fof(l37_altcat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( v2_altcat_1(k7_altcat_1(A))
        & v11_altcat_1(k7_altcat_1(A))
        & v12_altcat_1(k7_altcat_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_1,d16_altcat_1,t5_altcat_1,d16_altcat_1,d7_altcat_1,d17_altcat_1,d16_altcat_1,d16_altcat_1,d16_altcat_1,d4_altcat_1,d4_altcat_1,d4_altcat_1,t121_funct_2,d10_altcat_1,t18_altcat_1,d10_altcat_1,t18_altcat_1,d10_altcat_1,t18_altcat_1,t55_relat_1,t18_altcat_1,d10_altcat_1,d9_altcat_1,d16_altcat_1,t2_altcat_1,d16_altcat_1,t121_funct_2,t2_altcat_1,d10_altcat_1,t18_altcat_1,t23_funct_2,d18_altcat_1,d8_altcat_1,d16_altcat_1,t2_altcat_1,d16_altcat_1,t121_funct_2,t2_altcat_1,d10_altcat_1,t18_altcat_1,t23_funct_2]),
    [file(altcat_1,l37_altcat_1),interesting(1.00)]).

fof(t11_altcat_1,theorem,(
    ! [A,B,C] : k9_funct_2(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C) ),
    inference(mizar_proof,[status(thm)],[t35_zfmisc_1,t5_cqc_lang,d1_funct_2,t11_relset_1,d5_funct_2]),
    [file(altcat_1,t11_altcat_1),interesting(0.81)]).

fof(t12_altcat_1,theorem,(
    ! [A,B,C] : k1_binop_1(k9_funct_2(A,B,C),A,B) = C ),
    inference(mizar_proof,[status(thm)],[t11_altcat_1,t6_cqc_lang]),
    [file(altcat_1,t12_altcat_1),interesting(0.81)]).

fof(t3_altcat_1,theorem,(
    k1_funct_2(k1_xboole_0,k1_xboole_0) = k1_tarski(k6_relat_1(k1_xboole_0)) ),
    inference(mizar_proof,[status(thm)],[t121_funct_2,d4_relat_1,d1_funct_2,d1_funct_2,d10_relat_1,d1_tarski,d3_tarski,d10_xboole_0,t2_altcat_1,t37_zfmisc_1]),
    [file(altcat_1,t3_altcat_1),interesting(0.76)]).

fof(t2_altcat_1,theorem,(
    ! [A] : r2_hidden(k6_relat_1(A),k1_funct_2(A,A)) ),
    inference(mizar_proof,[status(thm)],[t71_relat_1,d2_funct_2]),
    [file(altcat_1,t2_altcat_1),interesting(0.75)]).

fof(t14_altcat_1,theorem,(
    ! [A,B,C] : r1_tarski(k2_relat_1(k6_altcat_1(k1_funct_2(A,B),k1_funct_2(B,C))),k1_funct_2(A,C)) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_funct_1,d11_altcat_1,d3_pboole,t106_zfmisc_1,t4_altcat_1]),
    [file(altcat_1,t14_altcat_1),interesting(0.75)]).

fof(t27_altcat_1,theorem,
    ( v14_altcat_1(k7_altcat_1(1))
    & v3_realset2(k7_altcat_1(1)) ),
    inference(mizar_proof,[status(thm)],[d16_altcat_1,t1_card_5,d1_tarski,d16_altcat_1,t3_altcat_1,d21_altcat_1,d7_realset2,d1_tarski]),
    [file(altcat_1,t27_altcat_1),interesting(0.68)]).

fof(t5_altcat_1,theorem,(
    ! [A,B,C] : ~ ( k1_funct_2(A,B) != k1_xboole_0
      & k1_funct_2(B,C) != k1_xboole_0
      & k1_funct_2(A,C) = k1_xboole_0 ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d1_xboole_0,t121_funct_2,t121_funct_2,t4_altcat_1]),
    [file(altcat_1,t5_altcat_1),interesting(0.67)]).

fof(t4_altcat_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( ( r2_hidden(D,k1_funct_2(A,B))
              & r2_hidden(E,k1_funct_2(B,C)) )
           => r2_hidden(k5_relat_1(D,E),k1_funct_2(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_relat_1,d2_funct_2,t46_relat_1,t1_xboole_1,d2_funct_2]),
    [file(altcat_1,t4_altcat_1),interesting(0.61)]).

fof(t8_altcat_1,theorem,(
    ! [A,B,C] : 
      ( m1_pboole(C,k2_zfmisc_1(A,B))
     => ! [D] : 
          ( m1_pboole(D,k2_zfmisc_1(A,B))
         => ( ! [E,F] : 
                ( ( r2_hidden(E,A)
                  & r2_hidden(F,B) )
               => k1_binop_1(C,E,F) = k1_binop_1(D,E,F) )
           => r6_pboole(k2_zfmisc_1(A,B),D,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t113_zfmisc_1,t9_domain_1,t9_funct_1]),
    [file(altcat_1,t8_altcat_1),interesting(0.59)]).

fof(t15_altcat_1,theorem,(
    ! [A] : k6_altcat_1(k1_tarski(k6_relat_1(A)),k1_tarski(k6_relat_1(A))) = k9_funct_2(k6_relat_1(A),k6_relat_1(A),k6_relat_1(A)) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d3_tarski,d5_funct_1,d11_altcat_1,t106_zfmisc_1,d1_tarski,t43_funct_1,d1_tarski,d1_funct_2,t11_relset_1,d5_funct_2]),
    [file(altcat_1,t15_altcat_1),interesting(0.56)]).

fof(t23_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_hidden(k8_altcat_1(A,B),k1_altcat_1(A,B,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_altcat_1]),
    [file(altcat_1,t23_altcat_1),interesting(0.56)]).

fof(t21_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_altcat_1(A,B,B) != k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[d18_altcat_1,d9_altcat_1]),
    [file(altcat_1,t21_altcat_1),interesting(0.55)]).

fof(s1_altcat_1,theorem,(
    ? [A] : 
      ( m1_pboole(A,k2_zfmisc_1(f1_s1_altcat_1,f2_s1_altcat_1))
      & ! [B,C] : 
          ( ( r2_hidden(B,f1_s1_altcat_1)
            & r2_hidden(C,f2_s1_altcat_1) )
         => k1_binop_1(A,B,C) = f3_s1_altcat_1(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d3_pboole,t106_zfmisc_1,t7_mcart_1]),
    [file(altcat_1,s1_altcat_1),interesting(0.54)]).

fof(s3_altcat_1,theorem,(
    ? [A] : 
      ( m1_pboole(A,k3_zfmisc_1(f1_s3_altcat_1,f2_s3_altcat_1,f3_s3_altcat_1))
      & ! [B,C,D] : 
          ( ( r2_hidden(B,f1_s3_altcat_1)
            & r2_hidden(C,f2_s3_altcat_1)
            & r2_hidden(D,f3_s3_altcat_1) )
         => k1_multop_1(A,B,C,D) = f4_s3_altcat_1(B,C,D) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,d3_pboole,t73_mcart_1,t7_mcart_1,t7_mcart_1,d3_mcart_1,d1_multop_1]),
    [file(altcat_1,s3_altcat_1),interesting(0.49)]).

fof(t10_altcat_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,k3_zfmisc_1(A,A,A))
     => ! [C] : 
          ( m1_pboole(C,k3_zfmisc_1(A,A,A))
         => ( ! [D,E,F] : 
                ( ( r2_hidden(D,A)
                  & r2_hidden(E,A)
                  & r2_hidden(F,A) )
               => k1_multop_1(B,D,E,F) = k1_multop_1(C,D,E,F) )
           => r6_pboole(k3_zfmisc_1(A,A,A),C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t35_mcart_1,t15_domain_1,d1_multop_1,d1_multop_1,t9_funct_1]),
    [file(altcat_1,t10_altcat_1),interesting(0.49)]).

fof(t16_altcat_1,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( v1_fraenkel(B)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(B))
                 => k6_altcat_1(C,D) = k7_relat_1(k6_altcat_1(A,B),k12_mcart_1(B,A,D,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t91_relat_1,d3_pboole,d11_altcat_1,t72_funct_1,d11_altcat_1,d12_altcat_1]),
    [file(altcat_1,t16_altcat_1),interesting(0.47)]).

fof(t9_altcat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_pboole(C,k2_zfmisc_1(A,B))
             => ! [D] : 
                  ( m1_pboole(D,k2_zfmisc_1(A,B))
                 => ( ! [E] : 
                        ( m1_subset_1(E,A)
                       => ! [F] : 
                            ( m1_subset_1(F,B)
                           => k1_binop_1(C,E,F) = k1_binop_1(D,E,F) ) )
                   => r6_pboole(k2_zfmisc_1(A,B),D,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_altcat_1]),
    [file(altcat_1,t9_altcat_1),interesting(0.46)]).

fof(s2_altcat_1,theorem,(
    ? [A] : 
      ( m1_pboole(A,k2_zfmisc_1(f1_s2_altcat_1,f2_s2_altcat_1))
      & ! [B] : 
          ( m1_subset_1(B,f1_s2_altcat_1)
         => ! [C] : 
              ( m1_subset_1(C,f2_s2_altcat_1)
             => k1_binop_1(A,B,C) = f3_s2_altcat_1(B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_altcat_1]),
    [file(altcat_1,s2_altcat_1),interesting(0.44)]).

fof(t26_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v14_altcat_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => k1_altcat_1(A,B,B) = k1_tarski(k8_altcat_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_altcat_1,d21_altcat_1,d4_realset1,d1_tarski,t23_altcat_1,d1_tarski,d21_altcat_1]),
    [file(altcat_1,t26_altcat_1),interesting(0.43)]).

fof(s4_altcat_1,theorem,(
    ? [A] : 
      ( m1_pboole(A,k3_zfmisc_1(f1_s4_altcat_1,f2_s4_altcat_1,f3_s4_altcat_1))
      & ! [B] : 
          ( m1_subset_1(B,f1_s4_altcat_1)
         => ! [C] : 
              ( m1_subset_1(C,f2_s4_altcat_1)
             => ! [D] : 
                  ( m1_subset_1(D,f3_s4_altcat_1)
                 => k1_multop_1(A,B,C,D) = f4_s4_altcat_1(B,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s3_altcat_1]),
    [file(altcat_1,s4_altcat_1),interesting(0.39)]).

fof(t24_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_altcat_1(A,B,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => k5_altcat_1(A,B,C,C,D,k8_altcat_1(A,C)) = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_altcat_1,d9_altcat_1,t23_altcat_1,d19_altcat_1,d10_altcat_1,d10_altcat_1]),
    [file(altcat_1,t24_altcat_1),interesting(0.37)]).

fof(t7_altcat_1,theorem,(
    ! [A,B,C] : 
      ( m1_pboole(C,k2_zfmisc_1(B,A))
     => ! [D] : 
          ( m1_subset_1(D,k1_zfmisc_1(A))
         => ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(B))
             => ! [F,G] : 
                  ( ( r2_hidden(F,D)
                    & r2_hidden(G,E) )
                 => k1_binop_1(C,G,F) = k1_binop_1(k7_relat_1(C,k12_mcart_1(B,A,E,D)),G,F) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,t72_funct_1]),
    [file(altcat_1,t7_altcat_1),interesting(0.32)]).

fof(t13_altcat_1,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( v1_fraenkel(B)
         => ! [C] : 
              ( ( v7_altcat_1(C)
                & m1_pboole(C,k2_zfmisc_1(A,B)) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( ( r2_hidden(D,A)
                          & r2_hidden(E,B) )
                       => k1_binop_1(C,D,E) = k5_relat_1(E,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t106_zfmisc_1,d11_altcat_1,t33_zfmisc_1]),
    [file(altcat_1,t13_altcat_1),interesting(0.31)]).

fof(t28_altcat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k9_altcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k9_altcat_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k9_altcat_1(A)))
                 => ( ~ ( B = C
                        & C = D )
                   => k4_altcat_1(u1_struct_0(k9_altcat_1(A)),u1_altcat_1(k9_altcat_1(A)),u2_altcat_1(k9_altcat_1(A)),B,C,D) = k1_xboole_0 ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d20_altcat_1,t113_zfmisc_1,d1_funct_2,t64_relat_1]),
    [file(altcat_1,t28_altcat_1),interesting(0.26)]).

fof(t29_altcat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k9_altcat_1(A)))
         => k4_altcat_1(u1_struct_0(k9_altcat_1(A)),u1_altcat_1(k9_altcat_1(A)),u2_altcat_1(k9_altcat_1(A)),B,B,B) = k9_funct_2(k6_relat_1(B),k6_relat_1(B),k6_relat_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d22_altcat_1,d5_funct_2]),
    [file(altcat_1,t29_altcat_1),interesting(0.23)]).

fof(t18_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_altcat_1(A)
        & l2_altcat_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))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & k1_altcat_1(A,B,D) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & ? [G] : 
                                  ( v1_relat_1(G)
                                  & v1_funct_1(G)
                                  & ? [H] : 
                                      ( v1_relat_1(H)
                                      & v1_funct_1(H)
                                      & E = G
                                      & F = H
                                      & k5_altcat_1(A,B,C,D,E,F) != k5_relat_1(G,H) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_altcat_1,t89_relat_1,d1_funct_2,t106_zfmisc_1,d11_altcat_1,t33_zfmisc_1,d10_altcat_1,t72_funct_1]),
    [file(altcat_1,t18_altcat_1),interesting(0.20)]).

fof(t25_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & l2_altcat_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))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                          & k1_altcat_1(A,C,D) != k1_xboole_0
                          & k1_altcat_1(A,D,E) != k1_xboole_0
                          & ~ ! [F] : 
                                ( m1_subset_1(F,k1_altcat_1(A,B,C))
                               => ! [G] : 
                                    ( m1_subset_1(G,k1_altcat_1(A,C,D))
                                   => ! [H] : 
                                        ( m1_subset_1(H,k1_altcat_1(A,D,E))
                                       => k5_altcat_1(A,B,D,E,k5_altcat_1(A,B,C,D,F,G),H) = k5_altcat_1(A,B,C,E,F,k5_altcat_1(A,C,D,E,G,H)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_altcat_1,d4_altcat_1,d10_altcat_1,d4_altcat_1,d10_altcat_1,d10_altcat_1,d7_altcat_1,d10_altcat_1]),
    [file(altcat_1,t25_altcat_1),interesting(0.10)]).

fof(d4_altcat_1,definition,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ( v2_altcat_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))
                   => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                        & k1_altcat_1(A,C,D) != k1_xboole_0
                        & k1_altcat_1(A,B,D) = k1_xboole_0 ) ) ) ) ) ) ),
    file(altcat_1,d4_altcat_1),
    [interesting(0.00)]).

fof(d16_altcat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_altcat_1(B)
            & v10_altcat_1(B)
            & l2_altcat_1(B) )
         => ( B = k7_altcat_1(A)
          <=> ( u1_struct_0(B) = A
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(B))
                     => k1_altcat_1(B,C,D) = k1_funct_2(C,D) ) ) ) ) ) ) ),
    file(altcat_1,d16_altcat_1),
    [interesting(0.00)]).

fof(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.00)]).

fof(t121_funct_2,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,k1_funct_2(A,B))
     => ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) ) ) ),
    file(funct_2,t121_funct_2),
    [interesting(0.00)]).

fof(t45_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)) ) ) ),
    file(relat_1,t45_relat_1),
    [interesting(0.00)]).

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.00)]).

fof(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(d7_altcat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,k2_zfmisc_1(A,A))
         => ! [C] : 
              ( m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B))
             => ( v3_altcat_1(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => ! [F] : 
                            ( m1_subset_1(F,A)
                           => ! [G] : 
                                ( m1_subset_1(G,A)
                               => ! [H,I,J] : 
                                    ( ( r2_hidden(H,k1_binop_1(B,D,E))
                                      & r2_hidden(I,k1_binop_1(B,E,F))
                                      & r2_hidden(J,k1_binop_1(B,F,G)) )
                                   => k1_binop_1(k4_altcat_1(A,B,C,D,F,G),J,k1_binop_1(k4_altcat_1(A,B,C,D,E,F),I,H)) = k1_binop_1(k4_altcat_1(A,B,C,D,E,G),k1_binop_1(k4_altcat_1(A,B,C,E,F,G),J,I),H) ) ) ) ) ) ) ) ) ) ),
    file(altcat_1,d7_altcat_1),
    [interesting(0.00)]).

fof(d17_altcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ( v11_altcat_1(A)
      <=> v3_altcat_1(u2_altcat_1(A),u1_struct_0(A),u1_altcat_1(A)) ) ) ),
    file(altcat_1,d17_altcat_1),
    [interesting(0.00)]).

fof(d10_altcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_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))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & ~ ! [E] : 
                            ( m1_subset_1(E,k1_altcat_1(A,B,C))
                           => ! [F] : 
                                ( m1_subset_1(F,k1_altcat_1(A,C,D))
                               => k5_altcat_1(A,B,C,D,E,F) = k1_binop_1(k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),B,C,D),F,E) ) ) ) ) ) ) ) ),
    file(altcat_1,d10_altcat_1),
    [interesting(0.00)]).

fof(d15_altcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ( v10_altcat_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))
                   => k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),B,C,D) = k7_relat_1(k6_altcat_1(k1_funct_2(B,C),k1_funct_2(C,D)),k2_zfmisc_1(k1_altcat_1(A,C,D),k1_altcat_1(A,B,C))) ) ) ) ) ) ),
    file(altcat_1,d15_altcat_1),
    [interesting(0.00)]).

fof(t89_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) ) ),
    file(relat_1,t89_relat_1),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(d11_altcat_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v7_altcat_1(A)
      <=> ! [B] : ~ ( r2_hidden(B,k1_relat_1(A))
            & ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ! [D] : 
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D) )
                   => ~ ( B = k4_tarski(D,C)
                        & k1_funct_1(A,B) = k5_relat_1(C,D) ) ) ) ) ) ) ),
    file(altcat_1,d11_altcat_1),
    [interesting(0.00)]).

fof(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    [interesting(0.00)]).

fof(t72_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t72_funct_1),
    [interesting(0.00)]).

fof(t55_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ),
    file(relat_1,t55_relat_1),
    [interesting(0.00)]).

fof(d9_altcat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,k2_zfmisc_1(A,A))
         => ! [C] : 
              ( m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B))
             => ( v5_altcat_1(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ? [E] : 
                        ( r2_hidden(E,k1_binop_1(B,D,D))
                        & ! [F] : 
                            ( m1_subset_1(F,A)
                           => ! [G] : 
                                ( r2_hidden(G,k1_binop_1(B,F,D))
                               => k1_binop_1(k4_altcat_1(A,B,C,F,D,D),E,G) = G ) ) ) ) ) ) ) ) ),
    file(altcat_1,d9_altcat_1),
    [interesting(0.00)]).

fof(t71_relat_1,theorem,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    [interesting(0.00)]).

fof(t23_funct_2,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ),
    file(funct_2,t23_funct_2),
    [interesting(0.00)]).

fof(d18_altcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ( v12_altcat_1(A)
      <=> ( v5_altcat_1(u2_altcat_1(A),u1_struct_0(A),u1_altcat_1(A))
          & v4_altcat_1(u2_altcat_1(A),u1_struct_0(A),u1_altcat_1(A)) ) ) ) ),
    file(altcat_1,d18_altcat_1),
    [interesting(0.00)]).

fof(d8_altcat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,k2_zfmisc_1(A,A))
         => ! [C] : 
              ( m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B))
             => ( v4_altcat_1(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ? [E] : 
                        ( r2_hidden(E,k1_binop_1(B,D,D))
                        & ! [F] : 
                            ( m1_subset_1(F,A)
                           => ! [G] : 
                                ( r2_hidden(G,k1_binop_1(B,D,F))
                               => k1_binop_1(k4_altcat_1(A,B,C,D,D,F),G,E) = G ) ) ) ) ) ) ) ) ),
    file(altcat_1,d8_altcat_1),
    [interesting(0.00)]).

fof(s3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s3_funct_1
      & ! [B] : 
          ( r2_hidden(B,f1_s3_funct_1)
         => k1_funct_1(A,B) = f2_s3_funct_1(B) ) ) ),
    file(funct_1,s3_funct_1),
    [interesting(0.00)]).

fof(d3_pboole,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    [interesting(0.00)]).

fof(t7_mcart_1,theorem,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    [interesting(0.00)]).

fof(t73_mcart_1,theorem,(
    ! [A,B,C,D,E,F] : 
      ( r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F))
    <=> ( r2_hidden(A,D)
        & r2_hidden(B,E)
        & r2_hidden(C,F) ) ) ),
    file(mcart_1,t73_mcart_1),
    [interesting(0.00)]).

fof(d3_mcart_1,definition,(
    ! [A,B,C] : k3_mcart_1(A,B,C) = k4_tarski(k4_tarski(A,B),C) ),
    file(mcart_1,d3_mcart_1),
    [interesting(0.00)]).

fof(d1_multop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D] : k1_multop_1(A,B,C,D) = k1_funct_1(A,k3_mcart_1(B,C,D)) ) ),
    file(multop_1,d1_multop_1),
    [interesting(0.00)]).

fof(t35_mcart_1,theorem,(
    ! [A,B,C] : 
      ( ( A != k1_xboole_0
        & B != k1_xboole_0
        & C != k1_xboole_0 )
    <=> k3_zfmisc_1(A,B,C) != k1_xboole_0 ) ),
    file(mcart_1,t35_mcart_1),
    [interesting(0.00)]).

fof(t15_domain_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ! [D] : 
              ( ~ v1_xboole_0(D)
             => ( r2_hidden(A,k3_zfmisc_1(B,C,D))
              <=> ? [E] : 
                    ( m1_subset_1(E,B)
                    & ? [F] : 
                        ( m1_subset_1(F,C)
                        & ? [G] : 
                            ( m1_subset_1(G,D)
                            & A = k3_mcart_1(E,F,G) ) ) ) ) ) ) ) ),
    file(domain_1,t15_domain_1),
    [interesting(0.00)]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(t35_zfmisc_1,theorem,(
    ! [A,B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) ),
    file(zfmisc_1,t35_zfmisc_1),
    [interesting(0.00)]).

fof(t5_cqc_lang,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
      & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ),
    file(cqc_lang,t5_cqc_lang),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

fof(d5_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C))
        & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) )
     => D = k9_funct_2(A,B,C) ) ),
    file(funct_2,d5_funct_2),
    [interesting(0.00)]).

fof(t6_cqc_lang,theorem,(
    ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ),
    file(cqc_lang,t6_cqc_lang),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(t43_funct_1,theorem,(
    ! [A,B] : k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B)) ),
    file(funct_1,t43_funct_1),
    [interesting(0.00)]).

fof(t91_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    [interesting(0.00)]).

fof(d12_altcat_1,definition,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( v1_fraenkel(B)
         => ! [C] : 
              ( ( v1_funcop_1(C)
                & v7_altcat_1(C)
                & m1_pboole(C,k2_zfmisc_1(B,A)) )
             => C = k6_altcat_1(A,B) ) ) ) ),
    file(altcat_1,d12_altcat_1),
    [interesting(0.00)]).

fof(t17_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_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))
                 => ( v1_funct_1(k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),B,C,D))
                    & v1_funct_2(k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),B,C,D),k2_zfmisc_1(k1_altcat_1(A,C,D),k1_altcat_1(A,B,C)),k1_altcat_1(A,B,D))
                    & m2_relset_1(k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),B,C,D),k2_zfmisc_1(k1_altcat_1(A,C,D),k1_altcat_1(A,B,C)),k1_altcat_1(A,B,D)) ) ) ) ) ) ),
    file(altcat_1,t17_altcat_1),
    [interesting(0.00)]).

fof(t19_altcat_1,theorem,(
    $true ),
    file(altcat_1,t19_altcat_1),
    [interesting(0.00)]).

fof(t1_altcat_1,theorem,(
    $true ),
    file(altcat_1,t1_altcat_1),
    [interesting(0.00)]).

fof(t113_zfmisc_1,theorem,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) ),
    file(zfmisc_1,t113_zfmisc_1),
    [interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(t20_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_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))
                 => ( k1_relat_1(k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),B,C,D)) = k2_zfmisc_1(k1_altcat_1(A,C,D),k1_altcat_1(A,B,C))
                    & r1_tarski(k2_relat_1(k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),B,C,D)),k1_altcat_1(A,B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_1,t113_zfmisc_1,d1_funct_2,t12_relset_1]),
    [file(altcat_1,t20_altcat_1),interesting(0.00)]).

fof(t22_altcat_1,theorem,(
    $true ),
    file(altcat_1,t22_altcat_1),
    [interesting(0.00)]).

fof(d19_altcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_altcat_1(A,B,B))
             => ( C = k8_altcat_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( k1_altcat_1(A,B,D) != k1_xboole_0
                     => ! [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,D))
                         => k5_altcat_1(A,B,B,D,C,E) = E ) ) ) ) ) ) ) ),
    file(altcat_1,d19_altcat_1),
    [interesting(0.00)]).

fof(d21_altcat_1,definition,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( v14_altcat_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => v1_realset1(k1_altcat_1(A,B,B)) ) ) ) ),
    file(altcat_1,d21_altcat_1),
    [interesting(0.00)]).

fof(d4_realset1,definition,(
    ! [A] : 
      ( v1_realset1(A)
    <=> ~ ( ~ v1_xboole_0(A)
          & ! [B] : A != k1_tarski(B) ) ) ),
    file(realset1,d4_realset1),
    [interesting(0.00)]).

fof(t1_card_5,theorem,
    ( 1 = k1_tarski(0)
    & 2 = k2_tarski(0,1) ),
    file(card_5,t1_card_5),
    [interesting(0.00)]).

fof(d4_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_1),
    [interesting(0.00)]).

fof(d10_relat_1,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k6_relat_1(A)
      <=> ! [C,D] : 
            ( r2_hidden(k4_tarski(C,D),B)
          <=> ( r2_hidden(C,A)
              & C = D ) ) ) ) ),
    file(relat_1,d10_relat_1),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.00)]).

fof(d7_realset2,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_realset2(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) ) ),
    file(realset2,d7_realset2),
    [interesting(0.00)]).

fof(d20_altcat_1,definition,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( v13_altcat_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( k1_altcat_1(A,B,C) != k1_xboole_0
                 => B = C ) ) ) ) ) ),
    file(altcat_1,d20_altcat_1),
    [interesting(0.00)]).

fof(t64_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) ),
    file(relat_1,t64_relat_1),
    [interesting(0.00)]).

fof(d22_altcat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_altcat_1(B)
            & v13_altcat_1(B)
            & l2_altcat_1(B) )
         => ( B = k9_altcat_1(A)
          <=> ( u1_struct_0(B) = A
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(B))
                 => k1_altcat_1(B,C,C) = k1_tarski(k6_relat_1(C)) ) ) ) ) ) ),
    file(altcat_1,d22_altcat_1),
    [interesting(0.00)]).

fof(t6_altcat_1,theorem,(
    $true ),
    file(altcat_1,t6_altcat_1),
    [interesting(0.00)]).

fof(t9_domain_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ~ ( r2_hidden(A,k2_zfmisc_1(B,C))
              & ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( m1_subset_1(E,C)
                     => A != k4_tarski(D,E) ) ) ) ) ) ),
    file(domain_1,t9_domain_1),
    [interesting(0.00)]).