fof(t54_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k2_algstr_1,k31_grcat_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t51_grcat_1]),
    [file(grcat_1,t54_grcat_1),interesting(1.00)]).

fof(t51_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k2_algstr_1,k29_grcat_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t42_grcat_1]),
    [file(grcat_1,t51_grcat_1),interesting(0.99)]).

fof(t42_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k2_algstr_1,k19_grcat_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t41_grcat_1,d29_grcat_1]),
    [file(grcat_1,t42_grcat_1),interesting(0.97)]).

fof(t41_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ? [B] : 
          ( r2_hidden(B,A)
          & r1_grcat_1(B,k2_algstr_1) ) ) ),
    inference(mizar_proof,[status(thm)],[t62_classes2,d3_algstr_1,t6_grcat_1,t13_grcat_1,t6_grcat_1,t3_grcat_1,d28_grcat_1,d4_algstr_1]),
    [file(grcat_1,t41_grcat_1),interesting(0.95)]).

fof(t13_grcat_1,theorem,(
    k7_vectsp_1(k2_algstr_1) = k7_vectsp_2 ),
    inference(mizar_proof,[status(thm)],[d4_algstr_1,d4_algstr_1,d1_tarski,t5_grcat_1,d4_algstr_1,d1_tarski,d25_vectsp_1,t18_funct_2]),
    [file(grcat_1,t13_grcat_1),interesting(0.77)]).

fof(t21_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => v1_grcat_1(k7_grcat_1(A),A,A) ) ),
    inference(mizar_proof,[status(thm)],[t11_grcat_1,d13_grcat_1]),
    [file(grcat_1,t21_grcat_1),interesting(0.68)]).

fof(t16_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v5_rlvect_1(B)
            & l1_rlvect_1(B) )
         => v1_grcat_1(k8_grcat_1(A,B),A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_grcat_1,d7_rlvect_1,d13_grcat_1]),
    [file(grcat_1,t16_grcat_1),interesting(0.60)]).

fof(t40_grcat_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_grcat_1(A,B)
        & r1_grcat_1(A,C) )
     => B = C ) ),
    inference(mizar_proof,[status(thm)],[d28_grcat_1,d28_grcat_1,t33_mcart_1]),
    [file(grcat_1,t40_grcat_1),interesting(0.60)]).

fof(t18_grcat_1,theorem,(
    ! [A] : 
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => v1_grcat_1(u3_grcat_1(A),u1_grcat_1(A),u2_grcat_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d18_grcat_1]),
    [file(grcat_1,t18_grcat_1),interesting(0.59)]).

fof(t3_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ( m1_subset_1(k3_mcart_1(B,C,D),A)
                        & m1_subset_1(k4_mcart_1(B,C,D,E),A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_mcart_1,d4_mcart_1,t64_classes2]),
    [file(grcat_1,t3_grcat_1),interesting(0.59)]).

fof(t31_grcat_1,theorem,(
    ! [A] : 
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] : 
          ( ( v2_grcat_1(B)
            & v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ( k9_grcat_1(B) = k10_grcat_1(A)
           => ( k9_grcat_1(k15_grcat_1(B,A)) = k9_grcat_1(A)
              & k10_grcat_1(k15_grcat_1(B,A)) = k10_grcat_1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_grcat_1]),
    [file(grcat_1,t31_grcat_1),interesting(0.56)]).

fof(t11_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t35_funct_1]),
    [file(grcat_1,t11_grcat_1),interesting(0.55)]).

fof(t28_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] : 
                  ( m1_grcat_1(D,B,C)
                 => ! [E] : 
                      ( m1_grcat_1(E,A,B)
                     => m1_grcat_1(k15_grcat_1(D,E),A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_grcat_1,t22_grcat_1,d19_grcat_1,d19_grcat_1,d21_grcat_1,d19_grcat_1]),
    [file(grcat_1,t28_grcat_1),interesting(0.55)]).

fof(t5_grcat_1,theorem,
    ( k1_binop_1(k2_midsp_1,k1_xboole_0,k1_xboole_0) = k1_xboole_0
    & k1_funct_1(k7_vectsp_2,k1_xboole_0) = k1_xboole_0
    & k8_vectsp_2 = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t34_zfmisc_1,t65_funct_2,t65_funct_2,d1_tarski]),
    [file(grcat_1,t5_grcat_1),interesting(0.55)]).

fof(t7_grcat_1,theorem,(
    v1_midsp_2(g1_rlvect_1(k1_tarski(k1_xboole_0),k2_midsp_1,k1_algstr_1(k1_xboole_0))) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d1_tarski,d1_tarski,d1_tarski,d5_midsp_2]),
    [file(grcat_1,t7_grcat_1),interesting(0.55)]).

fof(t2_grcat_1,theorem,(
    ! [A,B,C,D] : ~ ( r2_hidden(D,C)
      & r1_tarski(C,k2_zfmisc_1(A,B))
      & ! [E] : 
          ( m1_subset_1(E,A)
         => ! [F] : 
              ( m1_subset_1(F,B)
             => D != k4_tarski(E,F) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t103_zfmisc_1]),
    [file(grcat_1,t2_grcat_1),interesting(0.50)]).

fof(t4_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B,C] : 
          ( ( r2_hidden(B,C)
            & r2_hidden(C,A) )
         => r2_hidden(B,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ordinal1]),
    [file(grcat_1,t4_grcat_1),interesting(0.50)]).

fof(t12_grcat_1,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_struct_0(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_grcat_1(A),C) = C
                & k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_grcat_1(B)) = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,t77_relat_1,t79_relat_1]),
    [file(grcat_1,t12_grcat_1),interesting(0.49)]).

fof(t15_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k8_funct_2(u1_struct_0(A),u1_struct_0(B),k8_grcat_1(A,B),C) = k1_rlvect_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_funcop_1]),
    [file(grcat_1,t15_grcat_1),interesting(0.49)]).

fof(t37_grcat_1,theorem,(
    ! [A] : 
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v5_grcat_1(k1_tarski(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d23_grcat_1]),
    [file(grcat_1,t37_grcat_1),interesting(0.49)]).

fof(t46_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
             => ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(k28_grcat_1(A))))
              <=> k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_cat_1,d32_grcat_1,d3_cat_1,d33_grcat_1,d35_grcat_1]),
    [file(grcat_1,t46_grcat_1),interesting(0.48)]).

fof(t34_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ( k9_grcat_1(k13_grcat_1(A)) = A
        & k10_grcat_1(k13_grcat_1(A)) = A
        & ! [B] : 
            ( ( v2_grcat_1(B)
              & v3_grcat_1(B)
              & l1_grcat_1(B) )
           => ( k10_grcat_1(B) = A
             => k15_grcat_1(k13_grcat_1(A),B) = B ) )
        & ! [B] : 
            ( ( v2_grcat_1(B)
              & v3_grcat_1(B)
              & l1_grcat_1(B) )
           => ( k9_grcat_1(B) = A
             => k15_grcat_1(B,k13_grcat_1(A)) = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_grcat_1,t23_grcat_1,t12_grcat_1,d21_grcat_1,d19_grcat_1,t23_grcat_1,t12_grcat_1,d21_grcat_1]),
    [file(grcat_1,t34_grcat_1),interesting(0.48)]).

fof(t24_grcat_1,theorem,(
    ! [A] : 
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ? [B] : 
          ( ~ v3_struct_0(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & l1_rlvect_1(B)
          & ? [C] : 
              ( ~ v3_struct_0(C)
              & v4_rlvect_1(C)
              & v5_rlvect_1(C)
              & v6_rlvect_1(C)
              & l1_rlvect_1(C)
              & m1_grcat_1(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_grcat_1]),
    [file(grcat_1,t24_grcat_1),interesting(0.48)]).

fof(t45_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] : 
          ( m3_grcat_1(B,k20_grcat_1(A))
         => ! [C] : 
              ( m3_grcat_1(C,k20_grcat_1(A))
             => ( k21_grcat_1(A,B) = k22_grcat_1(A,C)
               => r2_hidden(k15_grcat_1(B,C),k20_grcat_1(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_grcat_1,d30_grcat_1]),
    [file(grcat_1,t45_grcat_1),interesting(0.43)]).

fof(t39_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v2_grcat_1(C)
                & m1_grcat_1(C,A,B) )
             => m4_grcat_1(k1_tarski(C),A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t38_grcat_1]),
    [file(grcat_1,t39_grcat_1),interesting(0.42)]).

fof(t43_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k19_grcat_1(A))
         => ( ~ v3_struct_0(B)
            & v1_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d29_grcat_1,d28_grcat_1]),
    [file(grcat_1,t43_grcat_1),interesting(0.42)]).

fof(t23_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v2_grcat_1(C)
                & m1_grcat_1(C,A,B) )
             => ? [D] : 
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
                  & C = g1_grcat_1(A,B,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_grcat_1]),
    [file(grcat_1,t23_grcat_1),interesting(0.40)]).

fof(t19_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v2_grcat_1(C)
                & l1_grcat_1(C) )
             => ( ( k9_grcat_1(C) = A
                  & k10_grcat_1(C) = B
                  & v1_grcat_1(k11_grcat_1(C),k9_grcat_1(C),k10_grcat_1(C)) )
               => ( v2_grcat_1(C)
                  & m1_grcat_1(C,A,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_grcat_1,d19_grcat_1]),
    [file(grcat_1,t19_grcat_1),interesting(0.40)]).

fof(t49_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] : 
              ( m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A)))
             => ( B = C
               => ( k2_cat_1(k28_grcat_1(A),B) = k21_grcat_1(k19_grcat_1(A),C)
                  & k3_cat_1(k28_grcat_1(A),B) = k22_grcat_1(k19_grcat_1(A),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_cat_1,d32_grcat_1,d3_cat_1,d33_grcat_1]),
    [file(grcat_1,t49_grcat_1),interesting(0.37)]).

fof(t48_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(k28_grcat_1(A)))
         => ! [C] : 
              ( m2_grcat_1(C,k19_grcat_1(A))
             => ( B = C
               => k5_cat_1(k28_grcat_1(A),B) = k23_grcat_1(k19_grcat_1(A),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_cat_1,d34_grcat_1]),
    [file(grcat_1,t48_grcat_1),interesting(0.37)]).

fof(t9_grcat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => r1_cat_2(g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_cat_2]),
    [file(grcat_1,t9_grcat_1),interesting(0.37)]).

fof(t22_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( m1_grcat_1(C,A,B)
             => ? [D] : 
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
                  & g1_grcat_1(u1_grcat_1(C),u2_grcat_1(C),u3_grcat_1(C)) = g1_grcat_1(A,B,D)
                  & v1_grcat_1(D,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_grcat_1,d19_grcat_1,t18_grcat_1]),
    [file(grcat_1,t22_grcat_1),interesting(0.32)]).

fof(t29_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] : 
                  ( m1_grcat_1(D,B,C)
                 => ! [E] : 
                      ( m1_grcat_1(E,A,B)
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
                            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,u1_struct_0(A),u1_struct_0(B))
                                & m2_relset_1(G,u1_struct_0(A),u1_struct_0(B)) )
                             => ( ( D = g1_grcat_1(B,C,F)
                                  & E = g1_grcat_1(A,B,G) )
                               => k16_grcat_1(A,B,C,D,E) = g1_grcat_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),G,F)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_grcat_1,d19_grcat_1,d21_grcat_1]),
    [file(grcat_1,t29_grcat_1),interesting(0.28)]).

fof(t30_grcat_1,theorem,(
    ! [A] : 
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] : 
          ( ( v2_grcat_1(B)
            & v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ~ ( k9_grcat_1(B) = k10_grcat_1(A)
              & ! [C] : 
                  ( ( ~ v3_struct_0(C)
                    & v4_rlvect_1(C)
                    & v5_rlvect_1(C)
                    & v6_rlvect_1(C)
                    & l1_rlvect_1(C) )
                 => ! [D] : 
                      ( ( ~ v3_struct_0(D)
                        & v4_rlvect_1(D)
                        & v5_rlvect_1(D)
                        & v6_rlvect_1(D)
                        & l1_rlvect_1(D) )
                     => ! [E] : 
                          ( ( ~ v3_struct_0(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & l1_rlvect_1(E) )
                         => ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                                & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                             => ! [G] : 
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(D),u1_struct_0(E))
                                    & m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) )
                                 => ~ ( A = g1_grcat_1(C,D,F)
                                      & B = g1_grcat_1(D,E,G)
                                      & k15_grcat_1(B,A) = g1_grcat_1(C,E,k7_funct_2(u1_struct_0(C),u1_struct_0(D),u1_struct_0(E),F,G)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_grcat_1,d19_grcat_1,t23_grcat_1,t29_grcat_1]),
    [file(grcat_1,t30_grcat_1),interesting(0.28)]).

fof(t20_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_grcat_1(C,A,B)
               => ( v2_grcat_1(g1_grcat_1(A,B,C))
                  & m1_grcat_1(g1_grcat_1(A,B,C),A,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_grcat_1]),
    [file(grcat_1,t20_grcat_1),interesting(0.28)]).

fof(t47_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] : 
              ( m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_cat_1(k28_grcat_1(A)))
                 => ! [E] : 
                      ( m2_grcat_1(E,k19_grcat_1(A))
                     => ( v2_grcat_1(B)
                        & m3_grcat_1(B,k20_grcat_1(k19_grcat_1(A)))
                        & m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
                        & v1_rlvect_1(D)
                        & m2_grcat_1(D,k19_grcat_1(A))
                        & m1_subset_1(E,u1_cat_1(k28_grcat_1(A))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d30_grcat_1,d29_grcat_1,d28_grcat_1]),
    [file(grcat_1,t47_grcat_1),interesting(0.27)]).

fof(s2_grcat_1,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,f1_s2_grcat_1)
       => ! [B] : 
            ( m1_subset_1(B,f2_s2_grcat_1)
           => ( p1_s2_grcat_1(A,B)
             => r2_hidden(f4_s2_grcat_1(A,B),f3_s2_grcat_1) ) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & m2_relset_1(A,k2_zfmisc_1(f1_s2_grcat_1,f2_s2_grcat_1),f3_s2_grcat_1)
        & ! [B] : 
            ( m1_subset_1(B,f1_s2_grcat_1)
           => ! [C] : 
                ( m1_subset_1(C,f2_s2_grcat_1)
               => ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
                <=> p1_s2_grcat_1(B,C) ) ) )
        & ! [B] : 
            ( m1_subset_1(B,f1_s2_grcat_1)
           => ! [C] : 
                ( m1_subset_1(C,f2_s2_grcat_1)
               => ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
                 => k1_funct_1(A,k4_tarski(B,C)) = f4_s2_grcat_1(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_grcat_1]),
    [file(grcat_1,s2_grcat_1),interesting(0.25)]).

fof(t25_grcat_1,theorem,(
    ! [A] : 
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ? [B] : 
          ( ~ v3_struct_0(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & l1_rlvect_1(B)
          & ? [C] : 
              ( ~ v3_struct_0(C)
              & v4_rlvect_1(C)
              & v5_rlvect_1(C)
              & v6_rlvect_1(C)
              & l1_rlvect_1(C)
              & ? [D] : 
                  ( v1_funct_1(D)
                  & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                  & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
                  & m1_grcat_1(A,B,C)
                  & A = g1_grcat_1(B,C,D)
                  & v1_grcat_1(D,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_grcat_1,t22_grcat_1]),
    [file(grcat_1,t25_grcat_1),interesting(0.23)]).

fof(d30_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v5_grcat_1(B) )
         => ( B = k20_grcat_1(A)
          <=> ! [C] : 
                ( r2_hidden(C,B)
              <=> ? [D] : 
                    ( v1_rlvect_1(D)
                    & m2_grcat_1(D,A)
                    & ? [E] : 
                        ( v1_rlvect_1(E)
                        & m2_grcat_1(E,A)
                        & v2_grcat_1(C)
                        & m1_grcat_1(C,D,E) ) ) ) ) ) ) ),
    file(grcat_1,d30_grcat_1),
    [interesting(0.00)]).

fof(d29_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( B = k19_grcat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,A)
                  & r1_grcat_1(D,C) ) ) ) ) ),
    file(grcat_1,d29_grcat_1),
    [interesting(0.00)]).

fof(d28_grcat_1,definition,(
    ! [A,B] : 
      ( r1_grcat_1(A,B)
    <=> ? [C,D,E,F] : 
          ( A = k4_mcart_1(C,D,E,F)
          & ? [G] : 
              ( ~ v3_struct_0(G)
              & v1_rlvect_1(G)
              & v4_rlvect_1(G)
              & v5_rlvect_1(G)
              & v6_rlvect_1(G)
              & l1_rlvect_1(G)
              & B = G
              & C = u1_struct_0(G)
              & D = u1_rlvect_1(G)
              & E = k7_vectsp_1(G)
              & F = u2_struct_0(G) ) ) ) ),
    file(grcat_1,d28_grcat_1),
    [interesting(0.00)]).

fof(d2_cat_1,definition,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) ) ) ),
    file(cat_1,d2_cat_1),
    [interesting(0.00)]).

fof(d32_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k20_grcat_1(A),A)
            & m2_relset_1(B,k20_grcat_1(A),A) )
         => ( B = k24_grcat_1(A)
          <=> ! [C] : 
                ( m3_grcat_1(C,k20_grcat_1(A))
               => k8_funct_2(k20_grcat_1(A),A,B,C) = k21_grcat_1(A,C) ) ) ) ) ),
    file(grcat_1,d32_grcat_1),
    [interesting(0.00)]).

fof(d3_cat_1,definition,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(A))
         => k3_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) ) ) ),
    file(cat_1,d3_cat_1),
    [interesting(0.00)]).

fof(d33_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k20_grcat_1(A),A)
            & m2_relset_1(B,k20_grcat_1(A),A) )
         => ( B = k25_grcat_1(A)
          <=> ! [C] : 
                ( m3_grcat_1(C,k20_grcat_1(A))
               => k8_funct_2(k20_grcat_1(A),A,B,C) = k22_grcat_1(A,C) ) ) ) ) ),
    file(grcat_1,d33_grcat_1),
    [interesting(0.00)]).

fof(d35_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & m2_relset_1(B,k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) )
         => ( B = k27_grcat_1(A)
          <=> ( ! [C] : 
                  ( m3_grcat_1(C,k20_grcat_1(A))
                 => ! [D] : 
                      ( m3_grcat_1(D,k20_grcat_1(A))
                     => ( r2_hidden(k4_tarski(C,D),k1_relat_1(B))
                      <=> k21_grcat_1(A,C) = k22_grcat_1(A,D) ) ) )
              & ! [C] : 
                  ( m3_grcat_1(C,k20_grcat_1(A))
                 => ! [D] : 
                      ( m3_grcat_1(D,k20_grcat_1(A))
                     => ( r2_hidden(k4_tarski(C,D),k1_relat_1(B))
                       => k1_funct_1(B,k4_tarski(C,D)) = k15_grcat_1(C,D) ) ) ) ) ) ) ) ),
    file(grcat_1,d35_grcat_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(t50_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
             => ! [D] : 
                  ( m3_grcat_1(D,k20_grcat_1(k19_grcat_1(A)))
                 => ! [E] : 
                      ( m3_grcat_1(E,k20_grcat_1(k19_grcat_1(A)))
                     => ( ( B = D
                          & C = E )
                       => ( ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
                           => k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D) )
                          & ( k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D)
                           => k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) )
                          & ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
                           => r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A)))) )
                          & ( r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A))))
                           => k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) )
                          & ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
                           => k4_cat_1(k28_grcat_1(A),B,C) = k15_grcat_1(E,D) )
                          & ( k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C)
                           => k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E) )
                          & ( k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E)
                           => k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) )
                          & ( k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C)
                           => k22_grcat_1(k19_grcat_1(A),D) = k22_grcat_1(k19_grcat_1(A),E) )
                          & ( k22_grcat_1(k19_grcat_1(A),D) = k22_grcat_1(k19_grcat_1(A),E)
                           => k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_grcat_1,t49_grcat_1,t49_grcat_1,t49_grcat_1,t49_grcat_1,d35_grcat_1,t46_grcat_1,d4_cat_1,d35_grcat_1,t49_grcat_1,t49_grcat_1]),
    [file(grcat_1,t50_grcat_1),interesting(0.00)]).

fof(d19_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v3_grcat_1(C)
                & l1_grcat_1(C) )
             => ( m1_grcat_1(C,A,B)
              <=> ( k9_grcat_1(C) = A
                  & k10_grcat_1(C) = B ) ) ) ) ) ),
    file(grcat_1,d19_grcat_1),
    [interesting(0.00)]).

fof(t44_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] : 
          ( m3_grcat_1(B,k20_grcat_1(A))
         => ! [C] : 
              ( m3_grcat_1(C,k20_grcat_1(A))
             => ~ ( k21_grcat_1(A,B) = k22_grcat_1(A,C)
                  & ! [D] : 
                      ( ( v1_rlvect_1(D)
                        & m2_grcat_1(D,A) )
                     => ! [E] : 
                          ( ( v1_rlvect_1(E)
                            & m2_grcat_1(E,A) )
                         => ! [F] : 
                              ( ( v1_rlvect_1(F)
                                & m2_grcat_1(F,A) )
                             => ~ ( m1_grcat_1(B,E,F)
                                  & m1_grcat_1(C,D,E) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d30_grcat_1,d19_grcat_1,d30_grcat_1,d19_grcat_1]),
    [file(grcat_1,t44_grcat_1),interesting(0.00)]).

fof(d18_grcat_1,definition,(
    ! [A] : 
      ( l1_grcat_1(A)
     => ( v3_grcat_1(A)
      <=> v1_grcat_1(k11_grcat_1(A),k9_grcat_1(A),k10_grcat_1(A)) ) ) ),
    file(grcat_1,d18_grcat_1),
    [interesting(0.00)]).

fof(d21_grcat_1,definition,(
    ! [A] : 
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] : 
          ( ( v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ( k9_grcat_1(A) = k10_grcat_1(B)
           => ! [C] : 
                ( ( v2_grcat_1(C)
                  & v3_grcat_1(C)
                  & l1_grcat_1(C) )
               => ( C = k15_grcat_1(A,B)
                <=> ! [D] : 
                      ( ( ~ v3_struct_0(D)
                        & v4_rlvect_1(D)
                        & v5_rlvect_1(D)
                        & v6_rlvect_1(D)
                        & l1_rlvect_1(D) )
                     => ! [E] : 
                          ( ( ~ v3_struct_0(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & l1_rlvect_1(E) )
                         => ! [F] : 
                              ( ( ~ v3_struct_0(F)
                                & v4_rlvect_1(F)
                                & v5_rlvect_1(F)
                                & v6_rlvect_1(F)
                                & l1_rlvect_1(F) )
                             => ! [G] : 
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(E),u1_struct_0(F))
                                    & m2_relset_1(G,u1_struct_0(E),u1_struct_0(F)) )
                                 => ! [H] : 
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,u1_struct_0(D),u1_struct_0(E))
                                        & m2_relset_1(H,u1_struct_0(D),u1_struct_0(E)) )
                                     => ( ( g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) = g1_grcat_1(E,F,G)
                                          & g1_grcat_1(u1_grcat_1(B),u2_grcat_1(B),u3_grcat_1(B)) = g1_grcat_1(D,E,H) )
                                       => C = g1_grcat_1(D,F,k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),H,G)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(grcat_1,d21_grcat_1),
    [interesting(0.00)]).

fof(l87_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
             => ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
               => ( k2_cat_1(k28_grcat_1(A),k4_cat_1(k28_grcat_1(A),B,C)) = k2_cat_1(k28_grcat_1(A),B)
                  & k3_cat_1(k28_grcat_1(A),k4_cat_1(k28_grcat_1(A),B,C)) = k3_cat_1(k28_grcat_1(A),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_grcat_1,t47_grcat_1,t50_grcat_1,t31_grcat_1,t45_grcat_1,t50_grcat_1,t50_grcat_1]),
    [file(grcat_1,l87_grcat_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(t32_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] : 
                  ( ( ~ v3_struct_0(D)
                    & v4_rlvect_1(D)
                    & v5_rlvect_1(D)
                    & v6_rlvect_1(D)
                    & l1_rlvect_1(D) )
                 => ! [E] : 
                      ( ( v2_grcat_1(E)
                        & m1_grcat_1(E,A,B) )
                     => ! [F] : 
                          ( ( v2_grcat_1(F)
                            & m1_grcat_1(F,B,C) )
                         => ! [G] : 
                              ( ( v2_grcat_1(G)
                                & m1_grcat_1(G,C,D) )
                             => k16_grcat_1(A,C,D,G,k16_grcat_1(A,B,C,F,E)) = k16_grcat_1(A,B,D,k16_grcat_1(B,C,D,G,F),E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_grcat_1,t23_grcat_1,t23_grcat_1,t29_grcat_1,t29_grcat_1,t29_grcat_1,t55_relat_1,t29_grcat_1]),
    [file(grcat_1,t32_grcat_1),interesting(0.00)]).

fof(t33_grcat_1,theorem,(
    ! [A] : 
      ( ( v2_grcat_1(A)
        & v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] : 
          ( ( v2_grcat_1(B)
            & v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ! [C] : 
              ( ( v2_grcat_1(C)
                & v3_grcat_1(C)
                & l1_grcat_1(C) )
             => ( ( k9_grcat_1(C) = k10_grcat_1(B)
                  & k9_grcat_1(B) = k10_grcat_1(A) )
               => k15_grcat_1(C,k15_grcat_1(B,A)) = k15_grcat_1(k15_grcat_1(C,B),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_grcat_1,d19_grcat_1,d19_grcat_1,t32_grcat_1]),
    [file(grcat_1,t33_grcat_1),interesting(0.00)]).

fof(l88_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u2_cat_1(k28_grcat_1(A)))
                 => ( ( k2_cat_1(k28_grcat_1(A),D) = k3_cat_1(k28_grcat_1(A),C)
                      & k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) )
                   => k4_cat_1(k28_grcat_1(A),k4_cat_1(k28_grcat_1(A),B,C),D) = k4_cat_1(k28_grcat_1(A),B,k4_cat_1(k28_grcat_1(A),C,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_grcat_1,t50_grcat_1,t50_grcat_1,t45_grcat_1,l87_grcat_1,l87_grcat_1,t50_grcat_1,t33_grcat_1,t50_grcat_1]),
    [file(grcat_1,l88_grcat_1),interesting(0.00)]).

fof(d5_cat_1,definition,(
    ! [A] : 
      ( l1_cat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(A))
         => k5_cat_1(A,B) = k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) ) ) ),
    file(cat_1,d5_cat_1),
    [interesting(0.00)]).

fof(d34_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_grcat_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k20_grcat_1(A))
            & m2_relset_1(B,A,k20_grcat_1(A)) )
         => ( B = k26_grcat_1(A)
          <=> ! [C] : 
                ( m2_grcat_1(C,A)
               => k8_funct_2(A,k20_grcat_1(A),B,C) = k23_grcat_1(A,C) ) ) ) ) ),
    file(grcat_1,d34_grcat_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(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(t77_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k5_relat_1(k6_relat_1(A),B) = B ) ) ),
    file(relat_1,t77_relat_1),
    [interesting(0.00)]).

fof(t79_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_relat_1(B),A)
       => k5_relat_1(B,k6_relat_1(A)) = B ) ) ),
    file(relat_1,t79_relat_1),
    [interesting(0.00)]).

fof(l89_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_cat_1(k28_grcat_1(A)))
         => ( k2_cat_1(k28_grcat_1(A),k5_cat_1(k28_grcat_1(A),B)) = B
            & k3_cat_1(k28_grcat_1(A),k5_cat_1(k28_grcat_1(A),B)) = B
            & ! [C] : 
                ( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
               => ( k3_cat_1(k28_grcat_1(A),C) = B
                 => k4_cat_1(k28_grcat_1(A),C,k5_cat_1(k28_grcat_1(A),B)) = C ) )
            & ! [C] : 
                ( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
               => ( k2_cat_1(k28_grcat_1(A),C) = B
                 => k4_cat_1(k28_grcat_1(A),k5_cat_1(k28_grcat_1(A),B),C) = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_grcat_1,t49_grcat_1,t49_grcat_1,t47_grcat_1,t49_grcat_1,t50_grcat_1,t34_grcat_1,t47_grcat_1,t49_grcat_1,t50_grcat_1,t34_grcat_1]),
    [file(grcat_1,l89_grcat_1),interesting(0.00)]).

fof(s5_partfun1,theorem,
    ( ! [A,B] : 
        ( p1_s5_partfun1(A,B)
       => r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1) )
   => ? [A] : 
        ( v1_funct_1(A)
        & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1)
        & ! [B,C] : 
            ( r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A))
          <=> ( r2_hidden(B,f1_s5_partfun1)
              & r2_hidden(C,f2_s5_partfun1)
              & p1_s5_partfun1(B,C) ) )
        & ! [B,C] : 
            ( r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A))
           => k1_funct_1(A,k4_tarski(B,C)) = f4_s5_partfun1(B,C) ) ) ),
    file(partfun1,s5_partfun1),
    [interesting(0.00)]).

fof(s1_grcat_1,theorem,
    ( ! [A,B] : 
        ( ( r2_hidden(A,f1_s1_grcat_1)
          & r2_hidden(B,f2_s1_grcat_1)
          & p1_s1_grcat_1(A,B) )
       => r2_hidden(f4_s1_grcat_1(A,B),f3_s1_grcat_1) )
   => ? [A] : 
        ( v1_funct_1(A)
        & m2_relset_1(A,k2_zfmisc_1(f1_s1_grcat_1,f2_s1_grcat_1),f3_s1_grcat_1)
        & ! [B,C] : 
            ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
          <=> ( r2_hidden(B,f1_s1_grcat_1)
              & r2_hidden(C,f2_s1_grcat_1)
              & p1_s1_grcat_1(B,C) ) )
        & ! [B,C] : 
            ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
           => k1_funct_1(A,k4_tarski(B,C)) = f4_s1_grcat_1(B,C) ) ) ),
    inference(mizar_proof,[status(thm)],[s5_partfun1]),
    [file(grcat_1,s1_grcat_1),interesting(0.00)]).

fof(t10_grcat_1,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => u1_cat_1(k6_grcat_1(A,B)) = B ) ) ),
    file(grcat_1,t10_grcat_1),
    [interesting(0.00)]).

fof(t21_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_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    [interesting(0.00)]).

fof(d13_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_grcat_1(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ),
    file(grcat_1,d13_grcat_1),
    [interesting(0.00)]).

fof(t14_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_rlvect_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v1_grcat_1(D,A,B)
                          & v1_grcat_1(E,B,C) )
                       => v1_grcat_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_funct_2,t21_funct_2,d13_grcat_1,d13_grcat_1,d13_grcat_1]),
    [file(grcat_1,t14_grcat_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(d7_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v5_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => k2_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ) ),
    file(rlvect_1,d7_rlvect_1),
    [interesting(0.00)]).

fof(t17_grcat_1,theorem,(
    ! [A] : 
      ( l1_grcat_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
                 => ( A = g1_grcat_1(B,C,D)
                   => ( k9_grcat_1(A) = B
                      & k10_grcat_1(A) = C
                      & k11_grcat_1(A) = D ) ) ) ) ) ) ),
    file(grcat_1,t17_grcat_1),
    [interesting(0.00)]).

fof(t1_grcat_1,theorem,(
    $true ),
    file(grcat_1,t1_grcat_1),
    [interesting(0.00)]).

fof(t35_funct_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k6_relat_1(A),B) = B ) ),
    file(funct_1,t35_funct_1),
    [interesting(0.00)]).

fof(t26_grcat_1,theorem,(
    ! [A] : 
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] : 
          ( ( v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ~ ( k9_grcat_1(A) = k10_grcat_1(B)
              & ! [C] : 
                  ( ( ~ v3_struct_0(C)
                    & v4_rlvect_1(C)
                    & v5_rlvect_1(C)
                    & v6_rlvect_1(C)
                    & l1_rlvect_1(C) )
                 => ! [D] : 
                      ( ( ~ v3_struct_0(D)
                        & v4_rlvect_1(D)
                        & v5_rlvect_1(D)
                        & v6_rlvect_1(D)
                        & l1_rlvect_1(D) )
                     => ! [E] : 
                          ( ( ~ v3_struct_0(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & l1_rlvect_1(E) )
                         => ~ ( m1_grcat_1(A,D,E)
                              & m1_grcat_1(B,C,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_grcat_1,d19_grcat_1,t24_grcat_1,d19_grcat_1]),
    [file(grcat_1,t26_grcat_1),interesting(0.00)]).

fof(t27_grcat_1,theorem,(
    $true ),
    file(grcat_1,t27_grcat_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(t35_grcat_1,theorem,(
    $true ),
    file(grcat_1,t35_grcat_1),
    [interesting(0.00)]).

fof(t36_grcat_1,theorem,(
    $true ),
    file(grcat_1,t36_grcat_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(d23_grcat_1,definition,(
    ! [A] : 
      ( v5_grcat_1(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => ( v2_grcat_1(B)
            & v3_grcat_1(B)
            & l1_grcat_1(B) ) ) ) ),
    file(grcat_1,d23_grcat_1),
    [interesting(0.00)]).

fof(d24_grcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v5_grcat_1(C) )
             => ( m4_grcat_1(C,A,B)
              <=> ! [D] : 
                    ( m3_grcat_1(D,C)
                   => ( v2_grcat_1(D)
                      & m1_grcat_1(D,A,B) ) ) ) ) ) ) ),
    file(grcat_1,d24_grcat_1),
    [interesting(0.00)]).

fof(t38_grcat_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & l1_rlvect_1(C) )
             => ( m4_grcat_1(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ( v2_grcat_1(D)
                      & m1_grcat_1(D,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_grcat_1,d23_grcat_1,d24_grcat_1]),
    [file(grcat_1,t38_grcat_1),interesting(0.00)]).

fof(t33_mcart_1,theorem,(
    ! [A,B,C,D,E,F,G,H] : 
      ( k4_mcart_1(A,B,C,D) = k4_mcart_1(E,F,G,H)
     => ( A = E
        & B = F
        & C = G
        & D = H ) ) ),
    file(mcart_1,t33_mcart_1),
    [interesting(0.00)]).

fof(t52_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => u1_cat_1(k30_grcat_1(A)) = k29_grcat_1(A) ) ),
    file(grcat_1,t52_grcat_1),
    [interesting(0.00)]).

fof(t53_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => u1_cat_1(k32_grcat_1(A)) = k31_grcat_1(A) ) ),
    file(grcat_1,t53_grcat_1),
    [interesting(0.00)]).

fof(t62_classes2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => r2_hidden(k1_xboole_0,A) ) ),
    file(classes2,t62_classes2),
    [interesting(0.00)]).

fof(d3_algstr_1,definition,(
    ! [A] : k1_algstr_1(A) = A ),
    file(algstr_1,d3_algstr_1),
    [interesting(0.00)]).

fof(t63_classes2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & v1_classes2(B) )
     => ( r2_hidden(A,B)
       => r2_hidden(k1_tarski(A),B) ) ) ),
    file(classes2,t63_classes2),
    [interesting(0.00)]).

fof(t64_classes2,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(C)
        & v1_classes2(C) )
     => ( ( r2_hidden(A,C)
          & r2_hidden(B,C) )
       => ( r2_hidden(k2_tarski(A,B),C)
          & r2_hidden(k4_tarski(A,B),C) ) ) ) ),
    file(classes2,t64_classes2),
    [interesting(0.00)]).

fof(t67_classes2,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(C)
        & v1_classes2(C) )
     => ( ( r2_hidden(A,C)
          & r2_hidden(B,C) )
       => ( r2_hidden(k2_zfmisc_1(A,B),C)
          & r2_hidden(k1_funct_2(A,B),C) ) ) ) ),
    file(classes2,t67_classes2),
    [interesting(0.00)]).

fof(t11_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => r2_hidden(C,k1_funct_2(A,B)) ) ) ),
    file(funct_2,t11_funct_2),
    [interesting(0.00)]).

fof(d2_ordinal1,definition,(
    ! [A] : 
      ( v1_ordinal1(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => r1_tarski(B,A) ) ) ),
    file(ordinal1,d2_ordinal1),
    [interesting(0.00)]).

fof(t6_grcat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_classes2(A) )
     => ( r2_hidden(k1_tarski(k1_xboole_0),A)
        & r2_hidden(k4_tarski(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A)
        & r2_hidden(k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A)
        & r2_hidden(k2_midsp_1,A)
        & r2_hidden(k7_vectsp_2,A) ) ) ),
    inference(mizar_proof,[status(thm)],[t62_classes2,t63_classes2,t64_classes2,t67_classes2,t67_classes2,t67_classes2,t11_funct_2,t4_grcat_1,t11_funct_2,t4_grcat_1]),
    [file(grcat_1,t6_grcat_1),interesting(0.00)]).

fof(d4_algstr_1,definition,(
    k2_algstr_1 = g1_rlvect_1(k1_tarski(k1_xboole_0),k2_midsp_1,k1_algstr_1(k1_xboole_0)) ),
    file(algstr_1,d4_algstr_1),
    [interesting(0.00)]).

fof(t34_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D)))
    <=> ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t34_zfmisc_1),
    [interesting(0.00)]).

fof(t65_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,k1_tarski(B))
        & m2_relset_1(D,A,k1_tarski(B)) )
     => ( r2_hidden(C,A)
       => k1_funct_1(D,C) = B ) ) ),
    file(funct_2,t65_funct_2),
    [interesting(0.00)]).

fof(d25_vectsp_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( B = k7_vectsp_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k5_rlvect_1(A,C) ) ) ) ) ),
    file(vectsp_1,d25_vectsp_1),
    [interesting(0.00)]).

fof(t18_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] : 
                ( r2_hidden(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) ),
    file(funct_2,t18_funct_2),
    [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(d4_mcart_1,definition,(
    ! [A,B,C,D] : k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D) ),
    file(mcart_1,d4_mcart_1),
    [interesting(0.00)]).

fof(d5_midsp_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v1_midsp_2(A)
      <=> ( ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ? [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                  & k1_midsp_2(A,C) = B ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ( k1_midsp_2(A,B) = k1_rlvect_1(A)
               => B = k1_rlvect_1(A) ) ) ) ) ) ),
    file(midsp_2,d5_midsp_2),
    [interesting(0.00)]).

fof(t8_grcat_1,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k2_algstr_1))
       => A = k1_xboole_0 )
    & ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k2_algstr_1))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(k2_algstr_1))
           => k4_rlvect_1(k2_algstr_1,A,B) = k1_xboole_0 ) )
    & ! [A] : 
        ( m1_subset_1(A,u1_struct_0(k2_algstr_1))
       => k5_rlvect_1(k2_algstr_1,A) = k1_xboole_0 )
    & k1_rlvect_1(k2_algstr_1) = k1_xboole_0 ),
    inference(mizar_proof,[status(thm)],[d4_algstr_1,d1_tarski]),
    [file(grcat_1,t8_grcat_1),interesting(0.00)]).

fof(t30_cat_2,theorem,(
    ! [A] : 
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,C,B)
                    & m2_relset_1(D,C,B) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,C,B)
                        & m2_relset_1(E,C,B) )
                     => ! [F] : 
                          ( ( v1_funct_1(F)
                            & m2_relset_1(F,k2_zfmisc_1(C,C),C) )
                         => ! [G] : 
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,B,C)
                                & m2_relset_1(G,B,C) )
                             => ( ( C = k3_tarski(a_2_0_cat_2(A,B))
                                  & D = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C)
                                  & E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)
                                  & F = k1_realset1(u5_cat_1(A),C)
                                  & G = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) )
                               => r1_cat_2(g1_cat_1(B,C,D,E,F,G),A) ) ) ) ) ) ) ) ) ),
    file(cat_2,t30_cat_2),
    [interesting(0.00)]).