% Mizar problem: t8_collsp,collsp,148,32 
fof(t8_collsp,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_collsp(A)
        & v3_collsp(A)
        & l1_collsp(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))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_collsp(A,B,C,D)
                              & r1_collsp(A,B,C,E)
                              & r1_collsp(A,B,C,F) )
                           => ( B = C
                              | r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,d2_collsp,d4_collsp,dt_k1_xboole_0,dt_k3_mcart_1,dt_k3_zfmisc_1,dt_k4_domain_1,dt_l1_collsp,dt_l1_struct_0,dt_m1_collsp,dt_m1_subset_1,dt_u1_collsp,dt_u1_struct_0,existence_l1_collsp,existence_l1_struct_0,existence_m1_collsp,existence_m1_subset_1,fc1_struct_0,fc1_xboole_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,redefinition_k4_domain_1,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole]),
    [file(collsp,t8_collsp)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(d2_collsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_collsp(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))
                 => ( r1_collsp(A,B,C,D)
                  <=> r2_hidden(k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D),u1_collsp(A)) ) ) ) ) ) ),
    file(collsp,d2_collsp),
    []).

fof(d4_collsp,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_collsp(A) )
     => ( v3_collsp(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))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r2_hidden(k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D),u1_collsp(A))
                                & r2_hidden(k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,E),u1_collsp(A))
                                & r2_hidden(k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,F),u1_collsp(A)) )
                             => ( B = C
                                | r2_hidden(k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,E,F),u1_collsp(A)) ) ) ) ) ) ) ) ) ) ),
    file(collsp,d4_collsp),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k3_mcart_1,axiom,(
    $true ),
    file(mcart_1,k3_mcart_1),
    []).

fof(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

fof(dt_k4_domain_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,A)
        & m1_subset_1(E,B)
        & m1_subset_1(F,C) )
     => m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)) ) ),
    file(domain_1,k4_domain_1),
    []).

fof(dt_l1_collsp,axiom,(
    ! [A] : 
      ( l1_collsp(A)
     => l1_struct_0(A) ) ),
    file(collsp,l1_collsp),
    []).

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

fof(dt_m1_collsp,axiom,(
    $true ),
    file(collsp,m1_collsp),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_u1_collsp,axiom,(
    ! [A] : 
      ( l1_collsp(A)
     => m1_collsp(u1_collsp(A),u1_struct_0(A)) ) ),
    file(collsp,u1_collsp),
    []).

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

fof(existence_l1_collsp,axiom,(
    ? [A] : l1_collsp(A) ),
    file(collsp,l1_collsp),
    []).

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

fof(existence_m1_collsp,axiom,(
    ! [A] : 
    ? [B] : m1_collsp(B,A) ),
    file(collsp,m1_collsp),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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

fof(redefinition_k4_domain_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,A)
        & m1_subset_1(E,B)
        & m1_subset_1(F,C) )
     => k4_domain_1(A,B,C,D,E,F) = k3_mcart_1(D,E,F) ) ),
    file(domain_1,k4_domain_1),
    []).

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(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),
    []).