% Mizar problem: t32_connsp_1,connsp_1,1034,18 
fof(t32_connsp_1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_connsp_1(A,B,C) ) )
       => v1_connsp_1(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,t30_connsp_1,t31_connsp_1]),
    [file(connsp_1,t32_connsp_1)]).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

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_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

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(t30_connsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_connsp_1(A,B,C) ) )
       => v1_connsp_1(A) ) ) ),
    file(connsp_1,t30_connsp_1),
    []).

fof(t31_connsp_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ( ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_connsp_1(A,B,C) ) )
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_connsp_1(A,B,C) ) ) ) ) ),
    file(connsp_1,t31_connsp_1),
    []).