% Mizar problem: t67_extreal2,extreal2,1572,49 
fof(t67_extreal2,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( ( A = k5_measure6
          | A = k4_measure6 )
       => k4_extreal1(A) = k5_measure6 ) ) ),
    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_k3_supinf_2,dt_k4_extreal1,dt_k4_measure6,dt_k4_supinf_1,dt_k5_measure6,dt_k5_supinf_1,dt_m1_subset_1,existence_m1_subset_1,involutiveness_k3_supinf_2,redefinition_k4_measure6,redefinition_k4_supinf_1,redefinition_k5_measure6,redefinition_k5_supinf_1,reflexivity_r1_supinf_1,t19_supinf_2,t36_extreal1,t37_extreal1,t4_extreal1]),
    [file(extreal2,t67_extreal2)]).

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_k3_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => m1_subset_1(k3_supinf_2(A),k3_supinf_1) ) ),
    file(supinf_2,k3_supinf_2),
    []).

fof(dt_k4_extreal1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => m1_subset_1(k4_extreal1(A),k3_supinf_1) ) ),
    file(extreal1,k4_extreal1),
    []).

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_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(involutiveness_k3_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => k3_supinf_2(k3_supinf_2(A)) = A ) ),
    file(supinf_2,k3_supinf_2),
    []).

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(t36_extreal1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( ~ r1_supinf_1(A,k1_supinf_2)
       => k4_extreal1(A) = A ) ) ),
    file(extreal1,t36_extreal1),
    []).

fof(t37_extreal1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( ~ r1_supinf_1(k1_supinf_2,A)
       => k4_extreal1(A) = k3_supinf_2(A) ) ) ),
    file(extreal1,t37_extreal1),
    []).

fof(t4_extreal1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( ( A = k5_measure6
         => k3_supinf_2(A) = k4_measure6 )
        & ( k3_supinf_2(A) = k4_measure6
         => A = k5_measure6 )
        & ( A = k4_measure6
         => k3_supinf_2(A) = k5_measure6 )
        & ( k3_supinf_2(A) = k5_measure6
         => A = k4_measure6 ) ) ) ),
    file(extreal1,t4_extreal1),
    []).