SET007 Axioms: SET007+435.ax


%------------------------------------------------------------------------------
% File     : SET007+435 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Indexed Category
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : index_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  113 (   2 unit)
%            Number of atoms       :  847 (  76 equality)
%            Maximal formula depth :   23 (  10 average)
%            Number of connectives :  779 (  45 ~  ;   0  |; 384  &)
%                                         (  18 <=>; 332 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   33 (   1 propositional; 0-7 arity)
%            Number of functors    :   62 (   3 constant; 0-6 arity)
%            Number of variables   :  449 (   0 singleton; 435 !;  14 ?)
%            Maximal term depth    :    7 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_index_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_pboole(B,A)
          & v1_relat_1(B)
          & ~ v3_relat_1(B)
          & v1_funct_1(B) ) ) )).

fof(cc1_index_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) )).

fof(rc2_index_1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_index_1(A) ) )).

fof(rc3_index_1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_index_1(B) ) )).

fof(fc1_index_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & v1_index_1(k2_funcop_1(A,B)) ) ) )).

fof(cc2_index_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_pboole(B,A)
         => ~ v1_xboole_0(B) ) ) )).

fof(fc2_index_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_index_1(A) )
     => v2_cat_5(k2_relat_1(A)) ) )).

fof(fc3_index_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_index_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B))
        & v1_index_1(k5_relat_1(A,B)) ) ) )).

fof(rc4_index_1,axiom,(
    ! [A,B] :
    ? [C] :
      ( m1_index_1(C,A,B)
      & v2_index_1(C,A,B)
      & v3_index_1(C,A,B) ) )).

fof(fc4_index_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => v1_fraenkel(k2_relat_1(A)) ) )).

fof(rc5_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m3_index_1(E,A,B,C,D) )
     => ? [F] :
          ( m4_index_1(F,A,B,C,D,E)
          & v1_cat_1(F)
          & v2_cat_1(F)
          & v1_cat_5(F)
          & v3_cat_5(F)
          & v4_cat_5(F) ) ) )).

fof(fc5_index_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & v3_cat_5(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => ( v1_relat_1(k12_cat_1(A,B,C))
        & v1_funct_1(k12_cat_1(A,B,C))
        & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B))
        & v1_index_1(k12_cat_1(A,B,C)) ) ) )).

fof(t1_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & v3_cat_5(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,C) = k3_cat_1(A,B)
               => k4_cat_1(A,B,C) = k4_tarski(k12_cat_2(A,A,k2_cat_1(A,B),k3_cat_1(A,C)),k1_partfun1(u2_cat_1(k8_cat_5(A,B)),u2_cat_1(k9_cat_5(A,B)),u2_cat_1(k8_cat_5(A,C)),u2_cat_1(k9_cat_5(A,C)),k1_index_1(A,B),k1_index_1(A,C))) ) ) ) ) )).

fof(t2_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & v3_cat_5(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,C)
                     => ( D = E
                       => k12_cat_1(A,B,D) = k12_cat_1(A,C,E) ) ) ) ) ) ) )).

fof(d1_index_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_index_1(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => ( v2_cat_1(k1_funct_1(A,B))
              & l1_cat_1(k1_funct_1(A,B)) ) ) ) ) )).

fof(d2_index_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_index_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k3_index_1(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => ! [D] :
                      ( ( v2_cat_1(D)
                        & l1_cat_1(D) )
                     => ( D = k1_funct_1(A,C)
                       => k1_funct_1(B,C) = u1_cat_1(D) ) ) ) ) ) ) ) )).

fof(d3_index_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_index_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v2_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k4_index_1(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] :
                  ( r2_hidden(C,k1_relat_1(A))
                 => ! [D] :
                      ( ( v2_cat_1(D)
                        & l1_cat_1(D) )
                     => ( D = k1_funct_1(A,C)
                       => k1_funct_1(B,C) = u2_cat_1(D) ) ) ) ) ) ) ) )).

fof(t3_index_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(B)
        & l1_cat_1(B) )
     => ( k3_index_1(k2_pre_circ(A,B)) = k2_pre_circ(A,u1_cat_1(B))
        & k4_index_1(k2_pre_circ(A,B)) = k2_pre_circ(A,u2_cat_1(B)) ) ) )).

fof(d4_index_1,axiom,(
    ! [A,B,C] :
      ( m1_index_1(C,A,B)
    <=> ? [D] :
          ( m1_pboole(D,A)
          & ? [E] :
              ( m1_pboole(E,B)
              & C = k4_tarski(D,E) ) ) ) )).

fof(d5_index_1,axiom,(
    ! [A,B,C] :
      ( m1_index_1(C,A,B)
     => ( v2_index_1(C,A,B)
      <=> v1_index_1(k8_index_1(A,B,C)) ) ) )).

fof(d6_index_1,axiom,(
    ! [A,B,C] :
      ( m1_index_1(C,A,B)
     => ( v3_index_1(C,A,B)
      <=> v1_funcop_1(k9_index_1(A,B,C)) ) ) )).

fof(d7_index_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_index_1(B)
            & m1_pboole(B,A) )
         => ! [C] :
              ( ( v1_index_1(C)
                & m1_pboole(C,A) )
             => ! [D] :
                  ( ( v1_funcop_1(D)
                    & m1_pboole(D,A) )
                 => ( m2_index_1(D,A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,A)
                       => m2_cat_1(k1_funct_1(D,E),k2_index_1(A,B,E),k2_index_1(A,C,E)) ) ) ) ) ) ) )).

fof(d8_index_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( ( v2_index_1(E,A,B)
                        & m1_index_1(E,A,B) )
                     => ( m3_index_1(E,A,B,C,D)
                      <=> m2_index_1(k9_index_1(A,B,E),B,k7_pboole(B,A,C,k10_index_1(A,B,E)),k7_pboole(B,A,D,k10_index_1(A,B,E))) ) ) ) ) ) ) )).

fof(t4_index_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( m3_index_1(E,A,B,C,D)
                     => ! [F] :
                          ( m1_subset_1(F,B)
                         => m2_cat_1(k1_funct_1(k9_index_1(A,B,E),F),k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,C,F)),k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,D,F))) ) ) ) ) ) ) )).

fof(t5_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => m2_cat_1(k1_funct_1(k9_index_1(u1_cat_1(A),u2_cat_1(A),B),C),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k2_cat_1(A,C)),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k3_cat_1(A,C))) ) ) ) )).

fof(d9_index_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( m3_index_1(E,A,B,C,D)
                     => ! [F] :
                          ( ( v2_cat_1(F)
                            & v3_cat_5(F)
                            & l1_cat_1(F) )
                         => ( m4_index_1(F,A,B,C,D,E)
                          <=> ( ! [G] :
                                  ( m1_subset_1(G,A)
                                 => m1_subset_1(k2_index_1(A,k10_index_1(A,B,E),G),u1_cat_1(F)) )
                              & ! [G] :
                                  ( m1_subset_1(G,B)
                                 => m1_subset_1(k4_tarski(k4_tarski(k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,C,G)),k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,D,G))),k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,E)),k7_pboole(B,A,D,k10_index_1(A,B,E)),k14_index_1(A,B,C,D,E),G)),u2_cat_1(F)) ) ) ) ) ) ) ) ) ) )).

fof(d10_index_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ? [G] :
                                ( v2_cat_1(G)
                                & l1_cat_1(G)
                                & G = g1_cat_1(A,B,C,D,E,F) )
                           => ! [G] :
                                ( m3_index_1(G,A,B,C,D)
                               => ( m5_index_1(G,A,B,C,D,E,F)
                                <=> ( ! [H] :
                                        ( m1_subset_1(H,A)
                                       => k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),k7_pboole(B,A,D,k10_index_1(A,B,G)),k14_index_1(A,B,C,D,G),k8_funct_2(A,B,F,H)) = k15_cat_1(k2_index_1(A,k10_index_1(A,B,G),H)) )
                                    & ! [H] :
                                        ( m1_subset_1(H,B)
                                       => ! [I] :
                                            ( m1_subset_1(I,B)
                                           => ( k8_funct_2(B,A,C,I) = k8_funct_2(B,A,D,H)
                                             => k1_funct_1(k14_index_1(A,B,C,D,G),k1_funct_1(E,k4_tarski(I,H))) = k1_partfun1(u2_cat_1(k2_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),H)),u2_cat_1(k2_index_1(B,k7_pboole(B,A,D,k10_index_1(A,B,G)),H)),u2_cat_1(k2_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),I)),u2_cat_1(k2_index_1(B,k7_pboole(B,A,D,k10_index_1(A,B,G)),I)),k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),k7_pboole(B,A,D,k10_index_1(A,B,G)),k14_index_1(A,B,C,D,G),H),k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),k7_pboole(B,A,D,k10_index_1(A,B,G)),k14_index_1(A,B,C,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t6_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A))
         => ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
          <=> ( ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),k10_cat_1(A,C)) = k15_cat_1(k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C)) )
              & ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( k2_cat_1(A,D) = k3_cat_1(A,C)
                       => k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),k4_cat_1(A,C,D)) = k1_partfun1(u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),C),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),D)) ) ) ) ) ) ) ) )).

fof(t7_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m3_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A))
         => ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
          <=> ( ! [C] :
                  ( m1_subset_1(C,u1_cat_1(A))
                 => k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),k10_cat_1(A,C)) = k15_cat_1(k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C)) )
              & ! [C] :
                  ( m1_subset_1(C,u2_cat_1(A))
                 => ! [D] :
                      ( m1_subset_1(D,u2_cat_1(A))
                     => ( k2_cat_1(A,D) = k3_cat_1(A,C)
                       => k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),k4_cat_1(A,C,D)) = k1_partfun1(u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),D),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),C)) ) ) ) ) ) ) ) )).

fof(t8_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
        <=> m5_index_1(B,u1_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(A)),u3_cat_1(k2_oppcat_1(A)),u4_cat_1(k2_oppcat_1(A)),u5_cat_1(k2_oppcat_1(A)),u6_cat_1(k2_oppcat_1(A))) ) ) )).

fof(t9_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ( ~ v1_xboole_0(k6_cat_1(A,C,D))
                   => ! [E] :
                        ( m1_cat_1(E,A,C,D)
                       => m2_cat_1(k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),E),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),D)) ) ) ) ) ) ) )).

fof(t10_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u1_cat_1(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => ( ~ v1_xboole_0(k6_cat_1(A,C,D))
                   => ! [E] :
                        ( m1_cat_1(E,A,C,D)
                       => m2_cat_1(k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),E),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),D),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C)) ) ) ) ) ) ) )).

fof(d11_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( m2_cat_1(D,A,C)
                 => ( D = k15_index_1(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u2_cat_1(A))
                       => k8_funct_2(u2_cat_1(A),u2_cat_1(C),D,E) = k4_tarski(k4_tarski(k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k2_cat_1(A,E)),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k3_cat_1(A,E))),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),E)) ) ) ) ) ) ) )).

fof(t11_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( m4_index_1(D,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
                 => ( k15_index_1(A,B,C) = k15_index_1(A,B,D)
                    & k12_cat_1(A,C,k15_index_1(A,B,C)) = k12_cat_1(A,D,k15_index_1(A,B,D)) ) ) ) ) ) )).

fof(t12_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => k12_cat_1(A,C,k15_index_1(A,B,C)) = k10_index_1(u1_cat_1(A),u2_cat_1(A),B) ) ) ) )).

fof(t13_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( m1_subset_1(D,u1_cat_1(A))
                 => k13_cat_1(A,C,k15_index_1(A,B,C),D) = k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),D) ) ) ) ) )).

fof(d12_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( ( v1_cat_1(C)
                & m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) )
             => ( C = k16_index_1(A,B)
              <=> ! [D] :
                    ( m4_index_1(D,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
                   => C = k7_cat_5(A,D,k15_index_1(A,B,D)) ) ) ) ) ) )).

fof(t14_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( ( v2_cat_1(C)
                & v3_cat_5(C)
                & l1_cat_1(C) )
             => ( m3_cat_2(k16_index_1(A,B),C)
              <=> m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) ) ) ) ) )).

fof(d13_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => k17_index_1(A,B,C) = k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),C) ) ) ) )).

fof(d14_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
         => ! [C] :
              ( m1_subset_1(C,u2_cat_1(A))
             => k18_index_1(A,B,C) = k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),C) ) ) ) )).

fof(t15_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ( m5_index_1(k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
            & m5_index_1(k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))),u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)) ) ) ) )).

fof(t16_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => m5_index_1(k4_tarski(k12_cat_1(A,B,C),k16_mcart_1(C)),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ) ) )).

fof(d15_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => k19_index_1(A,B,C) = k4_tarski(k12_cat_1(A,B,C),k16_mcart_1(C)) ) ) ) )).

fof(t17_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => m4_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k19_index_1(A,B,C)) ) ) ) )).

fof(t18_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m4_index_1(D,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k19_index_1(A,B,C))
                 => C = k15_index_1(A,k19_index_1(A,B,C),D) ) ) ) ) )).

fof(t19_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & v3_cat_5(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,A,C)
                     => ( D = E
                       => k19_index_1(A,B,D) = k19_index_1(A,C,E) ) ) ) ) ) ) )).

fof(t20_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => k16_mcart_1(k15_index_1(A,B,C)) = k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) ) ) ) )).

fof(t21_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => k19_index_1(A,C,k15_index_1(A,B,C)) = B ) ) ) )).

fof(d16_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m5_index_1(E,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C))
                     => ( m3_cat_2(k7_cat_5(A,B,D),C)
                       => ! [F] :
                            ( m5_index_1(F,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
                           => ( F = k20_index_1(A,B,C,D,E)
                            <=> ! [G] :
                                  ( m2_cat_1(G,A,C)
                                 => ( G = D
                                   => F = k19_index_1(A,k16_index_1(C,E),k14_cat_1(A,C,k16_index_1(C,E),G,k15_index_1(C,E,k16_index_1(C,E)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m5_index_1(E,u1_cat_1(D),u2_cat_1(D),u3_cat_1(D),u4_cat_1(D),u5_cat_1(D),u6_cat_1(D))
                     => ! [F] :
                          ( m2_cat_1(F,A,B)
                         => ! [G] :
                              ( m2_cat_1(G,A,C)
                             => ( ( m3_cat_2(k7_cat_5(A,B,F),D)
                                  & m3_cat_2(k7_cat_5(A,C,G),D)
                                  & F = G )
                               => k20_index_1(A,B,D,F,E) = k20_index_1(A,C,D,G,E) ) ) ) ) ) ) ) ) )).

fof(t23_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
                     => k20_index_1(A,B,B,C,D) = k19_index_1(A,E,k14_cat_1(A,B,E,C,k15_index_1(B,D,E))) ) ) ) ) ) )).

fof(t24_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
                     => m4_index_1(E,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k20_index_1(A,B,B,C,D)) ) ) ) ) ) )).

fof(t25_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
                     => m3_cat_2(k16_index_1(A,k20_index_1(A,B,B,C,D)),E) ) ) ) ) ) )).

fof(t26_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( ( v2_cat_1(C)
                & l1_cat_1(C) )
             => ! [D] :
                  ( m2_cat_1(D,A,B)
                 => ! [E] :
                      ( m2_cat_1(E,B,C)
                     => ! [F] :
                          ( m5_index_1(F,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C))
                         => k20_index_1(A,B,B,D,k20_index_1(B,C,C,E,F)) = k20_index_1(A,C,C,k14_cat_1(A,B,C,D,E),F) ) ) ) ) ) ) )).

fof(d17_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( ( v2_cat_1(C)
                & v3_cat_5(C)
                & l1_cat_1(C) )
             => ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
               => ! [D] :
                    ( ( v2_cat_1(D)
                      & v3_cat_5(D)
                      & l1_cat_1(D) )
                   => ! [E] :
                        ( m2_cat_1(E,C,D)
                       => ! [F] :
                            ( m5_index_1(F,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
                           => ( F = k21_index_1(A,B,C,D,E)
                            <=> ! [G] :
                                  ( m4_index_1(G,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
                                 => ! [H] :
                                      ( m2_cat_1(H,G,D)
                                     => ( ( G = C
                                          & H = E )
                                       => F = k19_index_1(A,D,k14_cat_1(A,G,D,k15_index_1(A,B,G),H)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t27_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & v3_cat_5(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( ( v2_cat_1(E)
                        & v3_cat_5(E)
                        & l1_cat_1(E) )
                     => ! [F] :
                          ( m2_cat_1(F,C,D)
                         => ! [G] :
                              ( m2_cat_1(G,C,E)
                             => ( F = G
                               => k21_index_1(A,B,C,D,F) = k21_index_1(A,B,C,E,G) ) ) ) ) ) ) ) ) )).

fof(t28_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & v3_cat_5(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,C,D)
                     => m4_index_1(k7_cat_5(C,D,E),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k21_index_1(A,B,C,D,E)) ) ) ) ) ) )).

fof(t29_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & v3_cat_5(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,C,D)
                     => m4_index_1(D,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k21_index_1(A,B,C,D,E)) ) ) ) ) ) )).

fof(t30_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & v3_cat_5(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,C,D)
                     => m3_cat_2(k16_index_1(A,k21_index_1(A,B,C,D,E)),k7_cat_5(C,D,E)) ) ) ) ) ) )).

fof(t31_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & v3_cat_5(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( ( v2_cat_1(E)
                        & v3_cat_5(E)
                        & l1_cat_1(E) )
                     => ! [F] :
                          ( m2_cat_1(F,C,D)
                         => ! [G] :
                              ( m2_cat_1(G,D,E)
                             => k21_index_1(A,B,C,E,k14_cat_1(C,D,E,F,G)) = k21_index_1(A,k21_index_1(A,B,C,D,F),D,E,G) ) ) ) ) ) ) ) )).

fof(d18_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m5_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
                 => k22_index_1(A,B,C,D) = k20_index_1(A,k16_index_1(A,C),B,k15_index_1(A,C,k16_index_1(A,C)),D) ) ) ) ) )).

fof(t32_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m5_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),C)
                     => ( m4_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),C)
                       => k22_index_1(A,B,C,D) = k20_index_1(A,E,B,k15_index_1(A,C,E),D) ) ) ) ) ) ) )).

fof(t33_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & v3_cat_5(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m5_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
                     => ( m4_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),C)
                       => k22_index_1(A,B,C,D) = k21_index_1(A,C,B,E,k15_index_1(B,D,E)) ) ) ) ) ) ) )).

fof(t34_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
                     => ! [F] :
                          ( ( v2_cat_1(F)
                            & v3_cat_5(F)
                            & l1_cat_1(F) )
                         => ! [G] :
                              ( m2_cat_1(G,E,F)
                             => k20_index_1(A,B,B,C,k21_index_1(B,D,E,F,G)) = k21_index_1(A,k20_index_1(A,B,B,C,D),E,F,G) ) ) ) ) ) ) ) )).

fof(t35_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( ( v2_cat_1(D)
                    & v3_cat_5(D)
                    & l1_cat_1(D) )
                 => ! [E] :
                      ( m2_cat_1(E,C,D)
                     => ! [F] :
                          ( m5_index_1(F,u1_cat_1(D),u2_cat_1(D),u3_cat_1(D),u4_cat_1(D),u5_cat_1(D),u6_cat_1(D))
                         => k22_index_1(A,C,B,k20_index_1(C,D,D,E,F)) = k22_index_1(A,D,k21_index_1(A,B,C,D,E),F) ) ) ) ) ) ) )).

fof(t36_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),D)
                     => ! [F] :
                          ( ( v2_cat_1(F)
                            & v3_cat_5(F)
                            & l1_cat_1(F) )
                         => ! [G] :
                              ( m2_cat_1(G,E,F)
                             => k22_index_1(A,C,B,k21_index_1(C,D,E,F,G)) = k21_index_1(A,k22_index_1(A,C,B,D),E,F,G) ) ) ) ) ) ) ) )).

fof(t37_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( ( v2_cat_1(B)
            & l1_cat_1(B) )
         => ! [C] :
              ( m2_cat_1(C,A,B)
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
                     => ! [F] :
                          ( m5_index_1(F,u1_cat_1(E),u2_cat_1(E),u3_cat_1(E),u4_cat_1(E),u5_cat_1(E),u6_cat_1(E))
                         => k20_index_1(A,B,B,C,k22_index_1(B,E,D,F)) = k22_index_1(A,E,k20_index_1(A,B,B,C,D),F) ) ) ) ) ) ) )).

fof(t38_index_1,axiom,(
    ! [A] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A) )
     => ! [B] :
          ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
         => ! [C] :
              ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
             => ! [D] :
                  ( m5_index_1(D,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C))
                 => ! [E] :
                      ( m4_index_1(E,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),D)
                     => ! [F] :
                          ( m5_index_1(F,u1_cat_1(E),u2_cat_1(E),u3_cat_1(E),u4_cat_1(E),u5_cat_1(E),u6_cat_1(E))
                         => k22_index_1(A,C,B,k22_index_1(C,E,D,F)) = k22_index_1(A,E,k22_index_1(A,C,B,D),F) ) ) ) ) ) ) )).

fof(s1_index_1,axiom,
    ( ! [A] :
        ( m1_subset_1(A,f1_s1_index_1)
       => m2_cat_1(f4_s1_index_1(A),k2_index_1(f1_s1_index_1,f2_s1_index_1,A),k2_index_1(f1_s1_index_1,f3_s1_index_1,A)) )
   => ? [A] :
        ( m2_index_1(A,f1_s1_index_1,f2_s1_index_1,f3_s1_index_1)
        & ! [B] :
            ( m1_subset_1(B,f1_s1_index_1)
           => k1_funct_1(A,B) = f4_s1_index_1(B) ) ) )).

fof(dt_m1_index_1,axiom,(
    $true )).

fof(existence_m1_index_1,axiom,(
    ! [A,B] :
    ? [C] : m1_index_1(C,A,B) )).

fof(dt_m2_index_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & v1_index_1(C)
        & m1_pboole(C,A) )
     => ! [D] :
          ( m2_index_1(D,A,B,C)
         => ( v1_funcop_1(D)
            & m1_pboole(D,A) ) ) ) )).

fof(existence_m2_index_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & v1_index_1(C)
        & m1_pboole(C,A) )
     => ? [D] : m2_index_1(D,A,B,C) ) )).

fof(dt_m3_index_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ! [E] :
          ( m3_index_1(E,A,B,C,D)
         => ( v2_index_1(E,A,B)
            & m1_index_1(E,A,B) ) ) ) )).

fof(existence_m3_index_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ? [E] : m3_index_1(E,A,B,C,D) ) )).

fof(dt_m4_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m3_index_1(E,A,B,C,D) )
     => ! [F] :
          ( m4_index_1(F,A,B,C,D,E)
         => ( v2_cat_1(F)
            & v3_cat_5(F)
            & l1_cat_1(F) ) ) ) )).

fof(existence_m4_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m3_index_1(E,A,B,C,D) )
     => ? [F] : m4_index_1(F,A,B,C,D,E) ) )).

fof(dt_m5_index_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B) )
     => ! [G] :
          ( m5_index_1(G,A,B,C,D,E,F)
         => m3_index_1(G,A,B,C,D) ) ) )).

fof(existence_m5_index_1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & v1_funct_1(E)
        & m1_relset_1(E,k2_zfmisc_1(B,B),B)
        & v1_funct_1(F)
        & v1_funct_2(F,A,B)
        & m1_relset_1(F,A,B) )
     => ? [G] : m5_index_1(G,A,B,C,D,E,F) ) )).

fof(dt_k1_index_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => m2_cat_1(k1_index_1(A,B),k8_cat_5(A,B),k9_cat_5(A,B)) ) )).

fof(redefinition_k1_index_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & v3_cat_5(A)
        & l1_cat_1(A)
        & m1_subset_1(B,u2_cat_1(A)) )
     => k1_index_1(A,B) = k2_mcart_1(B) ) )).

fof(dt_k2_index_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( v2_cat_1(k2_index_1(A,B,C))
        & l1_cat_1(k2_index_1(A,B,C)) ) ) )).

fof(redefinition_k2_index_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k2_index_1(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k3_index_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_index_1(A) )
     => ( v1_relat_1(k3_index_1(A))
        & v2_relat_1(k3_index_1(A))
        & v1_funct_1(k3_index_1(A)) ) ) )).

fof(dt_k4_index_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_index_1(A) )
     => ( v1_relat_1(k4_index_1(A))
        & v2_relat_1(k4_index_1(A))
        & v1_funct_1(k4_index_1(A)) ) ) )).

fof(dt_k5_index_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A) )
     => ( v2_relat_1(k5_index_1(A,B))
        & m1_pboole(k5_index_1(A,B),A) ) ) )).

fof(redefinition_k5_index_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A) )
     => k5_index_1(A,B) = k3_index_1(B) ) )).

fof(dt_k6_index_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A) )
     => ( v2_relat_1(k6_index_1(A,B))
        & m1_pboole(k6_index_1(A,B),A) ) ) )).

fof(redefinition_k6_index_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A) )
     => k6_index_1(A,B) = k4_index_1(B) ) )).

fof(dt_k7_index_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_pboole(C,A)
        & m1_pboole(D,B) )
     => m1_index_1(k7_index_1(A,B,C,D),A,B) ) )).

fof(redefinition_k7_index_1,axiom,(
    ! [A,B,C,D] :
      ( ( m1_pboole(C,A)
        & m1_pboole(D,B) )
     => k7_index_1(A,B,C,D) = k4_tarski(C,D) ) )).

fof(dt_k8_index_1,axiom,(
    ! [A,B,C] :
      ( m1_index_1(C,A,B)
     => m1_pboole(k8_index_1(A,B,C),A) ) )).

fof(redefinition_k8_index_1,axiom,(
    ! [A,B,C] :
      ( m1_index_1(C,A,B)
     => k8_index_1(A,B,C) = k1_mcart_1(C) ) )).

fof(dt_k9_index_1,axiom,(
    ! [A,B,C] :
      ( m1_index_1(C,A,B)
     => m1_pboole(k9_index_1(A,B,C),B) ) )).

fof(redefinition_k9_index_1,axiom,(
    ! [A,B,C] :
      ( m1_index_1(C,A,B)
     => k9_index_1(A,B,C) = k2_mcart_1(C) ) )).

fof(dt_k10_index_1,axiom,(
    ! [A,B,C] :
      ( ( v2_index_1(C,A,B)
        & m1_index_1(C,A,B) )
     => ( v1_index_1(k10_index_1(A,B,C))
        & m1_pboole(k10_index_1(A,B,C),A) ) ) )).

fof(redefinition_k10_index_1,axiom,(
    ! [A,B,C] :
      ( ( v2_index_1(C,A,B)
        & m1_index_1(C,A,B) )
     => k10_index_1(A,B,C) = k1_mcart_1(C) ) )).

fof(dt_k11_index_1,axiom,(
    ! [A,B,C] :
      ( ( v3_index_1(C,A,B)
        & m1_index_1(C,A,B) )
     => ( v1_funcop_1(k11_index_1(A,B,C))
        & m1_pboole(k11_index_1(A,B,C),B) ) ) )).

fof(redefinition_k11_index_1,axiom,(
    ! [A,B,C] :
      ( ( v3_index_1(C,A,B)
        & m1_index_1(C,A,B) )
     => k11_index_1(A,B,C) = k2_mcart_1(C) ) )).

fof(dt_k12_index_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_index_1(C)
        & m1_pboole(C,A)
        & v1_funcop_1(D)
        & m1_pboole(D,B) )
     => ( v2_index_1(k12_index_1(A,B,C,D),A,B)
        & v3_index_1(k12_index_1(A,B,C,D),A,B)
        & m1_index_1(k12_index_1(A,B,C,D),A,B) ) ) )).

fof(redefinition_k12_index_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_index_1(C)
        & m1_pboole(C,A)
        & v1_funcop_1(D)
        & m1_pboole(D,B) )
     => k12_index_1(A,B,C,D) = k4_tarski(C,D) ) )).

fof(dt_k13_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & v1_index_1(C)
        & m1_pboole(C,A)
        & m2_index_1(D,A,B,C)
        & m1_subset_1(E,A) )
     => m2_cat_1(k13_index_1(A,B,C,D,E),k2_index_1(A,B,E),k2_index_1(A,C,E)) ) )).

fof(redefinition_k13_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & v1_index_1(B)
        & m1_pboole(B,A)
        & v1_index_1(C)
        & m1_pboole(C,A)
        & m2_index_1(D,A,B,C)
        & m1_subset_1(E,A) )
     => k13_index_1(A,B,C,D,E) = k1_funct_1(D,E) ) )).

fof(dt_k14_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m3_index_1(E,A,B,C,D) )
     => m2_index_1(k14_index_1(A,B,C,D,E),B,k7_pboole(B,A,C,k10_index_1(A,B,E)),k7_pboole(B,A,D,k10_index_1(A,B,E))) ) )).

fof(redefinition_k14_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,A)
        & m1_relset_1(C,B,A)
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A)
        & m3_index_1(E,A,B,C,D) )
     => k14_index_1(A,B,C,D,E) = k2_mcart_1(E) ) )).

fof(dt_k15_index_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
        & m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) )
     => m2_cat_1(k15_index_1(A,B,C),A,C) ) )).

fof(dt_k16_index_1,axiom,(
    ! [A,B] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) )
     => ( v1_cat_1(k16_index_1(A,B))
        & m4_index_1(k16_index_1(A,B),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) ) ) )).

fof(dt_k17_index_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => m2_cat_1(k17_index_1(A,B,C),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k2_cat_1(A,C)),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k3_cat_1(A,C))) ) )).

fof(dt_k18_index_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
        & m1_subset_1(C,u2_cat_1(A)) )
     => m2_cat_1(k18_index_1(A,B,C),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k3_cat_1(A,C)),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k2_cat_1(A,C))) ) )).

fof(dt_k19_index_1,axiom,(
    ! [A,B,C] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & v3_cat_5(B)
        & l1_cat_1(B)
        & m2_cat_1(C,A,B) )
     => m5_index_1(k19_index_1(A,B,C),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) )).

fof(dt_k20_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & v2_cat_1(C)
        & l1_cat_1(C)
        & m2_cat_1(D,A,B)
        & m5_index_1(E,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C)) )
     => m5_index_1(k20_index_1(A,B,C,D,E),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) )).

fof(dt_k21_index_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
        & v2_cat_1(C)
        & v3_cat_5(C)
        & l1_cat_1(C)
        & v2_cat_1(D)
        & v3_cat_5(D)
        & l1_cat_1(D)
        & m2_cat_1(E,C,D) )
     => m5_index_1(k21_index_1(A,B,C,D,E),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) )).

fof(dt_k22_index_1,axiom,(
    ! [A,B,C,D] :
      ( ( v2_cat_1(A)
        & l1_cat_1(A)
        & v2_cat_1(B)
        & l1_cat_1(B)
        & m5_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
        & m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) )
     => m5_index_1(k22_index_1(A,B,C,D),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) )).
%------------------------------------------------------------------------------