SET007 Axioms: SET007+554.ax


%------------------------------------------------------------------------------
% File     : SET007+554 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Product of the Families of the Groups
% 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    : group_7 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  113 (   0 unit)
%            Number of atoms       :  986 (  82 equality)
%            Maximal formula depth :   28 (  10 average)
%            Number of connectives : 1065 ( 192 ~  ;   0  |; 645  &)
%                                         (  10 <=>; 218 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   30 (   0 propositional; 1-3 arity)
%            Number of functors    :   48 (   4 constant; 0-6 arity)
%            Number of variables   :  326 (   0 singleton; 320 !;   6 ?)
%            Maximal term depth    :    5 (   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(cc1_group_7,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_group_7(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_pralg_1(A) ) ) )).

fof(rc1_group_7,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v1_group_7(B) ) )).

fof(rc2_group_7,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_pralg_1(A)
      & v1_group_7(A) ) )).

fof(fc1_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k12_pralg_1(A,B))
        & v2_relat_1(k12_pralg_1(A,B))
        & v1_funct_1(k12_pralg_1(A,B)) ) ) )).

fof(fc2_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k2_group_7(A,B))
        & v1_group_1(k2_group_7(A,B))
        & v1_monoid_0(k2_group_7(A,B)) ) ) )).

fof(rc3_group_7,axiom,(
    ! [A] :
    ? [B] :
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_pralg_1(B)
      & v1_group_7(B)
      & v2_group_7(B,A)
      & v3_group_7(B,A)
      & v4_group_7(B,A) ) )).

fof(fc3_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & v2_group_7(B,A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k2_group_7(A,B))
        & v1_group_1(k2_group_7(A,B))
        & v2_group_1(k2_group_7(A,B))
        & v3_group_1(k2_group_7(A,B))
        & v1_monoid_0(k2_group_7(A,B)) ) ) )).

fof(fc4_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & v3_group_7(B,A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k2_group_7(A,B))
        & v1_group_1(k2_group_7(A,B))
        & v4_group_1(k2_group_7(A,B))
        & v1_monoid_0(k2_group_7(A,B)) ) ) )).

fof(fc5_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & v4_group_7(B,A)
        & m1_pboole(B,A) )
     => ( ~ v3_struct_0(k2_group_7(A,B))
        & v1_group_1(k2_group_7(A,B))
        & v7_group_1(k2_group_7(A,B))
        & v1_monoid_0(k2_group_7(A,B)) ) ) )).

fof(fc6_group_7,axiom,(
    ! [A,B,C,D] :
      ( ( v1_group_7(B)
        & v2_group_7(B,A)
        & v3_group_7(B,A)
        & m1_pboole(B,A)
        & m1_subset_1(C,u1_struct_0(k3_group_7(A,B)))
        & m1_subset_1(D,u1_struct_0(k3_group_7(A,B))) )
     => ( v1_relat_1(k1_binop_1(u1_group_1(k3_group_7(A,B)),C,D))
        & v1_funct_1(k1_binop_1(u1_group_1(k3_group_7(A,B)),C,D)) ) ) )).

fof(cc2_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(k12_pralg_1(k18_group_2(k1_numbers,np__1),k4_group_7(A))))
         => v1_finseq_1(B) ) ) )).

fof(cc3_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k4_group_7(A))))
         => ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finset_1(B)
            & v1_finseq_1(B) ) ) ) )).

fof(cc4_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k4_card_3(k12_pralg_1(k2_tarski(np__1,np__2),k11_group_7(A,B))))
         => v1_finseq_1(C) ) ) )).

fof(cc5_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))))
         => ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finset_1(C)
            & v1_finseq_1(C) ) ) ) )).

fof(cc6_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & l1_group_1(C) )
     => ! [D] :
          ( m1_subset_1(D,k4_card_3(k12_pralg_1(k1_enumset1(np__1,np__2,np__3),k18_group_7(A,B,C))))
         => v1_finseq_1(D) ) ) )).

fof(cc7_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & l1_group_1(C) )
     => ! [D] :
          ( m1_subset_1(D,u1_struct_0(k2_group_7(k1_enumset1(np__1,np__2,np__3),k18_group_7(A,B,C))))
         => ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finset_1(D)
            & v1_finseq_1(D) ) ) ) )).

fof(t1_group_7,axiom,(
    ! [A,B] :
      ( k9_finseq_1(A) = k9_finseq_1(B)
     => A = B ) )).

fof(t2_group_7,axiom,(
    ! [A,B,C,D] :
      ( k10_finseq_1(A,B) = k10_finseq_1(C,D)
     => ( A = C
        & B = D ) ) )).

fof(t3_group_7,axiom,(
    ! [A,B,C,D,E,F] :
      ( k11_finseq_1(A,B,C) = k11_finseq_1(D,E,F)
     => ( A = D
        & B = E
        & C = F ) ) )).

fof(d1_group_7,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_group_7(A)
      <=> ! [B] :
            ( r2_hidden(B,k2_relat_1(A))
           => ( ~ v3_struct_0(B)
              & l1_group_1(B) ) ) ) ) )).

fof(d2_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ! [C] :
          ( ( v1_group_1(C)
            & l1_group_1(C) )
         => ( C = k2_group_7(A,B)
          <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
              & ! [D] :
                  ( m1_pralg_2(D,k4_card_3(k12_pralg_1(A,B)))
                 => ! [E] :
                      ( m1_pralg_2(E,k4_card_3(k12_pralg_1(A,B)))
                     => ! [F] :
                          ~ ( r2_hidden(F,A)
                            & ! [G] :
                                ( ( ~ v3_struct_0(G)
                                  & l1_group_1(G) )
                               => ! [H] :
                                    ( ( v1_relat_1(H)
                                      & v1_funct_1(H) )
                                   => ~ ( G = k1_funct_1(B,F)
                                        & H = k1_binop_1(u1_group_1(C),D,E)
                                        & k1_funct_1(H,F) = k1_binop_1(u1_group_1(G),k1_funct_1(D,F),k1_funct_1(E,F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t4_group_7,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ! [E] :
              ( ( v1_relat_1(E)
                & v1_funct_1(E) )
             => ! [F] :
                  ( ( v1_group_7(F)
                    & m1_pboole(F,A) )
                 => ! [G] :
                      ( ( ~ v3_struct_0(G)
                        & l1_group_1(G) )
                     => ! [H] :
                          ( m1_subset_1(H,u1_struct_0(k2_group_7(A,F)))
                         => ! [I] :
                              ( m1_subset_1(I,u1_struct_0(k2_group_7(A,F)))
                             => ! [J] :
                                  ( m1_subset_1(J,u1_struct_0(G))
                                 => ! [K] :
                                      ( m1_subset_1(K,u1_struct_0(G))
                                     => ( ( r2_hidden(B,A)
                                          & G = k1_funct_1(F,B)
                                          & C = H
                                          & D = I
                                          & E = k1_group_1(k2_group_7(A,F),H,I)
                                          & k1_funct_1(C,B) = J
                                          & k1_funct_1(D,B) = K )
                                       => k1_group_1(G,J,K) = k1_funct_1(E,B) ) ) ) ) ) ) ) ) ) ) )).

fof(d3_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( v2_group_7(B,A)
      <=> ! [C] :
            ~ ( r2_hidden(C,A)
              & ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v3_group_1(D)
                    & l1_group_1(D) )
                 => D != k1_funct_1(B,C) ) ) ) ) )).

fof(d4_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( v3_group_7(B,A)
      <=> ! [C] :
            ~ ( r2_hidden(C,A)
              & ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v4_group_1(D)
                    & l1_group_1(D) )
                 => D != k1_funct_1(B,C) ) ) ) ) )).

fof(d5_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( v4_group_7(B,A)
      <=> ! [C] :
            ~ ( r2_hidden(C,A)
              & ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & v7_group_1(D)
                    & l1_group_1(D) )
                 => D != k1_funct_1(B,C) ) ) ) ) )).

fof(d6_group_7,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_group_7(B)
            & m1_pboole(B,A) )
         => ( v2_group_7(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => v3_group_1(k1_group_7(A,B,C)) ) ) ) ) )).

fof(d7_group_7,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_group_7(B)
            & m1_pboole(B,A) )
         => ( v3_group_7(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => v4_group_1(k1_group_7(A,B,C)) ) ) ) ) )).

fof(d8_group_7,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_group_7(B)
            & m1_pboole(B,A) )
         => ( v4_group_7(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => v7_group_1(k1_group_7(A,B,C)) ) ) ) ) )).

fof(t5_group_7,axiom,(
    ! [A,B,C] :
      ( ( v1_group_7(C)
        & m1_pboole(C,A) )
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & l1_group_1(D) )
         => ( ( r2_hidden(B,A)
              & D = k1_funct_1(C,B)
              & v3_group_1(k2_group_7(A,C)) )
           => v3_group_1(D) ) ) ) )).

fof(t6_group_7,axiom,(
    ! [A,B,C] :
      ( ( v1_group_7(C)
        & m1_pboole(C,A) )
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & l1_group_1(D) )
         => ( ( r2_hidden(B,A)
              & D = k1_funct_1(C,B)
              & v4_group_1(k2_group_7(A,C)) )
           => v4_group_1(D) ) ) ) )).

fof(t7_group_7,axiom,(
    ! [A,B,C] :
      ( ( v1_group_7(C)
        & m1_pboole(C,A) )
     => ! [D] :
          ( ( ~ v3_struct_0(D)
            & l1_group_1(D) )
         => ( ( r2_hidden(B,A)
              & D = k1_funct_1(C,B)
              & v7_group_1(k2_group_7(A,C)) )
           => v7_group_1(D) ) ) ) )).

fof(t8_group_7,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => ! [C] :
          ( ( v1_group_7(C)
            & v2_group_7(C,A)
            & m1_pboole(C,A) )
         => ( ! [D] :
                ~ ( r2_hidden(D,A)
                  & ! [E] :
                      ( ( ~ v3_struct_0(E)
                        & v3_group_1(E)
                        & l1_group_1(E) )
                     => ~ ( E = k1_funct_1(C,D)
                          & k1_funct_1(B,D) = k2_group_1(E) ) ) )
           => B = k2_group_1(k2_group_7(A,C)) ) ) ) )).

fof(t9_group_7,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_group_7(D)
            & v2_group_7(D,A)
            & m1_pboole(D,A) )
         => ! [E] :
              ( ( ~ v3_struct_0(E)
                & v3_group_1(E)
                & l1_group_1(E) )
             => ( ( r2_hidden(B,A)
                  & E = k1_funct_1(D,B)
                  & C = k2_group_1(k2_group_7(A,D)) )
               => k1_funct_1(C,B) = k2_group_1(E) ) ) ) ) )).

fof(t10_group_7,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( ( v1_group_7(D)
                & v2_group_7(D,A)
                & v3_group_7(D,A)
                & m1_pboole(D,A) )
             => ! [E] :
                  ( m1_subset_1(E,u1_struct_0(k2_group_7(A,D)))
                 => ( ( E = B
                      & ! [F] :
                          ~ ( r2_hidden(F,A)
                            & ! [G] :
                                ( ( ~ v3_struct_0(G)
                                  & v3_group_1(G)
                                  & v4_group_1(G)
                                  & l1_group_1(G) )
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(G))
                                   => ~ ( G = k1_funct_1(D,F)
                                        & k1_funct_1(C,F) = k3_group_1(G,H)
                                        & H = k1_funct_1(B,F) ) ) ) ) )
                   => C = k3_group_1(k2_group_7(A,D),E) ) ) ) ) ) )).

fof(t11_group_7,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] :
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ! [E] :
              ( ( v1_group_7(E)
                & v2_group_7(E,A)
                & v3_group_7(E,A)
                & m1_pboole(E,A) )
             => ! [F] :
                  ( m1_subset_1(F,u1_struct_0(k2_group_7(A,E)))
                 => ! [G] :
                      ( ( ~ v3_struct_0(G)
                        & v3_group_1(G)
                        & v4_group_1(G)
                        & l1_group_1(G) )
                     => ! [H] :
                          ( m1_subset_1(H,u1_struct_0(G))
                         => ( ( r2_hidden(B,A)
                              & G = k1_funct_1(E,B)
                              & C = F
                              & D = k3_group_1(k2_group_7(A,E),F)
                              & k1_funct_1(C,B) = H )
                           => k1_funct_1(D,B) = k3_group_1(G,H) ) ) ) ) ) ) ) )).

fof(d9_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & v2_group_7(B,A)
        & v3_group_7(B,A)
        & m1_pboole(B,A) )
     => ! [C] :
          ( ( v1_group_1(C)
            & m1_group_2(C,k2_group_7(A,B)) )
         => ( C = k3_group_7(A,B)
          <=> ! [D] :
                ( r2_hidden(D,u1_struct_0(C))
              <=> ? [E] :
                    ( m1_pralg_2(E,k4_card_3(k12_pralg_1(A,B)))
                    & ? [F] :
                        ( v1_finset_1(F)
                        & m1_subset_1(F,k1_zfmisc_1(A))
                        & ? [G] :
                            ( m1_pboole(G,F)
                            & E = k2_group_1(k2_group_7(A,B))
                            & D = k1_funct_4(E,G)
                            & ! [H] :
                                ~ ( r2_hidden(H,F)
                                  & ! [I] :
                                      ( ( ~ v3_struct_0(I)
                                        & v3_group_1(I)
                                        & l1_group_1(I) )
                                     => ~ ( I = k1_funct_1(B,H)
                                          & r2_hidden(k1_funct_1(G,H),u1_struct_0(I))
                                          & k1_funct_1(G,H) != k2_group_1(I) ) ) ) ) ) ) ) ) ) ) )).

fof(t12_group_7,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ! [B] :
          ( ( v1_group_7(B)
            & v2_group_7(B,A)
            & v3_group_7(B,A)
            & m1_pboole(B,A) )
         => k2_group_7(A,B) = k3_group_7(A,B) ) ) )).

fof(t13_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v1_group_7(k9_finseq_1(A))
        & m1_pboole(k9_finseq_1(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(t14_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k4_group_7(A))
        & v2_group_7(k4_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k4_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(t15_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k4_group_7(A))
        & v3_group_7(k4_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k4_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(t16_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k4_group_7(A))
        & v4_group_7(k4_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k4_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(t17_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k6_group_7(A))
        & v2_group_7(k6_group_7(A),k18_group_2(k1_numbers,np__1))
        & v3_group_7(k6_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k6_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(t18_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k8_group_7(A))
        & v2_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
        & v3_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
        & v4_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k8_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(t19_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ( v1_group_7(k10_finseq_1(A,B))
            & m1_pboole(k10_finseq_1(A,B),k2_tarski(np__1,np__2)) ) ) ) )).

fof(t20_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) )
         => ( v1_group_7(k11_group_7(A,B))
            & v2_group_7(k11_group_7(A,B),k2_tarski(np__1,np__2))
            & m1_pboole(k11_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) )).

fof(t21_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( v1_group_7(k11_group_7(A,B))
            & v3_group_7(k11_group_7(A,B),k2_tarski(np__1,np__2))
            & m1_pboole(k11_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) )).

fof(t22_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ( v1_group_7(k11_group_7(A,B))
            & v4_group_7(k11_group_7(A,B),k2_tarski(np__1,np__2))
            & m1_pboole(k11_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) )).

fof(t23_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ( v1_group_7(k13_group_7(A,B))
            & v2_group_7(k13_group_7(A,B),k2_tarski(np__1,np__2))
            & v3_group_7(k13_group_7(A,B),k2_tarski(np__1,np__2))
            & m1_pboole(k13_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) )).

fof(t24_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ( v1_group_7(k15_group_7(A,B))
            & v2_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
            & v3_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
            & v4_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
            & m1_pboole(k15_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) )).

fof(t25_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_group_1(C) )
             => ( v1_group_7(k11_finseq_1(A,B,C))
                & m1_pboole(k11_finseq_1(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) )).

fof(t26_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & l1_group_1(C) )
             => ( v1_group_7(k18_group_7(A,B,C))
                & v2_group_7(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
                & m1_pboole(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) )).

fof(t27_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ( v1_group_7(k18_group_7(A,B,C))
                & v3_group_7(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
                & m1_pboole(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) )).

fof(t28_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v7_group_1(C)
                & l1_group_1(C) )
             => ( v1_group_7(k18_group_7(A,B,C))
                & v4_group_7(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
                & m1_pboole(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) )).

fof(t29_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ( v1_group_7(k20_group_7(A,B,C))
                & v2_group_7(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
                & v3_group_7(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
                & m1_pboole(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) )).

fof(t30_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & v7_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & v7_group_1(C)
                & l1_group_1(C) )
             => ( v1_group_7(k22_group_7(A,B,C))
                & v2_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
                & v3_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
                & v4_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
                & m1_pboole(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) )).

fof(t31_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_group_1(k2_group_7(k18_group_2(k1_numbers,np__1),k4_group_7(A)),k10_group_7(A,B),k10_group_7(A,C)) = k10_group_7(A,k1_group_1(A,B,C)) ) ) ) )).

fof(t32_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => k1_group_1(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B)),k17_group_7(A,B,C,E),k17_group_7(A,B,D,F)) = k17_group_7(A,B,k1_group_1(A,C,D),k1_group_1(B,E,F)) ) ) ) ) ) ) )).

fof(t33_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(B))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(C))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(C))
                                     => k1_group_1(k2_group_7(k1_enumset1(np__1,np__2,np__3),k18_group_7(A,B,C)),k24_group_7(A,B,C,D,F,H),k24_group_7(A,B,C,E,G,I)) = k24_group_7(A,B,C,k1_group_1(A,D,E),k1_group_1(B,F,G),k1_group_1(C,H,I)) ) ) ) ) ) ) ) ) ) )).

fof(t34_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => k2_group_1(k2_group_7(k18_group_2(k1_numbers,np__1),k5_group_7(A))) = k10_group_7(A,k2_group_1(A)) ) )).

fof(t35_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) )
         => k2_group_1(k2_group_7(k2_tarski(np__1,np__2),k12_group_7(A,B))) = k17_group_7(A,B,k2_group_1(A),k2_group_1(B)) ) ) )).

fof(t36_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & l1_group_1(C) )
             => k2_group_1(k2_group_7(k1_enumset1(np__1,np__2,np__3),k19_group_7(A,B,C))) = k24_group_7(A,B,C,k2_group_1(A),k2_group_1(B),k2_group_1(C)) ) ) ) )).

fof(t37_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_group_1(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)),k10_group_7(A,B)) = k10_group_7(A,k3_group_1(A,B)) ) ) )).

fof(t38_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k3_group_1(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B)),k17_group_7(A,B,C,D)) = k17_group_7(A,B,k3_group_1(A,C),k3_group_1(B,D)) ) ) ) ) )).

fof(t39_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => k3_group_1(k2_group_7(k1_enumset1(np__1,np__2,np__3),k22_group_7(A,B,C)),k24_group_7(A,B,C,D,E,F)) = k24_group_7(A,B,C,k3_group_1(A,D),k3_group_1(B,E),k3_group_1(C,F)) ) ) ) ) ) ) )).

fof(t40_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k8_funct_2(u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))),B,C) = k10_group_7(A,C) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))))
              & v1_group_6(B,A,k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))
              & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))) ) ) ) ) )).

fof(t41_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))))
            & v1_group_6(B,A,k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))) )
         => ( ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k8_funct_2(u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))),B,C) = k10_group_7(A,C) )
           => v4_group_6(B,A,k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))) ) ) ) )).

fof(t42_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => r1_group_6(A,k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))) ) )).

fof(dt_k1_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_group_7(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ( ~ v3_struct_0(k1_group_7(A,B,C))
        & l1_group_1(k1_group_7(A,B,C)) ) ) )).

fof(redefinition_k1_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_group_7(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => k1_group_7(A,B,C) = k1_funct_1(B,C) ) )).

fof(dt_k2_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & m1_pboole(B,A) )
     => ( v1_group_1(k2_group_7(A,B))
        & l1_group_1(k2_group_7(A,B)) ) ) )).

fof(dt_k3_group_7,axiom,(
    ! [A,B] :
      ( ( v1_group_7(B)
        & v2_group_7(B,A)
        & v3_group_7(B,A)
        & m1_pboole(B,A) )
     => ( v1_group_1(k3_group_7(A,B))
        & m1_group_2(k3_group_7(A,B),k2_group_7(A,B)) ) ) )).

fof(dt_k4_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v1_group_7(k4_group_7(A))
        & m1_pboole(k4_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(redefinition_k4_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => k4_group_7(A) = k5_finseq_1(A) ) )).

fof(dt_k5_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k5_group_7(A))
        & v2_group_7(k5_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k5_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(redefinition_k5_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => k5_group_7(A) = k5_finseq_1(A) ) )).

fof(dt_k6_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k6_group_7(A))
        & v3_group_7(k6_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k6_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(redefinition_k6_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k6_group_7(A) = k5_finseq_1(A) ) )).

fof(dt_k7_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k7_group_7(A))
        & v4_group_7(k7_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k7_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(redefinition_k7_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => k7_group_7(A) = k5_finseq_1(A) ) )).

fof(dt_k8_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k8_group_7(A))
        & v2_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
        & v3_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k8_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(redefinition_k8_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k8_group_7(A) = k5_finseq_1(A) ) )).

fof(dt_k9_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_7(k9_group_7(A))
        & v2_group_7(k9_group_7(A),k18_group_2(k1_numbers,np__1))
        & v3_group_7(k9_group_7(A),k18_group_2(k1_numbers,np__1))
        & v4_group_7(k9_group_7(A),k18_group_2(k1_numbers,np__1))
        & m1_pboole(k9_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) )).

fof(redefinition_k9_group_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A) )
     => k9_group_7(A) = k5_finseq_1(A) ) )).

fof(dt_k10_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k10_group_7(A,B),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k4_group_7(A)))) ) )).

fof(redefinition_k10_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => k10_group_7(A,B) = k5_finseq_1(B) ) )).

fof(dt_k11_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ( v1_group_7(k11_group_7(A,B))
        & m1_pboole(k11_group_7(A,B),k2_tarski(np__1,np__2)) ) ) )).

fof(redefinition_k11_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B) )
     => k11_group_7(A,B) = k10_finseq_1(A,B) ) )).

fof(dt_k12_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & l1_group_1(B) )
     => ( v1_group_7(k12_group_7(A,B))
        & v2_group_7(k12_group_7(A,B),k2_tarski(np__1,np__2))
        & m1_pboole(k12_group_7(A,B),k2_tarski(np__1,np__2)) ) ) )).

fof(redefinition_k12_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & l1_group_1(B) )
     => k12_group_7(A,B) = k10_finseq_1(A,B) ) )).

fof(dt_k13_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( v1_group_7(k13_group_7(A,B))
        & v3_group_7(k13_group_7(A,B),k2_tarski(np__1,np__2))
        & m1_pboole(k13_group_7(A,B),k2_tarski(np__1,np__2)) ) ) )).

fof(redefinition_k13_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => k13_group_7(A,B) = k10_finseq_1(A,B) ) )).

fof(dt_k14_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v7_group_1(B)
        & l1_group_1(B) )
     => ( v1_group_7(k14_group_7(A,B))
        & v4_group_7(k14_group_7(A,B),k2_tarski(np__1,np__2))
        & m1_pboole(k14_group_7(A,B),k2_tarski(np__1,np__2)) ) ) )).

fof(redefinition_k14_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v7_group_1(B)
        & l1_group_1(B) )
     => k14_group_7(A,B) = k10_finseq_1(A,B) ) )).

fof(dt_k15_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( v1_group_7(k15_group_7(A,B))
        & v2_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
        & v3_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
        & m1_pboole(k15_group_7(A,B),k2_tarski(np__1,np__2)) ) ) )).

fof(redefinition_k15_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => k15_group_7(A,B) = k10_finseq_1(A,B) ) )).

fof(dt_k16_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & l1_group_1(B) )
     => ( v1_group_7(k16_group_7(A,B))
        & v2_group_7(k16_group_7(A,B),k2_tarski(np__1,np__2))
        & v3_group_7(k16_group_7(A,B),k2_tarski(np__1,np__2))
        & v4_group_7(k16_group_7(A,B),k2_tarski(np__1,np__2))
        & m1_pboole(k16_group_7(A,B),k2_tarski(np__1,np__2)) ) ) )).

fof(redefinition_k16_group_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & l1_group_1(B) )
     => k16_group_7(A,B) = k10_finseq_1(A,B) ) )).

fof(dt_k17_group_7,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => m1_subset_1(k17_group_7(A,B,C,D),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B)))) ) )).

fof(redefinition_k17_group_7,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(B)) )
     => k17_group_7(A,B,C,D) = k10_finseq_1(C,D) ) )).

fof(dt_k18_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & l1_group_1(C) )
     => ( v1_group_7(k18_group_7(A,B,C))
        & m1_pboole(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) )).

fof(redefinition_k18_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & l1_group_1(C) )
     => k18_group_7(A,B,C) = k11_finseq_1(A,B,C) ) )).

fof(dt_k19_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & l1_group_1(C) )
     => ( v1_group_7(k19_group_7(A,B,C))
        & v2_group_7(k19_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
        & m1_pboole(k19_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) )).

fof(redefinition_k19_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & l1_group_1(C) )
     => k19_group_7(A,B,C) = k11_finseq_1(A,B,C) ) )).

fof(dt_k20_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v4_group_1(C)
        & l1_group_1(C) )
     => ( v1_group_7(k20_group_7(A,B,C))
        & v3_group_7(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
        & m1_pboole(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) )).

fof(redefinition_k20_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v4_group_1(C)
        & l1_group_1(C) )
     => k20_group_7(A,B,C) = k11_finseq_1(A,B,C) ) )).

fof(dt_k21_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v7_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v7_group_1(C)
        & l1_group_1(C) )
     => ( v1_group_7(k21_group_7(A,B,C))
        & v4_group_7(k21_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
        & m1_pboole(k21_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) )).

fof(redefinition_k21_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v7_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v7_group_1(C)
        & l1_group_1(C) )
     => k21_group_7(A,B,C) = k11_finseq_1(A,B,C) ) )).

fof(dt_k22_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & l1_group_1(C) )
     => ( v1_group_7(k22_group_7(A,B,C))
        & v2_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
        & v3_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
        & m1_pboole(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) )).

fof(redefinition_k22_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & l1_group_1(C) )
     => k22_group_7(A,B,C) = k11_finseq_1(A,B,C) ) )).

fof(dt_k23_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & v7_group_1(C)
        & l1_group_1(C) )
     => ( v1_group_7(k23_group_7(A,B,C))
        & v2_group_7(k23_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
        & v3_group_7(k23_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
        & v4_group_7(k23_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
        & m1_pboole(k23_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) )).

fof(redefinition_k23_group_7,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & v3_group_1(C)
        & v4_group_1(C)
        & v7_group_1(C)
        & l1_group_1(C) )
     => k23_group_7(A,B,C) = k11_finseq_1(A,B,C) ) )).

fof(dt_k24_group_7,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & l1_group_1(C)
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(C)) )
     => m1_subset_1(k24_group_7(A,B,C,D,E,F),u1_struct_0(k2_group_7(k1_enumset1(np__1,np__2,np__3),k18_group_7(A,B,C)))) ) )).

fof(redefinition_k24_group_7,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & ~ v3_struct_0(B)
        & l1_group_1(B)
        & ~ v3_struct_0(C)
        & l1_group_1(C)
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(B))
        & m1_subset_1(F,u1_struct_0(C)) )
     => k24_group_7(A,B,C,D,E,F) = k11_finseq_1(D,E,F) ) )).
%------------------------------------------------------------------------------