) ),
    file(robbins3,l3_robbins3),
    []).

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(rc7_robbins3,axiom,(
    ? [A] : 
      ( l3_robbins3(A)
      & ~ v3_struct_0(A) ) ),
    file(robbins3,rc7_robbins3),
    []).

fof(rc9_robbins3,axiom,(
    ? [A] : 
      ( l3_robbins3(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)
      & v1_robbins3(A)
      & v2_robbins3(A) ) ),
    file(robbins3,rc9_robbins3),
    []).

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(cc14_robbins3,axiom,(
    ! [A] : 
      ( l3_robbins3(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v10_robbins3(A) )
       => ( ~ v3_struct_0(A)
          & v1_lattice3(A)
          & v2_lattice3(A) ) ) ) ),
    file(robbins3,cc14_robbins3),
    []).

fof(cc16_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v7_lattices(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v7_lattices(B) ) ) ) ),
    file(robbins3,cc16_robbins3),
    []).

fof(cc17_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v5_lattices(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v5_lattices(B) ) ) ) ),
    file(robbins3,cc17_robbins3),
    []).

fof(cc18_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_lattices(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v6_lattices(B) ) ) ) ),
    file(robbins3,cc18_robbins3),
    []).

fof(cc19_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v4_lattices(B) ) ) ) ),
    file(robbins3,cc19_robbins3),
    []).

fof(cc20_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v8_lattices(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v8_lattices(B) ) ) ) ),
    file(robbins3,cc20_robbins3),
    []).

fof(cc21_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v9_lattices(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v9_lattices(B) ) ) ) ),
    file(robbins3,cc21_robbins3),
    []).

fof(cc23_robbins3,axiom,(
    ! [A] : 
      ( l3_robbins3(A)
     => ( ( ~ v3_struct_0(A)
          & v6_lattices(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v10_robbins3(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A) ) ) ) ),
    file(robbins3,cc23_robbins3),
    []).

fof(cc24_robbins3,axiom,(
    ! [A] : 
      ( l3_robbins3(A)
     => ( ( ~ v3_struct_0(A)
          & v5_lattices(A)
          & v10_robbins3(A) )
       => ( ~ v3_struct_0(A)
          & v3_orders_2(A) ) ) ) ),
    file(robbins3,cc24_robbins3),
    []).

fof(cc25_robbins3,axiom,(
    ! [A] : 
      ( l3_robbins3(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v10_robbins3(A) )
       => ( ~ v3_struct_0(A)
          & v4_orders_2(A) ) ) ) ),
    file(robbins3,cc25_robbins3),
    []).

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(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(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(cc13_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v14_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v13_oposet_1(A) ) ) ) ),
    file(oposet_1,cc13_oposet_1),
    []).

fof(cc14_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v14_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v7_oposet_1(A)
          & v9_oposet_1(A) ) ) ) ),
    file(oposet_1,cc14_oposet_1),
    []).

fof(cc20_oposet_1,axiom,(
    ! [A] : 
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v14_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v7_oposet_1(A)
          & v9_oposet_1(A)
          & v13_oposet_1(A)
          & v14_oposet_1(A) ) ) ) ),
    file(oposet_1,cc20_oposet_1),
    []).

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

fof(existence_l4_robbins3,axiom,(
    ? [A] : l4_robbins3(A) ),
    file(robbins3,l4_robbins3),
    []).

fof(existence_m3_robbins3,axiom,(
    ! [A] : 
      ( l3_robbins1(A)
     => ? [B] : m3_robbins3(B,A) ) ),
    file(robbins3,m3_robbins3),
    []).

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

fof(dt_l4_robbins3,axiom,(
    ! [A] : 
      ( l4_robbins3(A)
     => ( l3_robbins3(A)
        & l3_robbins1(A)
        & l1_oposet_1(A) ) ) ),
    file(robbins3,l4_robbins3),
    []).

fof(dt_m3_robbins3,axiom,(
    ! [A] : 
      ( l3_robbins1(A)
     => ! [B] : 
          ( m3_robbins3(B,A)
         => l4_robbins3(B) ) ) ),
    file(robbins3,m3_robbins3),
    []).

fof(cc15_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ~ v3_struct_0(B) ) ) ),
    file(robbins3,cc15_robbins3),
    []).

fof(cc22_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v9_robbins3(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v9_robbins3(B) ) ) ) ),
    file(robbins3,cc22_robbins3),
    []).

fof(cc26_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v9_robbins1(A)
        & v8_robbins3(A)
        & v9_robbins3(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v4_lattices(B)
            & v5_lattices(B)
            & v6_lattices(B)
            & v7_lattices(B)
            & v8_lattices(B)
            & v9_lattices(B)
            & v10_lattices(B)
            & v1_robbins3(B)
            & v2_robbins3(B)
            & v8_robbins3(B)
            & v9_robbins3(B) ) ) ) ),
    file(robbins3,cc26_robbins3),
    []).

fof(cc27_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v9_robbins1(A)
        & v8_robbins3(A)
        & v9_robbins3(A)
        & l3_robbins1(A) )
     => ! [B] : 
          ( m3_robbins3(B,A)
         => ( ~ v3_struct_0(B)
            & v4_lattices(B)
            & v5_lattices(B)
            & v6_lattices(B)
            & v7_lattices(B)
            & v8_lattices(B)
            & v9_lattices(B)
            & v10_lattices(B)
            & v9_robbins1(B)
            & v1_robbins3(B)
            & v2_robbins3(B)
            & v8_robbins3(B)
            & v9_robbins3(B) ) ) ) ),
    file(robbins3,cc27_robbins3),
    []).

fof(t28_robbins3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l4_robbins3(A) )
     => ( ( v8_robbins3(A)
          & v9_robbins3(A)
          & v9_robbins1(A)
          & v10_lattices(A)
          & v10_robbins3(A) )
       => ( v21_oposet_1(A)
          & v14_oposet_1(A) ) ) ) ),
    file(robbins3,t28_robbins3),
    []).