% Mizar problem: t25_fuzzy_2,fuzzy_2,269,25 
fof(t25_fuzzy_2,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_fuzzy_1(B,A)
         => ! [C] : 
              ( m1_fuzzy_1(C,A)
             => r1_fuzzy_1(k6_fuzzy_1(A,B,C),k1_fuzzy_2(A,k2_fuzzy_1(A,B,C),k1_fuzzy_1(A,B,C))) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,commutativity_k1_fuzzy_1,commutativity_k1_square_1,commutativity_k2_fuzzy_1,commutativity_k2_square_1,commutativity_k3_square_1,commutativity_k4_square_1,commutativity_k6_fuzzy_1,connectedness_r1_xreal_0,d1_fuzzy_2,d3_fuzzy_1,d9_fuzzy_1,dt_k1_funct_1,dt_k1_fuzzy_1,dt_k1_fuzzy_2,dt_k1_numbers,dt_k1_square_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_fuzzy_1,dt_k2_seq_1,dt_k2_square_1,dt_k2_zfmisc_1,dt_k3_fuzzy_1,dt_k3_square_1,dt_k4_square_1,dt_k6_fuzzy_1,dt_m1_fuzzy_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,existence_m1_fuzzy_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc2_membered,fc6_membered,idempotence_k1_fuzzy_1,idempotence_k1_square_1,idempotence_k2_fuzzy_1,idempotence_k2_square_1,idempotence_k3_square_1,idempotence_k4_square_1,involutiveness_k3_fuzzy_1,rc1_membered,redefinition_k2_seq_1,redefinition_k3_square_1,redefinition_k4_square_1,redefinition_m2_relset_1,redefinition_r2_fuzzy_1,reflexivity_r1_fuzzy_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r2_fuzzy_1,t10_fuzzy_1,t12_fuzzy_1,t1_subset,t2_subset,t3_subset,t46_square_1,t4_subset,t5_subset,t6_boole,t6_fuzzy_1,t7_boole,t8_boole,t8_fuzzy_1]),
    [file(fuzzy_2,t25_fuzzy_2)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

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(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(cc6_membered,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    []).

fof(commutativity_k1_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => k1_fuzzy_1(A,B,C) = k1_fuzzy_1(A,C,B) ) ),
    file(fuzzy_1,k1_fuzzy_1),
    []).

fof(commutativity_k1_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => k1_square_1(A,B) = k1_square_1(B,A) ) ),
    file(square_1,k1_square_1),
    []).

fof(commutativity_k2_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => k2_fuzzy_1(A,B,C) = k2_fuzzy_1(A,C,B) ) ),
    file(fuzzy_1,k2_fuzzy_1),
    []).

fof(commutativity_k2_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => k2_square_1(A,B) = k2_square_1(B,A) ) ),
    file(square_1,k2_square_1),
    []).

fof(commutativity_k3_square_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_square_1(A,B) = k3_square_1(B,A) ) ),
    file(square_1,k3_square_1),
    []).

fof(commutativity_k4_square_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_square_1(A,B) = k4_square_1(B,A) ) ),
    file(square_1,k4_square_1),
    []).

fof(commutativity_k6_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => k6_fuzzy_1(A,B,C) = k6_fuzzy_1(A,C,B) ) ),
    file(fuzzy_1,k6_fuzzy_1),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d1_fuzzy_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_fuzzy_1(B,A)
         => ! [C] : 
              ( m1_fuzzy_1(C,A)
             => k1_fuzzy_2(A,B,C) = k1_fuzzy_1(A,B,k3_fuzzy_1(A,C)) ) ) ) ),
    file(fuzzy_2,d1_fuzzy_2),
    []).

fof(d3_fuzzy_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_fuzzy_1(B,A)
         => ! [C] : 
              ( m1_fuzzy_1(C,A)
             => ( r2_fuzzy_1(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => r1_xreal_0(k2_seq_1(A,k1_numbers,B,D),k2_seq_1(A,k1_numbers,C,D)) ) ) ) ) ) ),
    file(fuzzy_1,d3_fuzzy_1),
    []).

fof(d9_fuzzy_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_fuzzy_1(B,A)
         => ! [C] : 
              ( m1_fuzzy_1(C,A)
             => k6_fuzzy_1(A,B,C) = k2_fuzzy_1(A,k1_fuzzy_1(A,B,k3_fuzzy_1(A,C)),k1_fuzzy_1(A,k3_fuzzy_1(A,B),C)) ) ) ) ),
    file(fuzzy_1,d9_fuzzy_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => m1_fuzzy_1(k1_fuzzy_1(A,B,C),A) ) ),
    file(fuzzy_1,k1_fuzzy_1),
    []).

fof(dt_k1_fuzzy_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => m1_fuzzy_1(k1_fuzzy_2(A,B,C),A) ) ),
    file(fuzzy_2,k1_fuzzy_2),
    []).

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

fof(dt_k1_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => v1_xreal_0(k1_square_1(A,B)) ) ),
    file(square_1,k1_square_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_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => m1_fuzzy_1(k2_fuzzy_1(A,B,C),A) ) ),
    file(fuzzy_1,k2_fuzzy_1),
    []).

fof(dt_k2_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_seq_1(A,B,C,D),k1_numbers) ) ),
    file(seq_1,k2_seq_1),
    []).

fof(dt_k2_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => v1_xreal_0(k2_square_1(A,B)) ) ),
    file(square_1,k2_square_1),
    []).

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

fof(dt_k3_fuzzy_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A) )
     => m1_fuzzy_1(k3_fuzzy_1(A,B),A) ) ),
    file(fuzzy_1,k3_fuzzy_1),
    []).

fof(dt_k3_square_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k3_square_1(A,B),k1_numbers) ) ),
    file(square_1,k3_square_1),
    []).

fof(dt_k4_square_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k4_square_1(A,B),k1_numbers) ) ),
    file(square_1,k4_square_1),
    []).

fof(dt_k6_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => m1_fuzzy_1(k6_fuzzy_1(A,B,C),A) ) ),
    file(fuzzy_1,k6_fuzzy_1),
    []).

fof(dt_m1_fuzzy_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_fuzzy_1(B,A)
         => ( v1_funct_1(B)
            & m2_relset_1(B,A,k1_numbers) ) ) ) ),
    file(fuzzy_1,m1_fuzzy_1),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m1_fuzzy_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_fuzzy_1(B,A) ) ),
    file(fuzzy_1,m1_fuzzy_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc2_membered,axiom,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    []).

fof(fc6_membered,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    []).

fof(idempotence_k1_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => k1_fuzzy_1(A,B,B) = B ) ),
    file(fuzzy_1,k1_fuzzy_1),
    []).

fof(idempotence_k1_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => k1_square_1(A,A) = A ) ),
    file(square_1,k1_square_1),
    []).

fof(idempotence_k2_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => k2_fuzzy_1(A,B,B) = B ) ),
    file(fuzzy_1,k2_fuzzy_1),
    []).

fof(idempotence_k2_square_1,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => k2_square_1(A,A) = A ) ),
    file(square_1,k2_square_1),
    []).

fof(idempotence_k3_square_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_square_1(A,A) = A ) ),
    file(square_1,k3_square_1),
    []).

fof(idempotence_k4_square_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_square_1(A,A) = A ) ),
    file(square_1,k4_square_1),
    []).

fof(involutiveness_k3_fuzzy_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A) )
     => k3_fuzzy_1(A,k3_fuzzy_1(A,B)) = B ) ),
    file(fuzzy_1,k3_fuzzy_1),
    []).

fof(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(redefinition_k2_seq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v2_membered(B)
        & v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_seq_1(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(seq_1,k2_seq_1),
    []).

fof(redefinition_k3_square_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_square_1(A,B) = k1_square_1(A,B) ) ),
    file(square_1,k3_square_1),
    []).

fof(redefinition_k4_square_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_square_1(A,B) = k2_square_1(A,B) ) ),
    file(square_1,k4_square_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_r2_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => ( r2_fuzzy_1(A,B,C)
      <=> r1_fuzzy_1(B,C) ) ) ),
    file(fuzzy_1,r2_fuzzy_1),
    []).

fof(reflexivity_r1_fuzzy_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_seq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_seq_1(B) )
     => r1_fuzzy_1(A,A) ) ),
    file(fuzzy_1,r1_fuzzy_1),
    []).

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

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(reflexivity_r2_fuzzy_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_fuzzy_1(B,A)
        & m1_fuzzy_1(C,A) )
     => r2_fuzzy_1(A,B,B) ) ),
    file(fuzzy_1,r2_fuzzy_1),
    []).

fof(t10_fuzzy_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_fuzzy_1(B,A)
         => ! [C] : 
              ( m1_fuzzy_1(C,A)
             => ! [D] : 
                  ( m1_fuzzy_1(D,A)
                 => ( k1_fuzzy_1(A,B,k2_fuzzy_1(A,C,D)) = k2_fuzzy_1(A,k1_fuzzy_1(A,B,C),k1_fuzzy_1(A,B,D))
                    & k2_fuzzy_1(A,B,k1_fuzzy_1(A,C,D)) = k1_fuzzy_1(A,k2_fuzzy_1(A,B,C),k2_fuzzy_1(A,B,D)) ) ) ) ) ) ),
    file(fuzzy_1,t10_fuzzy_1),
    []).

fof(t12_fuzzy_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_fuzzy_1(B,A)
         => ! [C] : 
              ( m1_fuzzy_1(C,A)
             => ( k3_fuzzy_1(A,k2_fuzzy_1(A,B,C)) = k1_fuzzy_1(A,k3_fuzzy_1(A,B),k3_fuzzy_1(A,C))
                & k3_fuzzy_1(A,k1_fuzzy_1(A,B,C)) = k2_fuzzy_1(A,k3_fuzzy_1(A,B),k3_fuzzy_1(A,C)) ) ) ) ) ),
    file(fuzzy_1,t12_fuzzy_1),
    []).

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

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

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

fof(t46_square_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => r1_xreal_0(A,k2_square_1(A,B)) ) ) ),
    file(square_1,t46_square_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(t6_fuzzy_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_fuzzy_1(C,A)
             => ! [D] : 
                  ( m1_fuzzy_1(D,A)
                 => ( k3_square_1(k2_seq_1(A,k1_numbers,C,B),k2_seq_1(A,k1_numbers,D,B)) = k2_seq_1(A,k1_numbers,k1_fuzzy_1(A,C,D),B)
                    & k4_square_1(k2_seq_1(A,k1_numbers,C,B),k2_seq_1(A,k1_numbers,D,B)) = k2_seq_1(A,k1_numbers,k2_fuzzy_1(A,C,D),B) ) ) ) ) ) ),
    file(fuzzy_1,t6_fuzzy_1),
    []).

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_fuzzy_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_fuzzy_1(B,A)
         => ! [C] : 
              ( m1_fuzzy_1(C,A)
             => ! [D] : 
                  ( m1_fuzzy_1(D,A)
                 => ( k2_fuzzy_1(A,k2_fuzzy_1(A,B,C),D) = k2_fuzzy_1(A,B,k2_fuzzy_1(A,C,D))
                    & k1_fuzzy_1(A,k1_fuzzy_1(A,B,C),D) = k1_fuzzy_1(A,B,k1_fuzzy_1(A,C,D)) ) ) ) ) ) ),
    file(fuzzy_1,t8_fuzzy_1),
    []).