% Mizar problem: t48_midsp_1,midsp_1,446,46 
fof(t48_midsp_1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ? [B] : 
          ( m1_midsp_1(B,A)
          & ! [C] : 
              ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
             => ( r2_hidden(C,B)
              <=> k5_midsp_1(A,C) = k6_midsp_1(A,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_relset_1,d6_midsp_1,d7_midsp_1,dt_k1_mcart_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k5_midsp_1,dt_k6_midsp_1,dt_k7_midsp_1,dt_k8_midsp_1,dt_k9_midsp_1,dt_l1_midsp_1,dt_l1_struct_0,dt_m1_midsp_1,dt_m1_subset_1,dt_u1_struct_0,existence_l1_midsp_1,existence_l1_struct_0,existence_m1_midsp_1,existence_m1_subset_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_midsp_1,fc4_subset_1,fraenkel_a_2_0_midsp_1,rc1_subset_1,rc1_xboole_0,rc2_midsp_1,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,redefinition_k5_midsp_1,redefinition_k6_midsp_1,redefinition_k7_midsp_1,redefinition_k9_midsp_1,reflexivity_r1_tarski,reflexivity_r2_midsp_1,symmetry_r2_midsp_1,t1_subset,t21_midsp_1,t24_midsp_1,t2_subset,t2_tarski,t3_subset,t41_midsp_1,t4_subset,t5_subset,t6_boole,t7_boole,t7_mcart_1,t8_boole]),
    [file(midsp_1,t48_midsp_1)]).

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

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(d6_midsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
             => ( r2_midsp_1(A,B,C)
              <=> r1_midsp_1(A,k5_midsp_1(A,B),k6_midsp_1(A,B),k5_midsp_1(A,C),k6_midsp_1(A,C)) ) ) ) ) ),
    file(midsp_1,d6_midsp_1),
    []).

fof(d7_midsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
         => k8_midsp_1(A,B) = a_2_0_midsp_1(A,B) ) ) ),
    file(midsp_1,d7_midsp_1),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

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_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k5_midsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => m1_subset_1(k5_midsp_1(A,B),u1_struct_0(A)) ) ),
    file(midsp_1,k5_midsp_1),
    []).

fof(dt_k6_midsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => m1_subset_1(k6_midsp_1(A,B),u1_struct_0(A)) ) ),
    file(midsp_1,k6_midsp_1),
    []).

fof(dt_k7_midsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k7_midsp_1(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ),
    file(midsp_1,k7_midsp_1),
    []).

fof(dt_k8_midsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => m1_subset_1(k8_midsp_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ),
    file(midsp_1,k8_midsp_1),
    []).

fof(dt_k9_midsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => m1_midsp_1(k9_midsp_1(A,B),A) ) ),
    file(midsp_1,k9_midsp_1),
    []).

fof(dt_l1_midsp_1,axiom,(
    ! [A] : 
      ( l1_midsp_1(A)
     => l1_struct_0(A) ) ),
    file(midsp_1,l1_midsp_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_midsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] : 
          ( m1_midsp_1(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ) ) ),
    file(midsp_1,m1_midsp_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_midsp_1,axiom,(
    ? [A] : l1_midsp_1(A) ),
    file(midsp_1,l1_midsp_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_midsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ? [B] : m1_midsp_1(B,A) ) ),
    file(midsp_1,m1_midsp_1),
    []).

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

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

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

fof(fc2_midsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => ( v1_relat_1(k8_midsp_1(A,B))
        & ~ v1_xboole_0(k8_midsp_1(A,B)) ) ) ),
    file(midsp_1,fc2_midsp_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fraenkel_a_2_0_midsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & v2_midsp_1(B)
        & l1_midsp_1(B)
        & m1_subset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) )
     => ( r2_hidden(A,a_2_0_midsp_1(B,C))
      <=> ? [D] : 
            ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
            & A = D
            & r2_midsp_1(B,D,C) ) ) ) ),
    file(midsp_1,a_2_0_midsp_1),
    []).

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_midsp_1,axiom,(
    ? [A] : 
      ( l1_midsp_1(A)
      & ~ v3_struct_0(A) ) ),
    file(midsp_1,rc2_midsp_1),
    []).

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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k5_midsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => k5_midsp_1(A,B) = k1_mcart_1(B) ) ),
    file(midsp_1,k5_midsp_1),
    []).

fof(redefinition_k6_midsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => k6_midsp_1(A,B) = k2_mcart_1(B) ) ),
    file(midsp_1,k6_midsp_1),
    []).

fof(redefinition_k7_midsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k7_midsp_1(A,B,C) = k4_tarski(B,C) ) ),
    file(midsp_1,k7_midsp_1),
    []).

fof(redefinition_k9_midsp_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => k9_midsp_1(A,B) = k8_midsp_1(A,B) ) ),
    file(midsp_1,k9_midsp_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r2_midsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
        & m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => r2_midsp_1(A,B,B) ) ),
    file(midsp_1,r2_midsp_1),
    []).

fof(symmetry_r2_midsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
        & m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) )
     => ( r2_midsp_1(A,B,C)
       => r2_midsp_1(A,C,B) ) ) ),
    file(midsp_1,r2_midsp_1),
    []).

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

fof(t21_midsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_midsp_1(A,B,B,C,C) ) ) ) ),
    file(midsp_1,t21_midsp_1),
    []).

fof(t24_midsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_midsp_1(A,B,C,D,D)
                   => B = C ) ) ) ) ) ),
    file(midsp_1,t24_midsp_1),
    []).

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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

fof(t41_midsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_midsp_1(A)
        & l1_midsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
             => ( r2_hidden(B,k8_midsp_1(A,C))
              <=> r2_midsp_1(A,B,C) ) ) ) ) ),
    file(midsp_1,t41_midsp_1),
    []).

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(t7_mcart_1,axiom,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    []).

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