% Mizar problem: t25_extreal1,extreal1,821,48 
fof(t25_extreal1,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( ~ ( ~ r1_supinf_1(A,k1_supinf_2)
            & r1_supinf_1(k1_supinf_2,k3_supinf_2(A)) )
        & ~ ( ~ r1_supinf_1(k1_supinf_2,k3_supinf_2(A))
            & r1_supinf_1(A,k1_supinf_2) )
        & ~ ( ~ r1_supinf_1(k1_supinf_2,A)
            & r1_supinf_1(k3_supinf_2(A),k1_supinf_2) )
        & ~ ( ~ r1_supinf_1(k3_supinf_2(A),k1_supinf_2)
            & r1_supinf_1(k1_supinf_2,A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[involutiveness_k3_supinf_2,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,existence_m1_subset_1,dt_k1_supinf_2,dt_k3_supinf_1,dt_k3_supinf_2,dt_m1_subset_1,t24_extreal1,t17_supinf_2]),
    [file(extreal1,t25_extreal1)]).

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

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

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(t24_extreal1,axiom,(
    k3_supinf_2(k1_supinf_2) = k1_supinf_2 ),
    file(extreal1,t24_extreal1),
    []).

fof(t17_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( ~ ( ~ r1_supinf_1(B,A)
                & r1_supinf_1(k3_supinf_2(A),k3_supinf_2(B)) )
            & ~ ( ~ r1_supinf_1(k3_supinf_2(A),k3_supinf_2(B))
                & r1_supinf_1(B,A) ) ) ) ) ),
    file(supinf_2,t17_supinf_2),
    []).