% Mizar problem: t1_measure4,measure4,30,61 
fof(t1_measure4,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)
             => ( ( r1_supinf_1(k1_supinf_2,A)
                  & r1_supinf_1(k1_supinf_2,B)
                  & r1_supinf_1(k1_supinf_2,C) )
               => k2_supinf_2(k2_supinf_2(A,B),C) = k2_supinf_2(A,k2_supinf_2(B,C)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_1,cc1_supinf_1,cc2_supinf_1,commutativity_k12_supinf_1,commutativity_k2_supinf_2,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,connectedness_r1_supinf_1,d2_supinf_2,d2_tarski,d2_xboole_0,d6_supinf_1,dt_k12_supinf_1,dt_k1_numbers,dt_k1_supinf_1,dt_k1_supinf_2,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_supinf_1,dt_k2_supinf_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k3_real_1,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_k6_supinf_1,dt_m1_subset_1,existence_m1_subset_1,fc1_numbers,fc1_subset_1,fc1_supinf_1,fc1_xboole_0,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,idempotence_k2_xboole_0,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_supinf_1,redefinition_k12_supinf_1,redefinition_k3_real_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,redefinition_k6_supinf_1,reflexivity_r1_supinf_1,reflexivity_r1_tarski,t19_supinf_2,t1_boole,t1_subset,t1_supinf_2,t2_measure3,t2_subset,t31_supinf_1,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,t8_supinf_2,t9_supinf_2]),
    [file(measure4,t1_measure4)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => v3_supinf_1(A) ) ),
    file(supinf_1,cc1_supinf_1),
    []).

fof(cc2_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_supinf_1(A) ) ) ),
    file(supinf_1,cc2_supinf_1),
    []).

fof(commutativity_k12_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k12_supinf_1(A,B) = k12_supinf_1(B,A) ) ),
    file(supinf_1,k12_supinf_1),
    []).

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(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(commutativity_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k3_real_1(B,A) ) ),
    file(real_1,k3_real_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(d2_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)
             => ( ( ( r2_hidden(A,k6_supinf_1)
                    & r2_hidden(B,k6_supinf_1) )
                 => ( C = k2_supinf_2(A,B)
                  <=> ? [D] : 
                        ( m1_subset_1(D,k1_numbers)
                        & ? [E] : 
                            ( m1_subset_1(E,k1_numbers)
                            & A = D
                            & B = E
                            & C = k3_real_1(D,E) ) ) ) )
                & ( ( ( A = k4_supinf_1
                      & B != k5_supinf_1 )
                    | ( B = k4_supinf_1
                      & A != k5_supinf_1 ) )
                 => ( C = k2_supinf_2(A,B)
                  <=> C = k4_supinf_1 ) )
                & ( ( ( A = k5_supinf_1
                      & B != k4_supinf_1 )
                    | ( B = k5_supinf_1
                      & A != k4_supinf_1 ) )
                 => ( C = k2_supinf_2(A,B)
                  <=> C = k5_supinf_1 ) )
                & ~ ( ~ ( r2_hidden(A,k6_supinf_1)
                        & r2_hidden(B,k6_supinf_1) )
                    & ~ ( A = k4_supinf_1
                        & B != k5_supinf_1 )
                    & ~ ( B = k4_supinf_1
                        & A != k5_supinf_1 )
                    & ~ ( A = k5_supinf_1
                        & B != k4_supinf_1 )
                    & ~ ( B = k5_supinf_1
                        & A != k4_supinf_1 )
                    & ~ ( C = k2_supinf_2(A,B)
                      <=> C = k1_supinf_2 ) ) ) ) ) ) ),
    file(supinf_2,d2_supinf_2),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d6_supinf_1,axiom,(
    k3_supinf_1 = k2_xboole_0(k1_numbers,k2_tarski(k2_supinf_1,k1_supinf_1)) ),
    file(supinf_1,d6_supinf_1),
    []).

fof(dt_k12_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k12_supinf_1(A,B),k1_zfmisc_1(k3_supinf_1)) ) ),
    file(supinf_1,k12_supinf_1),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

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_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ),
    file(real_1,k3_real_1),
    []).

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

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

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

fof(dt_k6_supinf_1,axiom,
    ( ~ v1_xboole_0(k6_supinf_1)
    & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k3_supinf_1)) ),
    file(supinf_1,k6_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(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_supinf_1,axiom,(
    ~ v1_xboole_0(k3_supinf_1) ),
    file(supinf_1,fc1_supinf_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_supinf_1,axiom,(
    ? [A] : v3_supinf_1(A) ),
    file(supinf_1,rc3_supinf_1),
    []).

fof(redefinition_k12_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k12_supinf_1(A,B) = k2_tarski(A,B) ) ),
    file(supinf_1,k12_supinf_1),
    []).

fof(redefinition_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(real_1,k3_real_1),
    []).

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

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

fof(redefinition_k6_supinf_1,axiom,(
    k6_supinf_1 = k1_numbers ),
    file(supinf_1,k6_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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

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_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t1_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_subset_1(D,k1_numbers)
                 => ( ( A = C
                      & B = D )
                   => k2_supinf_2(A,B) = k3_real_1(C,D) ) ) ) ) ) ),
    file(supinf_2,t1_supinf_2),
    []).

fof(t2_measure3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ~ ( A != k5_supinf_1
          & A != k4_supinf_1
          & ~ m1_subset_1(A,k1_numbers) ) ) ),
    file(measure3,t2_measure3),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t31_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( r2_hidden(A,k1_numbers)
       => ( ~ r1_supinf_1(A,k5_supinf_1)
          & ~ r1_supinf_1(k4_supinf_1,A) ) ) ) ),
    file(supinf_1,t31_supinf_1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t8_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( k2_supinf_2(A,B) = k4_supinf_1
              & A != k4_supinf_1
              & B != k4_supinf_1 ) ) ) ),
    file(supinf_2,t8_supinf_2),
    []).

fof(t9_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ~ ( k2_supinf_2(A,B) = k5_supinf_1
              & A != k5_supinf_1
              & B != k5_supinf_1 ) ) ) ),
    file(supinf_2,t9_supinf_2),
    []).