fof(t17_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => v11_altcat_1(k6_altcat_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[t15_altcat_2,d17_altcat_1]),
    [file(altcat_2,t17_altcat_2),interesting(1.00)]).

fof(t18_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => v12_altcat_1(k6_altcat_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[t16_altcat_2,d18_altcat_1]),
    [file(altcat_2,t18_altcat_2),interesting(0.99)]).

fof(t15_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => v3_altcat_1(k5_altcat_2(A),u1_cat_1(A),k4_altcat_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d7_altcat_1,d3_altcat_2,d7_cat_1,d3_altcat_2,d7_cat_1,d3_altcat_2,d7_cat_1,t52_cat_1,t52_cat_1,t14_altcat_2,t14_altcat_2,t14_altcat_2,t54_cat_1,t14_altcat_2]),
    [file(altcat_2,t15_altcat_2),interesting(0.93)]).

fof(t21_altcat_2,theorem,(
    ! [A] : 
      ( l2_altcat_1(A)
     => m1_altcat_2(A,A) ) ),
    inference(mizar_proof,[status(thm)],[d11_altcat_2]),
    [file(altcat_2,t21_altcat_2),interesting(0.77)]).

fof(t16_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ( v5_altcat_1(k5_altcat_2(A),u1_cat_1(A),k4_altcat_2(A))
        & v4_altcat_1(k5_altcat_2(A),u1_cat_1(A),k4_altcat_2(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_altcat_1,t13_altcat_2,t56_cat_1,d3_altcat_2,d7_cat_1,t14_altcat_2,t57_cat_1,d8_altcat_1,t13_altcat_2,t56_cat_1,d3_altcat_2,d7_cat_1,t14_altcat_2,t58_cat_1]),
    [file(altcat_2,t16_altcat_2),interesting(0.73)]).

fof(t8_altcat_2,theorem,(
    ! [A,B,C] : 
      ( m1_pboole(C,A)
     => ! [D] : 
          ( m1_pboole(D,B)
         => ( ( r2_altcat_2(A,B,C,D)
              & r2_altcat_2(B,A,D,C) )
           => C = D ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_altcat_2,d10_xboole_0,d2_altcat_2,d10_xboole_0,t3_pboole]),
    [file(altcat_2,t8_altcat_2),interesting(0.65)]).

fof(t9_altcat_2,theorem,(
    ! [A,B,C,D] : 
      ( m1_pboole(D,A)
     => ! [E] : 
          ( m1_pboole(E,B)
         => ! [F] : 
              ( m1_pboole(F,C)
             => ( ( r2_altcat_2(A,B,D,E)
                  & r2_altcat_2(B,C,E,F) )
               => r2_altcat_2(A,C,D,F) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_altcat_2,d2_altcat_2,t1_xboole_1,d2_altcat_2,d2_altcat_2,t1_xboole_1]),
    [file(altcat_2,t9_altcat_2),interesting(0.62)]).

fof(t2_altcat_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => k2_funct_4(k5_relat_1(A,B)) = k5_relat_1(k2_funct_4(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_funct_1,d2_funct_4,t21_funct_1,d2_funct_4,t21_funct_1,t21_funct_1,t21_funct_1,d2_funct_4,d2_funct_4,t21_funct_1,t21_funct_1,t43_funct_4,t23_funct_1,t44_funct_4,t22_funct_1,d2_funct_4]),
    [file(altcat_2,t2_altcat_2),interesting(0.60)]).

fof(t19_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => v2_altcat_1(k6_altcat_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_1,d3_altcat_2,d3_altcat_2,d3_altcat_2,t52_cat_1]),
    [file(altcat_2,t19_altcat_2),interesting(0.59)]).

fof(s1_altcat_2,theorem,
    ( v1_relat_1(a_0_0_altcat_2)
    & v1_funct_1(a_0_0_altcat_2) ),
    inference(mizar_proof,[status(thm)],[d1_relat_1,d1_funct_1,t33_zfmisc_1,t33_zfmisc_1]),
    [file(altcat_2,s1_altcat_2),interesting(0.58)]).

fof(t22_altcat_2,theorem,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ! [B] : 
          ( l2_altcat_1(B)
         => ! [C] : 
              ( l2_altcat_1(C)
             => ( ( m1_altcat_2(A,B)
                  & m1_altcat_2(B,C) )
               => m1_altcat_2(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_altcat_2,t9_altcat_2,t1_xboole_1,d11_altcat_2]),
    [file(altcat_2,t22_altcat_2),interesting(0.58)]).

fof(l29_altcat_2,theorem,(
    ! [A] : 
      ( ( v6_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( v6_altcat_1(B)
            & l2_altcat_1(B) )
         => ( ( v1_xboole_0(u1_struct_0(A))
              & v1_xboole_0(u1_struct_0(B)) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t113_zfmisc_1,t113_zfmisc_1,t134_pboole,t134_pboole,t35_mcart_1,t35_mcart_1,t134_pboole,t134_pboole]),
    [file(altcat_2,l29_altcat_2),interesting(0.56)]).

fof(t30_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_altcat_2]),
    [file(altcat_2,t30_altcat_2),interesting(0.56)]).

fof(s2_altcat_2,theorem,
    ( f2_s2_altcat_2 = a_0_1_altcat_2
   => k1_relat_1(f2_s2_altcat_2) = a_0_2_altcat_2 ),
    inference(mizar_proof,[status(thm)],[t33_zfmisc_1,d4_relat_1]),
    [file(altcat_2,s2_altcat_2),interesting(0.55)]).

fof(t10_altcat_2,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_altcat_2(A,A,B,C)
          <=> r2_pboole(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_pboole,d2_altcat_2,d2_altcat_2,d5_pboole]),
    [file(altcat_2,t10_altcat_2),interesting(0.55)]).

fof(t20_altcat_2,theorem,(
    ! [A] : 
      ( ( v3_struct_0(A)
        & v6_altcat_1(A)
        & l2_altcat_1(A) )
     => A = k7_altcat_2 ) ),
    inference(mizar_proof,[status(thm)],[d1_struct_0,l29_altcat_2]),
    [file(altcat_2,t20_altcat_2),interesting(0.55)]).

fof(t23_altcat_2,theorem,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ! [B] : 
          ( l2_altcat_1(B)
         => ( ( m1_altcat_2(A,B)
              & m1_altcat_2(B,A) )
           => g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) = g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_altcat_2,t8_altcat_2,d10_xboole_0]),
    [file(altcat_2,t23_altcat_2),interesting(0.49)]).

fof(t26_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( ( u1_struct_0(B) = u1_struct_0(A)
              & u1_altcat_1(B) = u1_altcat_1(A) )
           => g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) = g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_struct_0,d4_altcat_1,d4_altcat_1,t21_altcat_2,t25_altcat_2,t23_altcat_2]),
    [file(altcat_2,t26_altcat_2),interesting(0.49)]).

fof(t4_altcat_2,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( r1_pzfmisc1(A,B,C)
               => ! [E] : 
                    ( m3_pboole(E,A,B,C)
                   => ! [F] : 
                        ( m3_pboole(F,A,C,D)
                       => m3_pboole(k13_pboole(E,F),A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_mssubfam,d18_pboole,d3_pzfmisc1,d18_pboole,d18_pboole,d3_pboole,d24_pboole,t19_funct_2]),
    [file(altcat_2,t4_altcat_2),interesting(0.49)]).

fof(t1_altcat_2,theorem,(
    ! [A,B,C,D] : k15_funct_3(k2_funcop_1(A,C),k2_funcop_1(B,D)) = k2_funcop_1(k2_zfmisc_1(A,B),k4_tarski(C,D)) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t19_funcop_1,t13_funcop_1,t106_zfmisc_1,t19_funcop_1,t13_funcop_1,d9_funct_3]),
    [file(altcat_2,t1_altcat_2),interesting(0.44)]).

fof(t3_altcat_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => k2_funct_4(k5_relat_1(k15_funct_3(B,C),A)) = k5_relat_1(k15_funct_3(C,B),k2_funct_4(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_funct_1,d9_funct_3,t103_zfmisc_1,d9_funct_3,t106_zfmisc_1,d9_funct_3,d9_funct_3,t21_funct_1,t43_funct_4,t21_funct_1,t21_funct_1,d9_funct_3,t106_zfmisc_1,d9_funct_3,t106_zfmisc_1,d9_funct_3,d9_funct_3,t21_funct_1,t43_funct_4,t21_funct_1,t21_funct_1,d9_funct_3,t106_zfmisc_1,t21_funct_1,d9_funct_3,t106_zfmisc_1,d9_funct_3,t23_funct_1,d9_funct_3,d2_funct_4,d9_funct_3,t22_funct_1,d2_funct_4]),
    [file(altcat_2,t3_altcat_2),interesting(0.44)]).

fof(t27_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & m1_altcat_2(C,A) )
             => ( ( u1_struct_0(B) = u1_struct_0(C)
                  & u1_altcat_1(B) = u1_altcat_1(C) )
               => g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) = g2_altcat_1(u1_struct_0(C),u1_altcat_1(C),u2_altcat_1(C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_altcat_2,t25_altcat_2,t23_altcat_2]),
    [file(altcat_2,t27_altcat_2),interesting(0.43)]).

fof(t13_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => r2_hidden(k10_cat_1(A,B),k1_binop_1(k4_altcat_2(A),B,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_cat_1,d3_altcat_2]),
    [file(altcat_2,t13_altcat_2),interesting(0.40)]).

fof(s3_altcat_2,theorem,
    ( ( f2_s3_altcat_2 = a_0_3_altcat_2
      & p1_s3_altcat_2(f3_s3_altcat_2) )
   => k1_funct_1(f2_s3_altcat_2,f3_s3_altcat_2) = f4_s3_altcat_2(f3_s3_altcat_2) ),
    inference(mizar_proof,[status(thm)],[s2_altcat_2,d4_funct_1]),
    [file(altcat_2,s3_altcat_2),interesting(0.39)]).

fof(t28_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( v2_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ( u1_struct_0(B) = u1_struct_0(A)
           => g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) = g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d13_altcat_2,t98_relat_1,t26_altcat_2]),
    [file(altcat_2,t28_altcat_2),interesting(0.38)]).

fof(t35_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( C = D
                   => k8_altcat_1(B,C) = k8_altcat_1(A,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_altcat_2,d14_altcat_2,t30_altcat_2,t32_altcat_2,t3_xboole_1,t34_altcat_2,t33_altcat_2,d19_altcat_1,d19_altcat_1]),
    [file(altcat_2,t35_altcat_2),interesting(0.35)]).

fof(t24_altcat_2,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(k8_altcat_2(A,B)))
             => C = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_altcat_2,d1_tarski]),
    [file(altcat_2,t24_altcat_2),interesting(0.32)]).

fof(t32_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_altcat_2(B,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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( C = E
                              & D = F )
                           => r1_tarski(k1_altcat_1(B,E,F),k1_altcat_1(A,C,D)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,d11_altcat_2,d2_altcat_2]),
    [file(altcat_2,t32_altcat_2),interesting(0.32)]).

fof(t34_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_altcat_2(B,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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( C = E
                              & D = F )
                           => ( k1_altcat_1(B,E,F) = k1_xboole_0
                              | ! [G] : 
                                  ( m1_subset_1(G,k1_altcat_1(B,E,F))
                                 => m1_subset_1(G,k1_altcat_1(A,C,D)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t32_altcat_2]),
    [file(altcat_2,t34_altcat_2),interesting(0.32)]).

fof(t31_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v2_altcat_2(C,A)
                & m1_altcat_2(C,A) )
             => ( u1_struct_0(B) = u1_struct_0(C)
               => g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) = g2_altcat_1(u1_struct_0(C),u1_altcat_1(C),u2_altcat_1(C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_altcat_2,d13_altcat_2,t27_altcat_2]),
    [file(altcat_2,t31_altcat_2),interesting(0.31)]).

fof(t5_altcat_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] : 
              ( m1_pboole(D,B)
             => ! [E] : 
                  ( m1_pboole(E,B)
                 => ! [F] : 
                      ( m3_pboole(F,B,D,E)
                     => m3_pboole(k7_pboole(A,B,C,F),A,k7_pboole(A,B,C,D),k7_pboole(A,B,C,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d1_funct_2,t23_funct_1,t7_funct_2,d18_pboole,t23_funct_1]),
    [file(altcat_2,t5_altcat_2),interesting(0.31)]).

fof(t6_altcat_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_pboole(C,k2_zfmisc_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => k1_binop_1(k18_pralg_1(A,B,C),E,D) = k1_binop_1(C,D,E) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,d3_pboole,d2_funct_4]),
    [file(altcat_2,t6_altcat_2),interesting(0.31)]).

fof(t25_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & m1_altcat_2(C,A) )
             => ( ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
                  & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_altcat_1(B),u1_altcat_1(C)) )
               => m1_altcat_2(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_altcat_2,t77_mcart_1,d2_altcat_2,t72_mcart_1,d4_altcat_1,t113_zfmisc_1,d1_funct_2,d4_altcat_1,t113_zfmisc_1,t106_zfmisc_1,d2_altcat_2,d1_funct_2,t119_zfmisc_1,d11_altcat_2,d1_multop_1,t73_mcart_1,d11_altcat_2,d1_multop_1,d2_altcat_2,d11_altcat_2,d1_multop_1,d2_altcat_2,t8_grfunc_1,t8_grfunc_1,d1_multop_1,t8_grfunc_1]),
    [file(altcat_2,t25_altcat_2),interesting(0.24)]).

fof(t29_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_2(B,A)
            & m1_altcat_2(B,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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( C = E
                              & D = F )
                           => k1_altcat_1(A,C,D) = k1_altcat_1(B,E,F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,t72_funct_1,d13_altcat_2]),
    [file(altcat_2,t29_altcat_2),interesting(0.08)]).

fof(t12_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => r1_tarski(k9_relat_1(u5_cat_1(A),k12_mcart_1(u2_cat_1(A),u2_cat_1(A),k6_cat_1(A,C,D),k6_cat_1(A,B,C))),k6_cat_1(A,B,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d12_funct_1,t10_mcart_1,t10_mcart_1,t23_mcart_1,d7_cat_1,t51_cat_1,d4_cat_1]),
    [file(altcat_2,t12_altcat_2),interesting(0.05)]).

fof(t33_altcat_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ~ ( k1_altcat_1(B,C,D) != k1_xboole_0
                          & k1_altcat_1(B,D,E) != k1_xboole_0
                          & ? [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                              & ? [G] : 
                                  ( m1_subset_1(G,u1_struct_0(A))
                                  & ? [H] : 
                                      ( m1_subset_1(H,u1_struct_0(A))
                                      & F = C
                                      & G = D
                                      & H = E
                                      & ? [I] : 
                                          ( m1_subset_1(I,k1_altcat_1(A,F,G))
                                          & ? [J] : 
                                              ( m1_subset_1(J,k1_altcat_1(A,G,H))
                                              & ? [K] : 
                                                  ( m1_subset_1(K,k1_altcat_1(B,C,D))
                                                  & ? [L] : 
                                                      ( m1_subset_1(L,k1_altcat_1(B,D,E))
                                                      & I = K
                                                      & J = L
                                                      & k5_altcat_1(A,F,G,H,I,J) != k5_altcat_1(B,C,D,E,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_1,d1_funct_2,t106_zfmisc_1,t73_mcart_1,d1_multop_1,d11_altcat_2,d2_altcat_2,t32_altcat_2,t3_xboole_1,d10_altcat_1,t8_grfunc_1,d10_altcat_1]),
    [file(altcat_2,t33_altcat_2),interesting(0.05)]).

fof(t11_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => r1_tarski(k12_mcart_1(u2_cat_1(A),u2_cat_1(A),k6_cat_1(A,C,D),k6_cat_1(A,B,C)),k1_relat_1(u5_cat_1(A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t10_mcart_1,t10_mcart_1,t23_mcart_1,t18_cat_1,t18_cat_1,t40_cat_1]),
    [file(altcat_2,t11_altcat_2),interesting(0.03)]).

fof(d1_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
    <=> ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D] : B != k4_tarski(C,D) ) ) ),
    file(relat_1,d1_relat_1),
    [interesting(0.00)]).

fof(d1_funct_1,definition,(
    ! [A] : 
      ( v1_funct_1(A)
    <=> ! [B,C,D] : 
          ( ( r2_hidden(k4_tarski(B,C),A)
            & r2_hidden(k4_tarski(B,D),A) )
         => C = D ) ) ),
    file(funct_1,d1_funct_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(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(d4_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( r2_hidden(B,k1_relat_1(A))
           => ( C = k1_funct_1(A,B)
            <=> r2_hidden(k4_tarski(B,C),A) ) )
          & ( ~ r2_hidden(B,k1_relat_1(A))
           => ( C = k1_funct_1(A,B)
            <=> C = k1_xboole_0 ) ) ) ) ),
    file(funct_1,d4_funct_1),
    [interesting(0.00)]).

fof(d5_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    [interesting(0.00)]).

fof(d2_altcat_2,definition,(
    ! [A,B,C] : 
      ( m1_pboole(C,A)
     => ! [D] : 
          ( m1_pboole(D,B)
         => ( r2_altcat_2(A,B,C,D)
          <=> ( r1_tarski(A,B)
              & ! [E] : 
                  ( r2_hidden(E,A)
                 => r1_tarski(k1_funct_1(C,E),k1_funct_1(D,E)) ) ) ) ) ) ),
    file(altcat_2,d2_altcat_2),
    [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(t10_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => ( r2_hidden(k1_mcart_1(A),B)
        & r2_hidden(k2_mcart_1(A),C) ) ) ),
    file(mcart_1,t10_mcart_1),
    [interesting(0.00)]).

fof(t23_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ),
    file(mcart_1,t23_mcart_1),
    [interesting(0.00)]).

fof(t18_cat_1,theorem,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(A))
                 => ( r2_hidden(D,k6_cat_1(A,B,C))
                  <=> ( k2_cat_1(A,D) = B
                      & k3_cat_1(A,D) = C ) ) ) ) ) ) ),
    file(cat_1,t18_cat_1),
    [interesting(0.00)]).

fof(t40_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,B) = k3_cat_1(A,C)
              <=> r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A))) ) ) ) ) ),
    file(cat_1,t40_cat_1),
    [interesting(0.00)]).

fof(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.00)]).

fof(d7_cat_1,definition,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ( k6_cat_1(A,B,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,u2_cat_1(A))
                   => ( m1_cat_1(D,A,B,C)
                    <=> r2_hidden(D,k6_cat_1(A,B,C)) ) ) ) ) ) ) ),
    file(cat_1,d7_cat_1),
    [interesting(0.00)]).

fof(t51_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] : 
                          ( m1_cat_1(F,A,C,D)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,C,D) != k1_xboole_0
                              & ~ r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D)) ) ) ) ) ) ) ) ),
    file(cat_1,t51_cat_1),
    [interesting(0.00)]).

fof(d4_cat_1,definition,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A)))
               => k4_cat_1(A,B,C) = k1_funct_1(u5_cat_1(A),k4_tarski(C,B)) ) ) ) ) ),
    file(cat_1,d4_cat_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(d3_altcat_2,definition,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_pboole(B,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)))
         => ( B = k4_altcat_2(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_cat_1(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_cat_1(A))
                   => k1_binop_1(B,C,D) = k6_cat_1(A,C,D) ) ) ) ) ) ),
    file(altcat_2,d3_altcat_2),
    [interesting(0.00)]).

fof(t52_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,C,D) != k1_xboole_0
                      & k6_cat_1(A,B,D) = k1_xboole_0 ) ) ) ) ) ),
    file(cat_1,t52_cat_1),
    [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(d4_altcat_2,definition,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m3_pboole(B,k3_zfmisc_1(u1_cat_1(A),u1_cat_1(A),u1_cat_1(A)),k3_altcat_1(u1_cat_1(A),k4_altcat_2(A),k4_altcat_2(A)),k2_altcat_1(u1_cat_1(A),k4_altcat_2(A)))
         => ( B = k5_altcat_2(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_cat_1(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_cat_1(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_cat_1(A))
                       => k4_altcat_1(u1_cat_1(A),k4_altcat_2(A),B,C,D,E) = k7_relat_1(u5_cat_1(A),k2_zfmisc_1(k1_binop_1(k4_altcat_2(A),D,E),k1_binop_1(k4_altcat_2(A),C,D))) ) ) ) ) ) ) ),
    file(altcat_2,d4_altcat_2),
    [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(t41_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(A))
             => ( k2_cat_1(A,B) = k3_cat_1(A,C)
               => k4_cat_1(A,C,B) = k1_funct_1(u5_cat_1(A),k4_tarski(B,C)) ) ) ) ) ),
    file(cat_1,t41_cat_1),
    [interesting(0.00)]).

fof(d13_cat_1,definition,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_cat_1(E,A,B,C)
                     => ! [F] : 
                          ( m1_cat_1(F,A,C,D)
                         => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                              & k6_cat_1(A,C,D) != k1_xboole_0
                              & k9_cat_1(A,B,C,D,E,F) != k4_cat_1(A,E,F) ) ) ) ) ) ) ) ),
    file(cat_1,d13_cat_1),
    [interesting(0.00)]).

fof(t14_altcat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                      & k6_cat_1(A,C,D) != k1_xboole_0
                      & ~ ! [E] : 
                            ( m1_cat_1(E,A,B,C)
                           => ! [F] : 
                                ( m1_cat_1(F,A,C,D)
                               => k1_binop_1(k4_altcat_1(u1_cat_1(A),k4_altcat_2(A),k5_altcat_2(A),B,C,D),F,E) = k9_cat_1(A,B,C,D,E,F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_cat_1,d7_cat_1,t18_cat_1,t18_cat_1,d3_altcat_2,d3_altcat_2,t106_zfmisc_1,d4_altcat_2,t72_funct_1,t41_cat_1,d13_cat_1]),
    [file(altcat_2,t14_altcat_2),interesting(0.00)]).

fof(t54_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_cat_1(A))
                     => ! [F] : 
                          ( m1_cat_1(F,A,B,C)
                         => ! [G] : 
                              ( m1_cat_1(G,A,C,D)
                             => ! [H] : 
                                  ( m1_cat_1(H,A,D,E)
                                 => ~ ( k6_cat_1(A,B,C) != k1_xboole_0
                                      & k6_cat_1(A,C,D) != k1_xboole_0
                                      & k6_cat_1(A,D,E) != k1_xboole_0
                                      & k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H)) != k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) ) ) ) ) ) ) ) ) ) ),
    file(cat_1,t54_cat_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(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(t55_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)) ) ) ),
    file(cat_1,t55_cat_1),
    [interesting(0.00)]).

fof(t56_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => k6_cat_1(A,B,B) != k1_xboole_0 ) ) ),
    file(cat_1,t56_cat_1),
    [interesting(0.00)]).

fof(t57_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => k9_cat_1(A,B,C,C,D,k10_cat_1(A,C)) = D ) ) ) ) ) ),
    file(cat_1,t57_cat_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(t58_cat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] : 
                  ( m1_cat_1(D,A,B,C)
                 => ( k6_cat_1(A,B,C) != k1_xboole_0
                   => k9_cat_1(A,B,B,C,k10_cat_1(A,B),D) = D ) ) ) ) ) ),
    file(cat_1,t58_cat_1),
    [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(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(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(d9_funct_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k15_funct_3(A,B)
              <=> ( k1_relat_1(C) = k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))
                  & ! [D,E] : 
                      ( ( r2_hidden(D,k1_relat_1(A))
                        & r2_hidden(E,k1_relat_1(B)) )
                     => k1_funct_1(C,k4_tarski(D,E)) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)) ) ) ) ) ) ) ),
    file(funct_3,d9_funct_3),
    [interesting(0.00)]).

fof(d1_struct_0,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_struct_0(A)
      <=> v1_xboole_0(u1_struct_0(A)) ) ) ),
    file(struct_0,d1_struct_0),
    [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(t134_pboole,theorem,(
    ! [A] : 
      ( m1_pboole(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(pboole,t134_pboole),
    [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(d11_altcat_2,definition,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ! [B] : 
          ( l2_altcat_1(B)
         => ( m1_altcat_2(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & r2_altcat_2(k3_zfmisc_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(B)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),u2_altcat_1(B),u2_altcat_1(A)) ) ) ) ) ),
    file(altcat_2,d11_altcat_2),
    [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(d12_altcat_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v6_altcat_1(C)
                & m1_altcat_2(C,A) )
             => ( C = k8_altcat_2(A,B)
              <=> ( u1_struct_0(C) = k1_struct_0(A,B)
                  & u1_altcat_1(C) = k9_funct_2(B,B,k1_altcat_1(A,B,B))
                  & u2_altcat_1(C) = k7_cat_1(k3_mcart_1(B,B,B),k4_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A),B,B,B)) ) ) ) ) ) ),
    file(altcat_2,d12_altcat_2),
    [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(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(d13_altcat_2,definition,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( v2_altcat_2(B,A)
          <=> u1_altcat_1(B) = k1_realset1(u1_altcat_1(A),u1_struct_0(B)) ) ) ) ),
    file(altcat_2,d13_altcat_2),
    [interesting(0.00)]).

fof(t98_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k7_relat_1(A,k1_relat_1(A)) = A ) ),
    file(relat_1,t98_relat_1),
    [interesting(0.00)]).

fof(t77_mcart_1,theorem,(
    ! [A,B,C,D,E,F] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D)
        & r1_tarski(E,F) )
     => r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)) ) ),
    file(mcart_1,t77_mcart_1),
    [interesting(0.00)]).

fof(t72_mcart_1,theorem,(
    ! [A,B,C,D] : ~ ( r2_hidden(A,k3_zfmisc_1(B,C,D))
      & ! [E,F,G] : ~ ( r2_hidden(E,B)
          & r2_hidden(F,C)
          & r2_hidden(G,D)
          & A = k3_mcart_1(E,F,G) ) ) ),
    file(mcart_1,t72_mcart_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(t119_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_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(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(t8_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(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) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_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(t3_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) ),
    file(pboole,t3_pboole),
    [interesting(0.00)]).

fof(t21_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
          <=> ( r2_hidden(A,k1_relat_1(C))
              & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) ) ) ) ) ),
    file(funct_1,t21_funct_1),
    [interesting(0.00)]).

fof(d2_funct_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_funct_4(A)
          <=> ( ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                <=> ? [D,E] : 
                      ( C = k4_tarski(E,D)
                      & r2_hidden(k4_tarski(D,E),k1_relat_1(A)) ) )
              & ! [C,D] : 
                  ( r2_hidden(k4_tarski(C,D),k1_relat_1(A))
                 => k1_funct_1(B,k4_tarski(D,C)) = k1_funct_1(A,k4_tarski(C,D)) ) ) ) ) ) ),
    file(funct_4,d2_funct_4),
    [interesting(0.00)]).

fof(t43_funct_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),k1_relat_1(C))
      <=> r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) ) ) ),
    file(funct_4,t43_funct_4),
    [interesting(0.00)]).

fof(t23_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.00)]).

fof(t44_funct_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),k1_relat_1(k2_funct_4(C)))
       => k1_funct_1(k2_funct_4(C),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(B,A)) ) ) ),
    file(funct_4,t44_funct_4),
    [interesting(0.00)]).

fof(t22_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    [interesting(0.00)]).

fof(d14_altcat_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
             => ( v3_altcat_2(B,A)
              <=> ! [C] : 
                    ( m1_subset_1(C,u1_struct_0(B))
                   => ! [D] : 
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ( C = D
                         => r2_hidden(k8_altcat_1(A,D),k1_altcat_1(B,C,C)) ) ) ) ) )
            & ( v3_struct_0(B)
             => v3_altcat_2(B,A) ) ) ) ) ),
    file(altcat_2,d14_altcat_2),
    [interesting(0.00)]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_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(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(t103_zfmisc_1,theorem,(
    ! [A,B,C,D] : ~ ( r1_tarski(A,k2_zfmisc_1(B,C))
      & r2_hidden(D,A)
      & ! [E,F] : ~ ( r2_hidden(E,B)
          & r2_hidden(F,C)
          & D = k4_tarski(E,F) ) ) ),
    file(zfmisc_1,t103_zfmisc_1),
    [interesting(0.00)]).

fof(t15_mssubfam,theorem,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_funcop_1(C)
            & m1_pboole(C,A) )
         => ( v1_funcop_1(k13_pboole(B,C))
            & m1_pboole(k13_pboole(B,C),A) ) ) ) ),
    file(mssubfam,t15_mssubfam),
    [interesting(0.00)]).

fof(d18_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(pboole,d18_pboole),
    [interesting(0.00)]).

fof(d3_pzfmisc1,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pzfmisc1(A,B,C)
          <=> ! [D] : 
                ( ( r2_hidden(D,A)
                  & k1_funct_1(C,D) = k1_xboole_0 )
               => k1_funct_1(B,D) = k1_xboole_0 ) ) ) ) ),
    file(pzfmisc1,d3_pzfmisc1),
    [interesting(0.00)]).

fof(d24_pboole,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( C = k13_pboole(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(pboole,d24_pboole),
    [interesting(0.00)]).

fof(t19_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ~ ( B = k1_xboole_0
                & C != k1_xboole_0
                & A != k1_xboole_0 )
           => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
              & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)
              & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) ) ) ) ) ),
    file(funct_2,t19_funct_2),
    [interesting(0.00)]).

fof(t7_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) ),
    file(funct_2,t7_funct_2),
    [interesting(0.00)]).

fof(t7_altcat_2,theorem,(
    $true ),
    file(altcat_2,t7_altcat_2),
    [interesting(0.00)]).