% Mizar problem: t40_extreal1,extreal1,1627,79 
fof(t40_extreal1,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( r1_supinf_1(A,B)
           => ( r1_supinf_1(k5_measure6,A)
              | r1_supinf_1(B,k4_measure6)
              | r1_supinf_1(k1_supinf_2,k4_supinf_2(B,A)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[connectedness_r1_supinf_1,dt_k1_supinf_1,dt_k1_supinf_2,dt_k2_supinf_1,dt_k3_supinf_1,dt_k4_measure6,dt_k4_supinf_1,dt_k4_supinf_2,dt_k5_measure6,dt_k5_supinf_1,dt_m1_subset_1,existence_m1_subset_1,redefinition_k4_measure6,redefinition_k4_supinf_1,redefinition_k5_measure6,redefinition_k5_supinf_1,reflexivity_r1_supinf_1,t19_supinf_2,t1_measure5,t7_supinf_2]),
    [file(extreal1,t40_extreal1)]).

fof(connectedness_r1_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => ( r1_supinf_1(A,B)
        | r1_supinf_1(B,A) ) ) ),
    file(supinf_1,r1_supinf_1),
    []).

fof(dt_k1_supinf_1,axiom,(
    $true ),
    file(supinf_1,k1_supinf_1),
    []).

fof(dt_k1_supinf_2,axiom,(
    m1_subset_1(k1_supinf_2,k3_supinf_1) ),
    file(supinf_2,k1_supinf_2),
    []).

fof(dt_k2_supinf_1,axiom,(
    $true ),
    file(supinf_1,k2_supinf_1),
    []).

fof(dt_k3_supinf_1,axiom,(
    $true ),
    file(supinf_1,k3_supinf_1),
    []).

fof(dt_k4_measure6,axiom,(
    m1_subset_1(k4_measure6,k3_supinf_1) ),
    file(measure6,k4_measure6),
    []).

fof(dt_k4_supinf_1,axiom,(
    m1_subset_1(k4_supinf_1,k3_supinf_1) ),
    file(supinf_1,k4_supinf_1),
    []).

fof(dt_k4_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k4_supinf_2(A,B),k3_supinf_1) ) ),
    file(supinf_2,k4_supinf_2),
    []).

fof(dt_k5_measure6,axiom,(
    m1_subset_1(k5_measure6,k3_supinf_1) ),
    file(measure6,k5_measure6),
    []).

fof(dt_k5_supinf_1,axiom,(
    m1_subset_1(k5_supinf_1,k3_supinf_1) ),
    file(supinf_1,k5_supinf_1),
    []).

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

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(redefinition_k4_measure6,axiom,(
    k4_measure6 = k2_supinf_1 ),
    file(measure6,k4_measure6),
    []).

fof(redefinition_k4_supinf_1,axiom,(
    k4_supinf_1 = k1_supinf_1 ),
    file(supinf_1,k4_supinf_1),
    []).

fof(redefinition_k5_measure6,axiom,(
    k5_measure6 = k1_supinf_1 ),
    file(measure6,k5_measure6),
    []).

fof(redefinition_k5_supinf_1,axiom,(
    k5_supinf_1 = k2_supinf_1 ),
    file(supinf_1,k5_supinf_1),
    []).

fof(reflexivity_r1_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => r1_supinf_1(A,A) ) ),
    file(supinf_1,r1_supinf_1),
    []).

fof(t19_supinf_2,axiom,
    ( ~ r1_supinf_1(k1_supinf_2,k5_supinf_1)
    & ~ r1_supinf_1(k4_supinf_1,k1_supinf_2) ),
    file(supinf_2,t19_supinf_2),
    []).

fof(t1_measure5,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( r1_supinf_1(A,B)
           => ( A = k5_supinf_1
              | A = k4_supinf_1
              | r1_supinf_1(k1_supinf_2,k4_supinf_2(B,A)) ) ) ) ) ),
    file(measure5,t1_measure5),
    []).

fof(t7_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( A != k5_supinf_1
       => ( k4_supinf_2(k5_supinf_1,A) = k5_supinf_1
          & k4_supinf_2(A,k5_supinf_1) = k4_supinf_1 ) ) ) ),
    file(supinf_2,t7_supinf_2),
    []).