% Mizar problem: t30_extreal1,extreal1,1485,59 
fof(t30_extreal1,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)
             => ~ ( ~ ( A = k5_measure6
                      & B = k5_measure6 )
                  & ~ ( A = k4_measure6
                      & B = k4_measure6 )
                  & C != k5_measure6
                  & C != k4_measure6
                  & k2_extreal1(C,k4_supinf_2(A,B)) != k4_supinf_2(k2_extreal1(C,A),k2_extreal1(C,B)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_extreal1,commutativity_k2_supinf_2,d4_supinf_2,dt_k1_extreal1,dt_k1_supinf_1,dt_k2_extreal1,dt_k2_supinf_1,dt_k2_supinf_2,dt_k3_supinf_1,dt_k3_supinf_2,dt_k4_measure6,dt_k4_supinf_2,dt_k5_measure6,dt_m1_subset_1,existence_m1_subset_1,involutiveness_k3_supinf_2,l34_extreal1,redefinition_k2_extreal1,redefinition_k4_measure6,redefinition_k5_measure6,t26_extreal1,t5_extreal1]),
    [file(extreal1,t30_extreal1)]).

fof(commutativity_k2_extreal1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k2_extreal1(A,B) = k2_extreal1(B,A) ) ),
    file(extreal1,k2_extreal1),
    []).

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(d4_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => k4_supinf_2(A,B) = k2_supinf_2(A,k3_supinf_2(B)) ) ) ),
    file(supinf_2,d4_supinf_2),
    []).

fof(dt_k1_extreal1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k1_extreal1(A,B),k3_supinf_1) ) ),
    file(extreal1,k1_extreal1),
    []).

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

fof(dt_k2_extreal1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k2_extreal1(A,B),k3_supinf_1) ) ),
    file(extreal1,k2_extreal1),
    []).

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_measure6,axiom,(
    m1_subset_1(k4_measure6,k3_supinf_1) ),
    file(measure6,k4_measure6),
    []).

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_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(l34_extreal1,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)
             => ~ ( A != k5_measure6
                  & A != k4_measure6
                  & k2_extreal1(A,k2_supinf_2(B,C)) != k2_supinf_2(k2_extreal1(A,B),k2_extreal1(A,C)) ) ) ) ) ),
    file(extreal1,l34_extreal1),
    []).

fof(redefinition_k2_extreal1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k2_extreal1(A,B) = k1_extreal1(A,B) ) ),
    file(extreal1,k2_extreal1),
    []).

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

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

fof(t26_extreal1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( k3_supinf_2(k2_extreal1(A,B)) = k2_extreal1(A,k3_supinf_2(B))
            & k3_supinf_2(k2_extreal1(A,B)) = k2_extreal1(k3_supinf_2(A),B) ) ) ) ),
    file(extreal1,t26_extreal1),
    []).

fof(t5_extreal1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => k4_supinf_2(A,k3_supinf_2(B)) = k2_supinf_2(A,B) ) ) ),
    file(extreal1,t5_extreal1),
    []).