SET007 Axioms: SET007+298.ax


%------------------------------------------------------------------------------
% File     : SET007+298 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Commutator and Center of a Group
% 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_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  118 (  13 unit)
%            Number of atoms       :  922 (  95 equality)
%            Maximal formula depth :   16 (   8 average)
%            Number of connectives :  919 ( 115 ~  ;   0  |; 473  &)
%                                         (  25 <=>; 306 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   1 propositional; 0-3 arity)
%            Number of functors    :   53 (   9 constant; 0-4 arity)
%            Number of variables   :  349 (   0 singleton; 323 !;  26 ?)
%            Maximal term depth    :    6 (   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(t1_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r1_rlvect_1(k5_group_2(B),A)
      <=> A = k2_group_1(B) ) ) )).

fof(t2_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( ( r1_rlvect_1(D,B)
                      & r1_rlvect_1(D,C) )
                   => r1_rlvect_1(D,k2_group_3(A,B,C)) ) ) ) ) ) )).

fof(t3_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_group_1(D)
                    & v1_group_3(D,A)
                    & m1_group_2(D,A) )
                 => ( r1_rlvect_1(D,B)
                   => r1_rlvect_1(D,k2_group_3(A,B,C)) ) ) ) ) ) )).

fof(t4_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_group_2(C,B)
         => ! [D] :
              ( m1_group_2(D,B)
             => ( r2_hidden(A,k7_group_4(B,C,D))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m1_subset_1(F,u1_struct_0(B))
                        & A = k1_group_1(B,E,F)
                        & r1_rlvect_1(C,E)
                        & r1_rlvect_1(D,F) ) ) ) ) ) ) )).

fof(t5_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_group_2(C,B)
         => ! [D] :
              ( m1_group_2(D,B)
             => ( k7_group_4(B,C,D) = k7_group_4(B,D,C)
               => ( r1_rlvect_1(k8_group_4(B,C,D),A)
                <=> ? [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                      & ? [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                          & A = k1_group_1(B,E,F)
                          & r1_rlvect_1(C,E)
                          & r1_rlvect_1(D,F) ) ) ) ) ) ) ) )).

fof(t6_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_group_2(C,B)
         => ! [D] :
              ( m1_group_2(D,B)
             => ( ( ~ v3_struct_0(B)
                  & v3_group_1(B)
                  & v4_group_1(B)
                  & v7_group_1(B)
                  & l1_group_1(B) )
               => ( r1_rlvect_1(k8_group_4(B,C,D),A)
                <=> ? [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                      & ? [F] :
                          ( m1_subset_1(F,u1_struct_0(B))
                          & A = k1_group_1(B,E,F)
                          & r1_rlvect_1(C,E)
                          & r1_rlvect_1(D,F) ) ) ) ) ) ) ) )).

fof(t7_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( ( v1_group_1(C)
            & v1_group_3(C,B)
            & m1_group_2(C,B) )
         => ! [D] :
              ( ( v1_group_1(D)
                & v1_group_3(D,B)
                & m1_group_2(D,B) )
             => ( r1_rlvect_1(k8_group_4(B,C,D),A)
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m1_subset_1(F,u1_struct_0(B))
                        & A = k1_group_1(B,E,F)
                        & r1_rlvect_1(C,E)
                        & r1_rlvect_1(D,F) ) ) ) ) ) ) )).

fof(t8_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( ( v1_group_3(C,A)
                & m1_group_2(C,A) )
             => k7_group_4(A,B,C) = k7_group_4(A,C,B) ) ) ) )).

fof(d1_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m2_finseq_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( D = k1_group_5(A,B,C)
                  <=> ( k3_finseq_1(D) = k3_finseq_1(B)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(B))
                           => k1_funct_1(D,E) = k2_group_3(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),C) ) ) ) ) ) ) ) ) )).

fof(t9_group_5,axiom,(
    $true )).

fof(t10_group_5,axiom,(
    $true )).

fof(t11_group_5,axiom,(
    $true )).

fof(t12_group_5,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))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => k8_finseq_1(u1_struct_0(A),k1_group_5(A,C,B),k1_group_5(A,D,B)) = k1_group_5(A,k8_finseq_1(u1_struct_0(A),C,D),B) ) ) ) ) )).

fof(t13_group_5,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))
         => k1_group_5(A,k6_finseq_1(u1_struct_0(A)),B) = k1_xboole_0 ) ) )).

fof(t14_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_group_5(A,k12_finseq_1(u1_struct_0(A),B),C) = k12_finseq_1(u1_struct_0(A),k2_group_3(A,B,C)) ) ) ) )).

fof(t15_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k1_group_5(A,k7_rlvect_1(A,B,C),D) = k7_rlvect_1(A,k2_group_3(A,B,D),k2_group_3(A,C,D)) ) ) ) ) )).

fof(t16_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k1_group_5(A,k8_rlvect_1(A,B,C,D),E) = k8_rlvect_1(A,k2_group_3(A,B,E),k2_group_3(A,C,E),k2_group_3(A,D,E)) ) ) ) ) ) )).

fof(t17_group_5,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))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => k3_group_4(A,k1_group_5(A,C,B)) = k2_group_3(A,k3_group_4(A,C),B) ) ) ) )).

fof(t18_group_5,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))
         => ! [C] :
              ( m2_finseq_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m2_finseq_1(D,k4_numbers)
                 => k4_group_4(A,D,k1_group_5(A,C,B)) = k1_group_5(A,k4_group_4(A,D,C),B) ) ) ) ) )).

fof(d2_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),B),C) ) ) ) )).

fof(t19_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),B),C)
                & k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k3_group_1(A,C),B)),C)
                & k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C))
                & k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k3_group_1(A,C),k1_group_1(A,B,C)))
                & k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),k1_group_1(A,B,C)) ) ) ) ) )).

fof(t20_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,k1_group_1(A,C,B)),k1_group_1(A,B,C)) ) ) ) )).

fof(t21_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_group_5(A,B,C) = k1_group_1(A,k2_group_3(A,k3_group_1(A,C),B),C)
                & k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k2_group_3(A,B,C)) ) ) ) ) )).

fof(t22_group_5,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))
         => ( k2_group_5(A,k2_group_1(A),B) = k2_group_1(A)
            & k2_group_5(A,B,k2_group_1(A)) = k2_group_1(A) ) ) ) )).

fof(t23_group_5,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))
         => k2_group_5(A,B,B) = k2_group_1(A) ) ) )).

fof(t24_group_5,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))
         => ( k2_group_5(A,B,k3_group_1(A,B)) = k2_group_1(A)
            & k2_group_5(A,k3_group_1(A,B),B) = k2_group_1(A) ) ) ) )).

fof(t25_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_group_1(A,k2_group_5(A,B,C)) = k2_group_5(A,C,B) ) ) ) )).

fof(t26_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k2_group_3(A,k2_group_5(A,B,C),D) = k2_group_5(A,k2_group_3(A,B,D),k2_group_3(A,C,D)) ) ) ) ) )).

fof(t27_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k6_group_1(A,np__2,k3_group_1(A,B)),k6_group_1(A,np__2,k1_group_1(A,B,k3_group_1(A,C)))),k6_group_1(A,np__2,C)) ) ) ) )).

fof(t28_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k2_group_5(A,k1_group_1(A,B,C),D) = k1_group_1(A,k2_group_3(A,k2_group_5(A,B,D),C),k2_group_5(A,C,D)) ) ) ) ) )).

fof(t29_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k2_group_5(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k2_group_5(A,B,D),k2_group_3(A,k2_group_5(A,B,C),D)) ) ) ) ) )).

fof(t30_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_5(A,k3_group_1(A,B),C) = k2_group_3(A,k2_group_5(A,C,B),k3_group_1(A,B)) ) ) ) )).

fof(t31_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_5(A,B,k3_group_1(A,C)) = k2_group_3(A,k2_group_5(A,C,B),k3_group_1(A,C)) ) ) ) )).

fof(t32_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_group_5(A,k3_group_1(A,B),k3_group_1(A,C)) = k2_group_3(A,k2_group_5(A,B,C),k3_group_1(A,k1_group_1(A,B,C)))
                & k2_group_5(A,k3_group_1(A,B),k3_group_1(A,C)) = k2_group_3(A,k2_group_5(A,B,C),k3_group_1(A,k1_group_1(A,C,B))) ) ) ) ) )).

fof(t33_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_5(A,B,k2_group_3(A,C,k3_group_1(A,B))) = k2_group_5(A,C,k3_group_1(A,B)) ) ) ) )).

fof(t34_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_5(A,k2_group_3(A,B,k3_group_1(A,C)),C) = k2_group_5(A,k3_group_1(A,C),B) ) ) ) )).

fof(t35_group_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k2_group_5(B,k6_group_1(B,A,C),D) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),C),k6_group_1(B,A,k2_group_3(B,C,D))) ) ) ) ) )).

fof(t36_group_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [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(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k2_group_5(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),k2_group_3(B,D,C)),k6_group_1(B,A,D)) ) ) ) ) )).

fof(t37_group_5,axiom,(
    ! [A] :
      ( v1_int_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(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k2_group_5(B,k6_group_1(B,A,C),D) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),C),k6_group_1(B,A,k2_group_3(B,C,D))) ) ) ) ) )).

fof(t38_group_5,axiom,(
    ! [A] :
      ( v1_int_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(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => k2_group_5(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),k2_group_3(B,D,C)),k6_group_1(B,A,D)) ) ) ) ) )).

fof(t39_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_group_5(A,B,C) = k2_group_1(A)
              <=> k1_group_1(A,B,C) = k1_group_1(A,C,B) ) ) ) ) )).

fof(t40_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & l1_group_1(A) )
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_group_5(A,B,C) = k2_group_1(A) ) ) ) ) )).

fof(t41_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ( ( r1_rlvect_1(D,B)
                      & r1_rlvect_1(D,C) )
                   => r1_rlvect_1(D,k2_group_5(A,B,C)) ) ) ) ) ) )).

fof(d3_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k3_group_5(A,B,C,D) = k2_group_5(A,k2_group_5(A,B,C),D) ) ) ) ) )).

fof(t42_group_5,axiom,(
    $true )).

fof(t43_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k3_group_5(A,B,C,k2_group_1(A)) = k2_group_1(A)
                & k3_group_5(A,B,k2_group_1(A),C) = k2_group_1(A)
                & k3_group_5(A,k2_group_1(A),B,C) = k2_group_1(A) ) ) ) ) )).

fof(t44_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_group_5(A,B,B,C) = k2_group_1(A) ) ) ) )).

fof(t45_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_group_5(A,B,C,B) = k2_group_5(A,k2_group_3(A,B,C),B) ) ) ) )).

fof(t46_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_group_5(A,B,C,C) = k2_group_3(A,k1_group_1(A,k2_group_5(A,B,k3_group_1(A,C)),k2_group_5(A,B,C)),C) ) ) ) )).

fof(t47_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_group_5(A,B,C,k2_group_3(A,C,B)) = k2_group_5(A,C,k2_group_5(A,C,B)) ) ) ) )).

fof(t48_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k2_group_5(A,k1_group_1(A,B,C),D) = k1_group_1(A,k1_group_1(A,k2_group_5(A,B,D),k3_group_5(A,B,D,C)),k2_group_5(A,C,D)) ) ) ) ) )).

fof(t49_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k2_group_5(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,k2_group_5(A,B,D),k2_group_5(A,B,C)),k3_group_5(A,B,C,D)) ) ) ) ) )).

fof(t50_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k1_group_1(A,k1_group_1(A,k2_group_3(A,k3_group_5(A,B,k3_group_1(A,C),D),C),k2_group_3(A,k3_group_5(A,C,k3_group_1(A,D),B),D)),k2_group_3(A,k3_group_5(A,D,k3_group_1(A,B),C),B)) = k2_group_1(A) ) ) ) ) )).

fof(t51_group_5,axiom,(
    $true )).

fof(t52_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
             => ( r2_hidden(A,k4_group_5(B,C,D))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m1_subset_1(F,u1_struct_0(B))
                        & A = k2_group_5(B,E,F)
                        & r2_hidden(E,C)
                        & r2_hidden(F,D) ) ) ) ) ) ) )).

fof(t53_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( k4_group_5(A,k1_subset_1(u1_struct_0(A)),B) = k1_xboole_0
            & k4_group_5(A,B,k1_subset_1(u1_struct_0(A))) = k1_xboole_0 ) ) ) )).

fof(t54_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_group_5(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C)) = k6_domain_1(u1_struct_0(A),k2_group_5(A,B,C)) ) ) ) )).

fof(t55_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(B,C)
                          & r1_tarski(D,E) )
                       => r1_tarski(k4_group_5(A,B,D),k4_group_5(A,C,E)) ) ) ) ) ) ) )).

fof(t56_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & l1_group_1(A) )
      <=> ! [B] :
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ~ ( B != k1_xboole_0
                    & C != k1_xboole_0
                    & k4_group_5(A,B,C) != k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) ) ) )).

fof(d5_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => k5_group_5(A,B,C) = k4_group_5(A,k7_group_2(A,B),k7_group_2(A,C)) ) ) ) )).

fof(t57_group_5,axiom,(
    $true )).

fof(t58_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_group_2(C,B)
         => ! [D] :
              ( m1_group_2(D,B)
             => ( r2_hidden(A,k5_group_5(B,C,D))
              <=> ? [E] :
                    ( m1_subset_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m1_subset_1(F,u1_struct_0(B))
                        & A = k2_group_5(B,E,F)
                        & r1_rlvect_1(C,E)
                        & r1_rlvect_1(D,F) ) ) ) ) ) ) )).

fof(t59_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => r2_hidden(k2_group_1(A),k5_group_5(A,B,C)) ) ) ) )).

fof(t60_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( k5_group_5(A,k5_group_2(A),B) = k6_domain_1(u1_struct_0(A),k2_group_1(A))
            & k5_group_5(A,B,k5_group_2(A)) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) )).

fof(t61_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( ( v1_group_1(C)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ( r1_tarski(k5_group_5(A,B,C),k7_group_2(A,C))
                & r1_tarski(k5_group_5(A,C,B),k7_group_2(A,C)) ) ) ) ) )).

fof(t62_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ! [E] :
                      ( m1_group_2(E,A)
                     => ( ( m1_group_2(B,C)
                          & m1_group_2(D,E) )
                       => r1_tarski(k5_group_5(A,B,D),k5_group_5(A,C,E)) ) ) ) ) ) ) )).

fof(t63_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & l1_group_1(A) )
      <=> ! [B] :
            ( m1_group_2(B,A)
           => ! [C] :
                ( m1_group_2(C,A)
               => k5_group_5(A,B,C) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) ) )).

fof(d6_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k6_group_5(A) = k5_group_5(A,k6_group_2(A),k6_group_2(A)) ) )).

fof(t64_group_5,axiom,(
    $true )).

fof(t65_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r2_hidden(A,k6_group_5(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & ? [D] :
                ( m1_subset_1(D,u1_struct_0(B))
                & A = k2_group_5(B,C,D) ) ) ) ) )).

fof(t66_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & l1_group_1(A) )
      <=> k6_group_5(A) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) )).

fof(d7_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k7_group_5(A,B,C) = k5_group_4(A,k4_group_5(A,B,C)) ) ) ) )).

fof(t67_group_5,axiom,(
    $true )).

fof(t68_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r2_hidden(B,D)
                          & r2_hidden(C,E) )
                       => r1_rlvect_1(k7_group_5(A,D,E),k2_group_5(A,B,C)) ) ) ) ) ) ) )).

fof(t69_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] :
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
             => ( r1_rlvect_1(k7_group_5(B,C,D),A)
              <=> ? [E] :
                    ( m2_finseq_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m2_finseq_1(F,k4_numbers)
                        & k3_finseq_1(E) = k3_finseq_1(F)
                        & r1_tarski(k2_relat_1(E),k4_group_5(B,C,D))
                        & A = k3_group_4(B,k4_group_4(B,F,E)) ) ) ) ) ) ) )).

fof(t70_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( r1_tarski(B,C)
                          & r1_tarski(D,E) )
                       => m1_group_2(k7_group_5(A,B,D),k7_group_5(A,C,E)) ) ) ) ) ) ) )).

fof(d8_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => k8_group_5(A,B,C) = k7_group_5(A,k7_group_2(A,B),k7_group_2(A,C)) ) ) ) )).

fof(t71_group_5,axiom,(
    $true )).

fof(t72_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => r1_group_2(A,k8_group_5(A,B,C),k5_group_4(A,k5_group_5(A,B,C))) ) ) ) )).

fof(t73_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] :
          ( m1_group_2(C,B)
         => ! [D] :
              ( m1_group_2(D,B)
             => ( r1_rlvect_1(k8_group_5(B,C,D),A)
              <=> ? [E] :
                    ( m2_finseq_1(E,u1_struct_0(B))
                    & ? [F] :
                        ( m2_finseq_1(F,k4_numbers)
                        & k3_finseq_1(E) = k3_finseq_1(F)
                        & r1_tarski(k2_relat_1(E),k5_group_5(B,C,D))
                        & A = k3_group_4(B,k4_group_4(B,F,E)) ) ) ) ) ) ) )).

fof(t74_group_5,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))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ! [E] :
                      ( m1_group_2(E,A)
                     => ( ( r1_rlvect_1(D,B)
                          & r1_rlvect_1(E,C) )
                       => r1_rlvect_1(k8_group_5(A,D,E),k2_group_5(A,B,C)) ) ) ) ) ) ) )).

fof(t75_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( m1_group_2(C,A)
             => ! [D] :
                  ( m1_group_2(D,A)
                 => ! [E] :
                      ( m1_group_2(E,A)
                     => ( ( m1_group_2(B,C)
                          & m1_group_2(D,E) )
                       => m1_group_2(k8_group_5(A,B,D),k8_group_5(A,C,E)) ) ) ) ) ) ) )).

fof(t76_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ! [C] :
              ( ( v1_group_1(C)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ( m1_group_2(k8_group_5(A,C,B),C)
                & m1_group_2(k8_group_5(A,B,C),C) ) ) ) ) )).

fof(t77_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_group_1(C)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ( v1_group_3(k8_group_5(A,B,C),A)
                & m1_group_2(k8_group_5(A,B,C),A) ) ) ) ) )).

fof(t78_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_group_3(C,A)
                & m1_group_2(C,A) )
             => r1_group_2(A,k8_group_5(A,B,C),k8_group_5(A,C,B)) ) ) ) )).

fof(t79_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_group_1(C)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ! [D] :
                  ( ( v1_group_1(D)
                    & v1_group_3(D,A)
                    & m1_group_2(D,A) )
                 => r1_group_2(A,k8_group_5(A,k8_group_4(A,B,C),D),k8_group_4(A,k8_group_5(A,B,D),k8_group_5(A,C,D))) ) ) ) ) )).

fof(t80_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & v1_group_3(B,A)
            & m1_group_2(B,A) )
         => ! [C] :
              ( ( v1_group_1(C)
                & v1_group_3(C,A)
                & m1_group_2(C,A) )
             => ! [D] :
                  ( ( v1_group_1(D)
                    & v1_group_3(D,A)
                    & m1_group_2(D,A) )
                 => r1_group_2(A,k8_group_5(A,B,k8_group_4(A,C,D)),k8_group_4(A,k8_group_5(A,B,C),k8_group_5(A,B,D))) ) ) ) ) )).

fof(d9_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k9_group_5(A) = k8_group_5(A,k6_group_2(A),k6_group_2(A)) ) )).

fof(t81_group_5,axiom,(
    $true )).

fof(t82_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => r1_group_2(A,k9_group_5(A),k5_group_4(A,k6_group_5(A))) ) )).

fof(t83_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r1_rlvect_1(k9_group_5(B),A)
      <=> ? [C] :
            ( m2_finseq_1(C,u1_struct_0(B))
            & ? [D] :
                ( m2_finseq_1(D,k4_numbers)
                & k3_finseq_1(C) = k3_finseq_1(D)
                & r1_tarski(k2_relat_1(C),k6_group_5(B))
                & A = k3_group_4(B,k4_group_4(B,D,C)) ) ) ) ) )).

fof(t84_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_rlvect_1(k9_group_5(A),k2_group_5(A,B,C)) ) ) ) )).

fof(t85_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & l1_group_1(A) )
      <=> r1_group_2(A,k9_group_5(A),k5_group_2(A)) ) ) )).

fof(t86_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( ( v1_finset_1(k14_group_2(A,B))
              & k17_group_2(A,B) = np__2 )
           => m1_group_2(k9_group_5(A),B) ) ) ) )).

fof(t87_group_5,axiom,(
    $true )).

fof(t88_group_5,axiom,(
    $true )).

fof(t89_group_5,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))
         => ( r1_rlvect_1(k10_group_5(A),B)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_group_1(A,B,C) = k1_group_1(A,C,B) ) ) ) ) )).

fof(t90_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_3(k10_group_5(A),A)
        & m1_group_2(k10_group_5(A),A) ) ) )).

fof(t91_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_group_2(B,A)
         => ( m1_group_2(B,k10_group_5(A))
           => ( v1_group_3(B,A)
              & m1_group_2(B,A) ) ) ) ) )).

fof(t92_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => v7_group_1(k10_group_5(A)) ) )).

fof(t93_group_5,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))
         => ( r1_rlvect_1(k10_group_5(A),B)
          <=> k7_group_3(A,B) = k6_domain_1(u1_struct_0(A),B) ) ) ) )).

fof(t94_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & l1_group_1(A) )
      <=> k10_group_5(A) = A ) ) )).

fof(dt_k1_group_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_finseq_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m2_finseq_1(k1_group_5(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k2_group_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_group_5(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k3_group_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k3_group_5(A,B,C,D),u1_struct_0(A)) ) )).

fof(dt_k4_group_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k4_group_5(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k5_group_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => m1_subset_1(k5_group_5(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k6_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => m1_subset_1(k6_group_5(A),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k7_group_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v1_group_1(k7_group_5(A,B,C))
        & m1_group_2(k7_group_5(A,B,C),A) ) ) )).

fof(dt_k8_group_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A)
        & m1_group_2(C,A) )
     => ( v1_group_1(k8_group_5(A,B,C))
        & m1_group_2(k8_group_5(A,B,C),A) ) ) )).

fof(dt_k9_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_1(k9_group_5(A))
        & v1_group_3(k9_group_5(A),A)
        & m1_group_2(k9_group_5(A),A) ) ) )).

fof(dt_k10_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_1(k10_group_5(A))
        & m1_group_2(k10_group_5(A),A) ) ) )).

fof(d4_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_group_5(A,B,C) = a_3_0_group_5(A,B,C) ) ) ) )).

fof(d10_group_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] :
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( B = k10_group_5(A)
          <=> u1_struct_0(B) = a_1_0_group_5(A) ) ) ) )).

fof(s1_group_5,axiom,(
    m1_subset_1(a_0_0_group_5,k1_zfmisc_1(f2_s1_group_5)) )).

fof(fraenkel_a_3_0_group_5,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
     => ( r2_hidden(A,a_3_0_group_5(B,C,D))
      <=> ? [E,F] :
            ( m1_subset_1(E,u1_struct_0(B))
            & m1_subset_1(F,u1_struct_0(B))
            & A = k2_group_5(B,E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) )).

fof(fraenkel_a_1_0_group_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ( r2_hidden(A,a_1_0_group_5(B))
      <=> ? [C] :
            ( m1_subset_1(C,u1_struct_0(B))
            & A = C
            & ! [D] :
                ( m1_subset_1(D,u1_struct_0(B))
               => k1_group_1(B,C,D) = k1_group_1(B,D,C) ) ) ) ) )).

fof(fraenkel_a_0_0_group_5,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_group_5)
    <=> ? [B,C,D] :
          ( m1_subset_1(B,f1_s1_group_5)
          & m1_subset_1(C,f2_s1_group_5)
          & m1_subset_1(D,f3_s1_group_5)
          & A = f4_s1_group_5(B,C,D)
          & p1_s1_group_5(B,C,D) ) ) )).
%------------------------------------------------------------------------------