% Mizar problem: t41_tsep_2,tsep_2,688,73 
fof(t41_tsep_2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ! [D] : 
                  ( ( ~ v3_struct_0(D)
                    & m1_pre_topc(D,A) )
                 => ! [E] : 
                      ( ( ~ v3_struct_0(E)
                        & m1_pre_topc(E,A) )
                     => ( ( r4_tsep_2(A,B,D)
                          & r4_tsep_2(A,C,E)
                          & r1_tsep_1(A,B,C)
                          & r4_tsep_1(A,D,E) )
                       => r3_tsep_1(A,B,C) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_pre_topc,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_pre_topc,irreflexivity_r4_tsep_2,rc3_struct_0,redefinition_r4_tsep_2,symmetry_r1_tsep_1,symmetry_r3_tsep_1,symmetry_r3_tsep_2,symmetry_r4_tsep_1,symmetry_r4_tsep_2,t39_tsep_2,t85_tsep_1]),
    [file(tsep_2,t41_tsep_2)]).

fof(cc1_pre_topc,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => v2_pre_topc(B) ) ) ),
    file(pre_topc,cc1_pre_topc),
    []).

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_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => l1_pre_topc(B) ) ) ),
    file(pre_topc,m1_pre_topc),
    []).

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_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : m1_pre_topc(B,A) ) ),
    file(pre_topc,m1_pre_topc),
    []).

fof(irreflexivity_r4_tsep_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A)
        & ~ v3_struct_0(C)
        & m1_pre_topc(C,A) )
     => ~ r4_tsep_2(A,B,B) ) ),
    file(tsep_2,r4_tsep_2),
    []).

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

fof(redefinition_r4_tsep_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A)
        & ~ v3_struct_0(C)
        & m1_pre_topc(C,A) )
     => ( r4_tsep_2(A,B,C)
      <=> r3_tsep_2(A,B,C) ) ) ),
    file(tsep_2,r4_tsep_2),
    []).

fof(symmetry_r1_tsep_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_pre_topc(A)
        & m1_pre_topc(B,A)
        & m1_pre_topc(C,A) )
     => ( r1_tsep_1(A,B,C)
       => r1_tsep_1(A,C,B) ) ) ),
    file(tsep_1,r1_tsep_1),
    []).

fof(symmetry_r3_tsep_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_pre_topc(A)
        & m1_pre_topc(B,A)
        & m1_pre_topc(C,A) )
     => ( r3_tsep_1(A,B,C)
       => r3_tsep_1(A,C,B) ) ) ),
    file(tsep_1,r3_tsep_1),
    []).

fof(symmetry_r3_tsep_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_pre_topc(B,A)
        & m1_pre_topc(C,A) )
     => ( r3_tsep_2(A,B,C)
       => r3_tsep_2(A,C,B) ) ) ),
    file(tsep_2,r3_tsep_2),
    []).

fof(symmetry_r4_tsep_1,axiom,(
    ! [A,B,C] : 
      ( ( l1_pre_topc(A)
        & m1_pre_topc(B,A)
        & m1_pre_topc(C,A) )
     => ( r4_tsep_1(A,B,C)
       => r4_tsep_1(A,C,B) ) ) ),
    file(tsep_1,r4_tsep_1),
    []).

fof(symmetry_r4_tsep_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A)
        & ~ v3_struct_0(B)
        & m1_pre_topc(B,A)
        & ~ v3_struct_0(C)
        & m1_pre_topc(C,A) )
     => ( r4_tsep_2(A,B,C)
       => r4_tsep_2(A,C,B) ) ) ),
    file(tsep_2,r4_tsep_2),
    []).

fof(t39_tsep_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_pre_topc(C,A)
             => ! [D] : 
                  ( m1_pre_topc(D,A)
                 => ! [E] : 
                      ( m1_pre_topc(E,A)
                     => ( ( r3_tsep_2(A,B,D)
                          & r3_tsep_2(A,C,E)
                          & r4_tsep_1(A,B,C) )
                       => r4_tsep_1(A,D,E) ) ) ) ) ) ) ),
    file(tsep_2,t39_tsep_2),
    []).

fof(t85_tsep_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_pre_topc(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & m1_pre_topc(C,A) )
             => ( ( r1_tsep_1(A,B,C)
                  & r4_tsep_1(A,B,C) )
              <=> r3_tsep_1(A,B,C) ) ) ) ) ),
    file(tsep_1,t85_tsep_1),
    []).