% Mizar problem: t71_extreal2,extreal2,1680,51 
fof(t71_extreal2,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] : 
                  ( m1_subset_1(D,k3_supinf_1)
                 => ~ ( ~ ( A = k5_measure6
                          & B = k4_measure6 )
                      & ~ ( A = k4_measure6
                          & B = k5_measure6 )
                      & r1_supinf_1(k4_extreal1(A),C)
                      & r1_supinf_1(k4_extreal1(B),D)
                      & ~ r1_supinf_1(k4_extreal1(k2_supinf_2(A,B)),k2_supinf_2(C,D)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_supinf_2,connectedness_r1_supinf_1,dt_k1_supinf_1,dt_k1_supinf_2,dt_k2_supinf_1,dt_k2_supinf_2,dt_k3_supinf_1,dt_k3_supinf_2,dt_k4_extreal1,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,involutiveness_k3_supinf_2,redefinition_k4_measure6,redefinition_k4_supinf_1,redefinition_k5_measure6,redefinition_k5_supinf_1,reflexivity_r1_supinf_1,t14_extreal2,t14_supinf_2,t17_supinf_2,t19_supinf_2,t29_supinf_1,t4_extreal1,t51_extreal2,t60_extreal2]),
    [file(extreal2,t71_extreal2)]).

fof(commutativity_k2_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k2_supinf_2(A,B) = k2_supinf_2(B,A) ) ),
    file(supinf_2,k2_supinf_2),
    []).

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_k2_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k2_supinf_2(A,B),k3_supinf_1) ) ),
    file(supinf_2,k2_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_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_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(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(t14_extreal2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( ~ ( A = k5_measure6
                  & B = k4_measure6 )
              & ~ ( A = k4_measure6
                  & B = k5_measure6 )
              & ~ ( k3_supinf_2(k2_supinf_2(A,B)) = k2_supinf_2(k3_supinf_2(A),k3_supinf_2(B))
                  & k3_supinf_2(k2_supinf_2(A,B)) = k4_supinf_2(k3_supinf_2(B),A)
                  & k3_supinf_2(k2_supinf_2(A,B)) = k4_supinf_2(k3_supinf_2(A),B) ) ) ) ) ),
    file(extreal2,t14_extreal2),
    []).

fof(t14_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ! [D] : 
                  ( m1_subset_1(D,k3_supinf_1)
                 => ~ ( ~ ( A = k4_supinf_1
                          & C = k5_supinf_1 )
                      & ~ ( A = k5_supinf_1
                          & C = k4_supinf_1 )
                      & ~ ( B = k4_supinf_1
                          & D = k5_supinf_1 )
                      & ~ ( B = k5_supinf_1
                          & D = k4_supinf_1 )
                      & r1_supinf_1(A,B)
                      & r1_supinf_1(C,D)
                      & ~ r1_supinf_1(k2_supinf_2(A,C),k2_supinf_2(B,D)) ) ) ) ) ) ),
    file(supinf_2,t14_supinf_2),
    []).

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),
    []).

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(t29_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r1_supinf_1(A,B)
                  & r1_supinf_1(B,C) )
               => r1_supinf_1(A,C) ) ) ) ) ),
    file(supinf_1,t29_supinf_1),
    []).

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),
    []).

fof(t51_extreal2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => r1_supinf_1(k1_supinf_2,k4_extreal1(A)) ) ),
    file(extreal2,t51_extreal2),
    []).

fof(t60_extreal2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( r1_supinf_1(k3_supinf_2(A),B)
              & r1_supinf_1(B,A) )
          <=> r1_supinf_1(k4_extreal1(B),A) ) ) ) ),
    file(extreal2,t60_extreal2),
    []).