SET007 Axioms: SET007+70.ax


%------------------------------------------------------------------------------
% File     : SET007+70 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Binary Operations Applied to Finite Sequences
% 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    : finseqop [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  112 (   6 unit)
%            Number of atoms       : 1194 ( 132 equality)
%            Maximal formula depth :   23 (  13 average)
%            Number of connectives : 1252 ( 170 ~  ;   2  |; 506  &)
%                                         (   3 <=>; 571 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   21 (   1 propositional; 0-3 arity)
%            Number of functors    :   35 (   3 constant; 0-6 arity)
%            Number of variables   :  571 (   0 singleton; 570 !;   1 ?)
%            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(t1_finseqop,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k13_funct_3(k1_xboole_0,A) = k1_xboole_0
        & k13_funct_3(A,k1_xboole_0) = k1_xboole_0 ) ) )).

fof(t2_finseqop,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k15_funct_3(k1_xboole_0,A) = k1_xboole_0
        & k15_funct_3(A,k1_xboole_0) = k1_xboole_0 ) ) )).

fof(t3_finseqop,axiom,(
    $true )).

fof(t4_finseqop,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k3_funcop_1(A,k1_xboole_0,B) = k1_xboole_0
            & k3_funcop_1(A,B,k1_xboole_0) = k1_xboole_0 ) ) ) )).

fof(t5_finseqop,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k4_funcop_1(B,k1_xboole_0,A) = k1_xboole_0 ) )).

fof(t6_finseqop,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k5_funcop_1(B,A,k1_xboole_0) = k1_xboole_0 ) )).

fof(t7_finseqop,axiom,(
    ! [A,B,C] : k13_funct_3(k2_funcop_1(A,B),k2_funcop_1(A,C)) = k2_funcop_1(A,k4_tarski(B,C)) )).

fof(t8_finseqop,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D] :
          ( r2_hidden(k4_tarski(C,D),k1_relat_1(A))
         => k3_funcop_1(A,k2_funcop_1(B,C),k2_funcop_1(B,D)) = k2_funcop_1(B,k1_funct_1(A,k4_tarski(C,D))) ) ) )).

fof(t9_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => k5_finseqop(A,B,k8_finseq_1(A,D,k12_finseq_1(A,C)),E) = k8_finseq_1(B,k5_finseqop(A,B,D,E),k12_finseq_1(B,k8_funct_2(A,B,E,C))) ) ) ) ) ) )).

fof(t10_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => k5_finseqop(A,B,k8_finseq_1(A,C,D),E) = k8_finseq_1(B,k5_finseqop(A,B,C,E),k5_finseqop(A,B,D,E)) ) ) ) ) ) )).

fof(t11_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( m1_subset_1(E,C)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(B,C),A)
                                & m2_relset_1(G,k2_zfmisc_1(B,C),A) )
                             => ! [H] :
                                  ( m2_finseq_2(H,B,k4_finseq_2(F,B))
                                 => ! [I] :
                                      ( m2_finseq_2(I,C,k4_finseq_2(F,C))
                                     => k1_finseqop(B,C,A,G,k8_finseq_1(B,H,k12_finseq_1(B,D)),k8_finseq_1(C,I,k12_finseq_1(C,E))) = k8_finseq_1(A,k1_finseqop(B,C,A,G,H,I),k12_finseq_1(A,k2_binop_1(B,C,A,G,D,E))) ) ) ) ) ) ) ) ) ) )).

fof(t12_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,C),A)
                            & m2_relset_1(F,k2_zfmisc_1(B,C),A) )
                         => ! [G] :
                              ( m2_finseq_2(G,B,k4_finseq_2(D,B))
                             => ! [H] :
                                  ( m2_finseq_2(H,C,k4_finseq_2(D,C))
                                 => ! [I] :
                                      ( m2_finseq_2(I,B,k4_finseq_2(E,B))
                                     => ! [J] :
                                          ( m2_finseq_2(J,C,k4_finseq_2(E,C))
                                         => k1_finseqop(B,C,A,F,k8_finseq_1(B,G,I),k8_finseq_1(C,H,J)) = k8_finseq_1(A,k1_finseqop(B,C,A,F,G,H),k1_finseqop(B,C,A,F,I,J)) ) ) ) ) ) ) ) ) ) ) )).

fof(t13_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,C)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,C),B)
                            & m2_relset_1(F,k2_zfmisc_1(A,C),B) )
                         => ! [G] :
                              ( m2_finseq_1(G,C)
                             => k3_finseqop(A,C,B,F,D,k8_finseq_1(C,G,k12_finseq_1(C,E))) = k8_finseq_1(B,k3_finseqop(A,C,B,F,D,G),k12_finseq_1(B,k2_binop_1(A,C,B,F,D,E))) ) ) ) ) ) ) ) )).

fof(t14_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,C),B)
                        & m2_relset_1(E,k2_zfmisc_1(A,C),B) )
                     => ! [F] :
                          ( m2_finseq_1(F,C)
                         => ! [G] :
                              ( m2_finseq_1(G,C)
                             => k3_finseqop(A,C,B,E,D,k8_finseq_1(C,F,G)) = k8_finseq_1(B,k3_finseqop(A,C,B,E,D,F),k3_finseqop(A,C,B,E,D,G)) ) ) ) ) ) ) ) )).

fof(t15_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(C,A),B)
                            & m2_relset_1(F,k2_zfmisc_1(C,A),B) )
                         => ! [G] :
                              ( m2_finseq_1(G,C)
                             => k2_finseqop(C,A,B,F,k8_finseq_1(C,G,k12_finseq_1(C,D)),E) = k8_finseq_1(B,k2_finseqop(C,A,B,F,G,E),k12_finseq_1(B,k2_binop_1(C,A,B,F,D,E))) ) ) ) ) ) ) ) )).

fof(t16_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(C,A),B)
                        & m2_relset_1(E,k2_zfmisc_1(C,A),B) )
                     => ! [F] :
                          ( m2_finseq_1(F,C)
                         => ! [G] :
                              ( m2_finseq_1(G,C)
                             => k2_finseqop(C,A,B,E,k8_finseq_1(C,F,G),D) = k8_finseq_1(B,k2_finseqop(C,A,B,E,F,D),k2_finseqop(C,A,B,E,G,D)) ) ) ) ) ) ) ) )).

fof(t17_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => k5_finseqop(A,B,k4_finseqop(A,D,C),E) = k4_finseqop(B,D,k8_funct_2(A,B,E,C)) ) ) ) ) ) )).

fof(t18_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,B),C)
                                & m2_relset_1(G,k2_zfmisc_1(A,B),C) )
                             => k1_finseqop(A,B,C,G,k4_finseqop(A,F,D),k4_finseqop(B,F,E)) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)) ) ) ) ) ) ) ) )).

fof(t19_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,B),C)
                                & m2_relset_1(G,k2_zfmisc_1(A,B),C) )
                             => k3_finseqop(A,B,C,G,D,k4_finseqop(B,F,E)) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)) ) ) ) ) ) ) ) )).

fof(t20_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,B),C)
                                & m2_relset_1(G,k2_zfmisc_1(A,B),C) )
                             => k2_finseqop(A,B,C,G,k4_finseqop(A,F,D),E) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)) ) ) ) ) ) ) ) )).

fof(t21_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,C),B)
                            & m2_relset_1(F,k2_zfmisc_1(A,C),B) )
                         => ! [G] :
                              ( m2_finseq_2(G,C,k4_finseq_2(E,C))
                             => k1_finseqop(A,C,B,F,k4_finseqop(A,E,D),G) = k3_finseqop(A,C,B,F,D,G) ) ) ) ) ) ) ) )).

fof(t22_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(C,A),B)
                            & m2_relset_1(F,k2_zfmisc_1(C,A),B) )
                         => ! [G] :
                              ( m2_finseq_2(G,C,k4_finseq_2(E,C))
                             => k3_funcop_1(F,G,k4_finseqop(C,E,D)) = k4_funcop_1(F,G,D) ) ) ) ) ) ) ) )).

fof(t23_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,C),B)
                            & m2_relset_1(F,k2_zfmisc_1(A,C),B) )
                         => ! [G] :
                              ( m2_finseq_2(G,C,k4_finseq_2(E,C))
                             => k3_finseqop(A,C,B,F,D,G) = k5_relat_1(G,k5_funcop_1(F,D,k6_partfun1(C))) ) ) ) ) ) ) ) )).

fof(t24_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(C,A),B)
                            & m2_relset_1(F,k2_zfmisc_1(C,A),B) )
                         => ! [G] :
                              ( m2_finseq_2(G,C,k4_finseq_2(E,C))
                             => k4_funcop_1(F,G,D) = k5_relat_1(G,k4_funcop_1(F,k6_partfun1(C),D)) ) ) ) ) ) ) ) )).

fof(t25_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( v2_binop_1(F,B)
                           => k7_funct_2(A,B,B,k6_funcop_1(B,A,F,D,E),k8_funcop_1(B,B,F,C,k6_partfun1(B))) = k6_funcop_1(B,A,F,k7_funct_2(A,B,B,D,k8_funcop_1(B,B,F,C,k6_partfun1(B))),E) ) ) ) ) ) ) ) )).

fof(t26_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ( v2_binop_1(F,B)
                           => k7_funct_2(A,B,B,k6_funcop_1(B,A,F,D,E),k7_funcop_1(B,B,F,k6_partfun1(B),C)) = k6_funcop_1(B,A,F,D,k7_funct_2(A,B,B,E,k7_funcop_1(B,B,F,k6_partfun1(B),C))) ) ) ) ) ) ) ) )).

fof(t27_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(C,A))
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(C,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( v2_binop_1(F,A)
                           => k5_finseqop(A,A,k1_finseqop(A,A,A,F,D,E),k8_funcop_1(A,A,F,B,k6_partfun1(A))) = k1_finseqop(A,A,A,F,k5_finseqop(A,A,D,k8_funcop_1(A,A,F,B,k6_partfun1(A))),E) ) ) ) ) ) ) ) )).

fof(t28_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(C,A))
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(C,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( v2_binop_1(F,A)
                           => k5_finseqop(A,A,k1_finseqop(A,A,A,F,D,E),k7_funcop_1(A,A,F,k6_partfun1(A),B)) = k1_finseqop(A,A,A,F,D,k5_finseqop(A,A,E,k7_funcop_1(A,A,F,k6_partfun1(A),B))) ) ) ) ) ) ) ) )).

fof(t29_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(B,A))
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(B,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( v2_binop_1(F,A)
                           => k1_finseqop(A,A,A,F,k1_finseqop(A,A,A,F,C,D),E) = k1_finseqop(A,A,A,F,C,k1_finseqop(A,A,A,F,D,E)) ) ) ) ) ) ) ) )).

fof(t30_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(D,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( v2_binop_1(F,A)
                           => k2_finseqop(A,A,A,F,k3_finseqop(A,A,A,F,B,E),C) = k3_finseqop(A,A,A,F,B,k2_finseqop(A,A,A,F,E,C)) ) ) ) ) ) ) ) )).

fof(t31_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(C,A))
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(C,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( v2_binop_1(F,A)
                           => k1_finseqop(A,A,A,F,k2_finseqop(A,A,A,F,D,B),E) = k1_finseqop(A,A,A,F,D,k3_finseqop(A,A,A,F,B,E)) ) ) ) ) ) ) ) )).

fof(t32_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(D,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( v2_binop_1(F,A)
                           => k3_finseqop(A,A,A,F,k2_binop_1(A,A,A,F,B,C),E) = k3_finseqop(A,A,A,F,B,k3_finseqop(A,A,A,F,C,E)) ) ) ) ) ) ) ) )).

fof(t33_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(D,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( v2_binop_1(F,A)
                           => k2_finseqop(A,A,A,F,E,k2_binop_1(A,A,A,F,B,C)) = k2_finseqop(A,A,A,F,k2_finseqop(A,A,A,F,E,B),C) ) ) ) ) ) ) ) )).

fof(t34_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(B,A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ( v1_binop_1(E,A)
                       => k1_finseqop(A,A,A,E,C,D) = k1_finseqop(A,A,A,E,D,C) ) ) ) ) ) ) )).

fof(t35_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(C,A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ( v1_binop_1(E,A)
                       => k3_finseqop(A,A,A,E,B,D) = k2_finseqop(A,A,A,E,D,B) ) ) ) ) ) ) )).

fof(t36_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(B,B),B)
                                & m2_relset_1(G,k2_zfmisc_1(B,B),B) )
                             => ( r6_binop_1(B,F,G)
                               => k8_funcop_1(B,A,F,k2_binop_1(B,B,B,G,C,D),E) = k6_funcop_1(B,A,G,k8_funcop_1(B,A,F,C,E),k8_funcop_1(B,A,F,D,E)) ) ) ) ) ) ) ) ) )).

fof(t37_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(B,B),B)
                            & m2_relset_1(F,k2_zfmisc_1(B,B),B) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(B,B),B)
                                & m2_relset_1(G,k2_zfmisc_1(B,B),B) )
                             => ( r6_binop_1(B,F,G)
                               => k7_funcop_1(B,A,F,E,k2_binop_1(B,B,B,G,C,D)) = k6_funcop_1(B,A,G,k7_funcop_1(B,A,F,E,C),k7_funcop_1(B,A,F,E,D)) ) ) ) ) ) ) ) ) )).

fof(t38_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,C)
                    & m2_relset_1(D,A,C) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,C,B)
                            & m2_relset_1(F,C,B) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(C,C),C)
                                & m2_relset_1(G,k2_zfmisc_1(C,C),C) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(B,B),B)
                                    & m2_relset_1(H,k2_zfmisc_1(B,B),B) )
                                 => ( ! [I] :
                                        ( m1_subset_1(I,C)
                                       => ! [J] :
                                            ( m1_subset_1(J,C)
                                           => k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)) = k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)) ) )
                                   => k7_funct_2(A,C,B,k6_funcop_1(C,A,G,D,E),F) = k6_funcop_1(B,A,H,k7_funct_2(A,C,B,D,F),k7_funct_2(A,C,B,E,F)) ) ) ) ) ) ) ) ) ) )).

fof(t39_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,C,B)
                            & m2_relset_1(F,C,B) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(C,C),C)
                                & m2_relset_1(G,k2_zfmisc_1(C,C),C) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(B,B),B)
                                    & m2_relset_1(H,k2_zfmisc_1(B,B),B) )
                                 => ( ! [I] :
                                        ( m1_subset_1(I,C)
                                       => ! [J] :
                                            ( m1_subset_1(J,C)
                                           => k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)) = k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)) ) )
                                   => k7_funct_2(A,C,B,k8_funcop_1(C,A,G,D,E),F) = k8_funcop_1(B,A,H,k8_funct_2(C,B,F,D),k7_funct_2(A,C,B,E,F)) ) ) ) ) ) ) ) ) ) )).

fof(t40_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,C)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,C)
                        & m2_relset_1(E,A,C) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,C,B)
                            & m2_relset_1(F,C,B) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(C,C),C)
                                & m2_relset_1(G,k2_zfmisc_1(C,C),C) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(B,B),B)
                                    & m2_relset_1(H,k2_zfmisc_1(B,B),B) )
                                 => ( ! [I] :
                                        ( m1_subset_1(I,C)
                                       => ! [J] :
                                            ( m1_subset_1(J,C)
                                           => k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)) = k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)) ) )
                                   => k7_funct_2(A,C,B,k7_funcop_1(C,A,G,E,D),F) = k7_funcop_1(B,A,H,k7_funct_2(A,C,B,E,F),k8_funct_2(C,B,F,D)) ) ) ) ) ) ) ) ) ) )).

fof(t41_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,B)
                            & m2_relset_1(F,B,B) )
                         => ( r7_binop_1(B,F,E)
                           => k7_funct_2(A,B,B,k6_funcop_1(B,A,E,C,D),F) = k6_funcop_1(B,A,E,k7_funct_2(A,B,B,C,F),k7_funct_2(A,B,B,D,F)) ) ) ) ) ) ) ) )).

fof(t42_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,B)
                            & m2_relset_1(F,B,B) )
                         => ( r7_binop_1(B,F,E)
                           => k7_funct_2(A,B,B,k8_funcop_1(B,A,E,C,D),F) = k8_funcop_1(B,A,E,k8_funct_2(B,B,F,C),k7_funct_2(A,B,B,D,F)) ) ) ) ) ) ) ) )).

fof(t43_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,B)
                            & m2_relset_1(F,B,B) )
                         => ( r7_binop_1(B,F,E)
                           => k7_funct_2(A,B,B,k7_funcop_1(B,A,E,D,C),F) = k7_funcop_1(B,A,E,k7_funct_2(A,B,B,D,F),k8_funct_2(B,B,F,C)) ) ) ) ) ) ) ) )).

fof(t44_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( v1_setwiseo(D,A)
                   => ( k3_funcop_1(D,k2_funcop_1(B,k3_binop_1(A,D)),C) = C
                      & k3_funcop_1(D,C,k2_funcop_1(B,k3_binop_1(A,D))) = C ) ) ) ) ) ) )).

fof(t45_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                    & m2_relset_1(D,k2_zfmisc_1(B,B),B) )
                 => ( v1_setwiseo(D,B)
                   => k8_funcop_1(B,A,D,k3_binop_1(B,D),C) = C ) ) ) ) ) )).

fof(t46_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(B,B),B)
                    & m2_relset_1(D,k2_zfmisc_1(B,B),B) )
                 => ( v1_setwiseo(D,B)
                   => k7_funcop_1(B,A,D,C,k3_binop_1(B,D)) = C ) ) ) ) ) )).

fof(t47_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(D,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,A),A)
                                & m2_relset_1(G,k2_zfmisc_1(A,A),A) )
                             => ( r6_binop_1(A,F,G)
                               => k3_finseqop(A,A,A,F,k2_binop_1(A,A,A,G,B,C),E) = k1_finseqop(A,A,A,G,k3_finseqop(A,A,A,F,B,E),k3_finseqop(A,A,A,F,C,E)) ) ) ) ) ) ) ) ) )).

fof(t48_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(D,A))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(A,A),A)
                                & m2_relset_1(G,k2_zfmisc_1(A,A),A) )
                             => ( r6_binop_1(A,F,G)
                               => k2_finseqop(A,A,A,F,E,k2_binop_1(A,A,A,G,B,C)) = k1_finseqop(A,A,A,G,k2_finseqop(A,A,A,F,E,B),k2_finseqop(A,A,A,F,E,C)) ) ) ) ) ) ) ) ) )).

fof(t49_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( m2_finseq_2(E,B,k4_finseq_2(C,B))
                     => ! [F] :
                          ( m2_finseq_2(F,B,k4_finseq_2(C,B))
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(B,B),B)
                                & m2_relset_1(G,k2_zfmisc_1(B,B),B) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,A),A)
                                    & m2_relset_1(H,k2_zfmisc_1(A,A),A) )
                                 => ( ! [I] :
                                        ( m1_subset_1(I,B)
                                       => ! [J] :
                                            ( m1_subset_1(J,B)
                                           => k8_funct_2(B,A,D,k2_binop_1(B,B,B,G,I,J)) = k2_binop_1(A,A,A,H,k8_funct_2(B,A,D,I),k8_funct_2(B,A,D,J)) ) )
                                   => k5_finseqop(B,A,k1_finseqop(B,B,B,G,E,F),D) = k1_finseqop(A,A,A,H,k5_finseqop(B,A,E,D),k5_finseqop(B,A,F,D)) ) ) ) ) ) ) ) ) ) )).

fof(t50_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] :
                          ( m2_finseq_2(F,B,k4_finseq_2(D,B))
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(B,B),B)
                                & m2_relset_1(G,k2_zfmisc_1(B,B),B) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,A),A)
                                    & m2_relset_1(H,k2_zfmisc_1(A,A),A) )
                                 => ( ! [I] :
                                        ( m1_subset_1(I,B)
                                       => ! [J] :
                                            ( m1_subset_1(J,B)
                                           => k8_funct_2(B,A,E,k2_binop_1(B,B,B,G,I,J)) = k2_binop_1(A,A,A,H,k8_funct_2(B,A,E,I),k8_funct_2(B,A,E,J)) ) )
                                   => k5_finseqop(B,A,k3_finseqop(B,B,B,G,C,F),E) = k3_finseqop(A,A,A,H,k8_funct_2(B,A,E,C),k5_finseqop(B,A,F,E)) ) ) ) ) ) ) ) ) ) )).

fof(t51_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,B)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] :
                          ( m2_finseq_2(F,B,k4_finseq_2(D,B))
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k2_zfmisc_1(B,B),B)
                                & m2_relset_1(G,k2_zfmisc_1(B,B),B) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,A),A)
                                    & m2_relset_1(H,k2_zfmisc_1(A,A),A) )
                                 => ( ! [I] :
                                        ( m1_subset_1(I,B)
                                       => ! [J] :
                                            ( m1_subset_1(J,B)
                                           => k8_funct_2(B,A,E,k2_binop_1(B,B,B,G,I,J)) = k2_binop_1(A,A,A,H,k8_funct_2(B,A,E,I),k8_funct_2(B,A,E,J)) ) )
                                   => k5_finseqop(B,A,k2_finseqop(B,B,B,G,F,C),E) = k2_finseqop(A,A,A,H,k5_finseqop(B,A,F,E),k8_funct_2(B,A,E,C)) ) ) ) ) ) ) ) ) ) )).

fof(t52_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(B,A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,A)
                            & m2_relset_1(F,A,A) )
                         => ( r7_binop_1(A,F,E)
                           => k5_finseqop(A,A,k1_finseqop(A,A,A,E,C,D),F) = k1_finseqop(A,A,A,E,k5_finseqop(A,A,C,F),k5_finseqop(A,A,D,F)) ) ) ) ) ) ) ) )).

fof(t53_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(C,A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,A)
                            & m2_relset_1(F,A,A) )
                         => ( r7_binop_1(A,F,E)
                           => k5_finseqop(A,A,k3_finseqop(A,A,A,E,B,D),F) = k3_finseqop(A,A,A,E,k8_funct_2(A,A,F,B),k5_finseqop(A,A,D,F)) ) ) ) ) ) ) ) )).

fof(t54_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(C,A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,A)
                            & m2_relset_1(F,A,A) )
                         => ( r7_binop_1(A,F,E)
                           => k5_finseqop(A,A,k2_finseqop(A,A,A,E,D,B),F) = k2_finseqop(A,A,A,E,k5_finseqop(A,A,D,F),k8_funct_2(A,A,F,B)) ) ) ) ) ) ) ) )).

fof(t55_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,A)
                        & m2_relset_1(E,A,A) )
                     => ( ( r6_binop_1(A,C,D)
                          & E = k8_funcop_1(A,A,C,B,k6_partfun1(A)) )
                       => r7_binop_1(A,E,D) ) ) ) ) ) ) )).

fof(t56_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,A)
                        & m2_relset_1(E,A,A) )
                     => ( ( r6_binop_1(A,C,D)
                          & E = k7_funcop_1(A,A,C,k6_partfun1(A),B) )
                       => r7_binop_1(A,E,D) ) ) ) ) ) ) )).

fof(t57_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( v1_setwiseo(D,A)
                   => ( k1_finseqop(A,A,A,D,k4_finseqop(A,B,k3_binop_1(A,D)),C) = C
                      & k1_finseqop(A,A,A,D,C,k4_finseqop(A,B,k3_binop_1(A,D))) = C ) ) ) ) ) ) )).

fof(t58_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( v1_setwiseo(D,A)
                   => k3_finseqop(A,A,A,D,k3_binop_1(A,D),C) = C ) ) ) ) ) )).

fof(t59_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( v1_setwiseo(D,A)
                   => k2_finseqop(A,A,A,D,C,k3_binop_1(A,D)) = C ) ) ) ) ) )).

fof(d1_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( r1_finseqop(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ( k2_binop_1(A,A,A,C,D,k8_funct_2(A,A,B,D)) = k3_binop_1(A,C)
                      & k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),D) = k3_binop_1(A,C) ) ) ) ) ) ) )).

fof(d2_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( v1_finseqop(B,A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & m2_relset_1(C,A,A)
                & r1_finseqop(A,C,B) ) ) ) ) )).

fof(d3_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( ( v1_setwiseo(B,A)
              & v2_binop_1(B,A)
              & v1_finseqop(B,A) )
           => ! [C] :
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,A,A)
                  & m2_relset_1(C,A,A) )
               => ( C = k6_finseqop(A,B)
                <=> r1_finseqop(A,C,B) ) ) ) ) ) )).

fof(t60_finseqop,axiom,(
    $true )).

fof(t61_finseqop,axiom,(
    $true )).

fof(t62_finseqop,axiom,(
    $true )).

fof(t63_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v1_setwiseo(C,A)
                  & v2_binop_1(C,A)
                  & v1_finseqop(C,A) )
               => ( k2_binop_1(A,A,A,C,k8_funct_2(A,A,k6_finseqop(A,C),B),B) = k3_binop_1(A,C)
                  & k2_binop_1(A,A,A,C,B,k8_funct_2(A,A,k6_finseqop(A,C),B)) = k3_binop_1(A,C) ) ) ) ) ) )).

fof(t64_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v1_setwiseo(D,A)
                      & v2_binop_1(D,A)
                      & v1_finseqop(D,A)
                      & k2_binop_1(A,A,A,D,B,C) = k3_binop_1(A,D) )
                   => ( B = k8_funct_2(A,A,k6_finseqop(A,D),C)
                      & k8_funct_2(A,A,k6_finseqop(A,D),B) = C ) ) ) ) ) ) )).

fof(t65_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( ( v1_setwiseo(B,A)
              & v2_binop_1(B,A)
              & v1_finseqop(B,A) )
           => k8_funct_2(A,A,k6_finseqop(A,B),k3_binop_1(A,B)) = k3_binop_1(A,B) ) ) ) )).

fof(t66_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v1_setwiseo(C,A)
                  & v2_binop_1(C,A)
                  & v1_finseqop(C,A) )
               => k8_funct_2(A,A,k6_finseqop(A,C),k8_funct_2(A,A,k6_finseqop(A,C),B)) = B ) ) ) ) )).

fof(t67_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ( ( v1_setwiseo(B,A)
              & v2_binop_1(B,A)
              & v1_binop_1(B,A)
              & v1_finseqop(B,A) )
           => r7_binop_1(A,k6_finseqop(A,B),B) ) ) ) )).

fof(t68_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ( ( v1_setwiseo(E,A)
                          & v2_binop_1(E,A)
                          & v1_finseqop(E,A) )
                       => ( ( k2_binop_1(A,A,A,E,B,C) != k2_binop_1(A,A,A,E,B,D)
                            & k2_binop_1(A,A,A,E,C,B) != k2_binop_1(A,A,A,E,D,B) )
                          | C = D ) ) ) ) ) ) ) )).

fof(t69_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v1_setwiseo(D,A)
                      & v2_binop_1(D,A)
                      & v1_finseqop(D,A) )
                   => ( ( k2_binop_1(A,A,A,D,B,C) != C
                        & k2_binop_1(A,A,A,D,C,B) != C )
                      | B = k3_binop_1(A,D) ) ) ) ) ) ) )).

fof(t70_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v2_binop_1(C,A)
                      & v1_setwiseo(C,A)
                      & v1_finseqop(C,A)
                      & r6_binop_1(A,D,C)
                      & B = k3_binop_1(A,C) )
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ( k2_binop_1(A,A,A,D,B,E) = B
                          & k2_binop_1(A,A,A,D,E,B) = B ) ) ) ) ) ) ) )).

fof(t71_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,A)
                            & m2_relset_1(F,A,A) )
                         => ( ( v1_setwiseo(D,A)
                              & v2_binop_1(D,A)
                              & v1_finseqop(D,A)
                              & F = k6_finseqop(A,D)
                              & r6_binop_1(A,E,D) )
                           => ( k8_funct_2(A,A,F,k2_binop_1(A,A,A,E,B,C)) = k2_binop_1(A,A,A,E,k8_funct_2(A,A,F,B),C)
                              & k8_funct_2(A,A,F,k2_binop_1(A,A,A,E,B,C)) = k2_binop_1(A,A,A,E,B,k8_funct_2(A,A,F,C)) ) ) ) ) ) ) ) ) )).

fof(t72_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => ( ( v1_setwiseo(B,A)
                      & v2_binop_1(B,A)
                      & v1_finseqop(B,A)
                      & D = k6_finseqop(A,B)
                      & r6_binop_1(A,C,B)
                      & v1_setwiseo(C,A) )
                   => k8_funcop_1(A,A,C,k8_funct_2(A,A,D,k3_binop_1(A,C)),k6_partfun1(A)) = D ) ) ) ) ) )).

fof(t73_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v2_binop_1(C,A)
                      & v1_setwiseo(C,A)
                      & v1_finseqop(C,A)
                      & r6_binop_1(A,D,C) )
                   => k8_funct_2(A,A,k8_funcop_1(A,A,D,B,k6_partfun1(A)),k3_binop_1(A,C)) = k3_binop_1(A,C) ) ) ) ) ) )).

fof(t74_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v2_binop_1(C,A)
                      & v1_setwiseo(C,A)
                      & v1_finseqop(C,A)
                      & r6_binop_1(A,D,C) )
                   => k8_funct_2(A,A,k7_funcop_1(A,A,D,k6_partfun1(A),B),k3_binop_1(A,C)) = k3_binop_1(A,C) ) ) ) ) ) )).

fof(t75_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v1_setwiseo(D,A)
                      & v2_binop_1(D,A)
                      & v1_finseqop(D,A) )
                   => ( k6_funcop_1(A,B,D,C,k7_funct_2(B,A,A,C,k6_finseqop(A,D))) = k2_funcop_1(B,k3_binop_1(A,D))
                      & k6_funcop_1(A,B,D,k7_funct_2(B,A,A,C,k6_finseqop(A,D)),C) = k2_funcop_1(B,k3_binop_1(A,D)) ) ) ) ) ) ) )).

fof(t76_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,B,A)
                & m2_relset_1(C,B,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ( ( v2_binop_1(E,A)
                          & v1_finseqop(E,A)
                          & v1_setwiseo(E,A)
                          & k6_funcop_1(A,B,E,C,D) = k2_funcop_1(B,k3_binop_1(A,E)) )
                       => ( C = k7_funct_2(B,A,A,D,k6_finseqop(A,E))
                          & k7_funct_2(B,A,A,C,k6_finseqop(A,E)) = D ) ) ) ) ) ) ) )).

fof(t77_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v1_setwiseo(D,A)
                      & v2_binop_1(D,A)
                      & v1_finseqop(D,A) )
                   => ( k1_finseqop(A,A,A,D,C,k5_finseqop(A,A,C,k6_finseqop(A,D))) = k4_finseqop(A,B,k3_binop_1(A,D))
                      & k1_finseqop(A,A,A,D,k5_finseqop(A,A,C,k6_finseqop(A,D)),C) = k4_finseqop(A,B,k3_binop_1(A,D)) ) ) ) ) ) ) )).

fof(t78_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(B,A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ( ( v2_binop_1(E,A)
                          & v1_finseqop(E,A)
                          & v1_setwiseo(E,A)
                          & k1_finseqop(A,A,A,E,C,D) = k4_finseqop(A,B,k3_binop_1(A,E)) )
                       => ( C = k5_finseqop(A,A,D,k6_finseqop(A,E))
                          & k5_finseqop(A,A,C,k6_finseqop(A,E)) = D ) ) ) ) ) ) ) )).

fof(t79_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( ( v2_binop_1(E,A)
                              & v1_setwiseo(E,A)
                              & C = k3_binop_1(A,E)
                              & v1_finseqop(E,A)
                              & r6_binop_1(A,F,E) )
                           => k8_funcop_1(A,B,F,C,D) = k2_funcop_1(B,C) ) ) ) ) ) ) ) )).

fof(t80_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(C,A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,A),A)
                            & m2_relset_1(F,k2_zfmisc_1(A,A),A) )
                         => ( ( v2_binop_1(E,A)
                              & v1_setwiseo(E,A)
                              & B = k3_binop_1(A,E)
                              & v1_finseqop(E,A)
                              & r6_binop_1(A,F,E) )
                           => k3_finseqop(A,A,A,F,B,D) = k4_finseqop(A,C,B) ) ) ) ) ) ) ) )).

fof(d4_finseqop,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => k7_finseqop(A,B,C) = k5_relat_1(k15_funct_3(B,C),A) ) ) ) )).

fof(t81_finseqop,axiom,(
    $true )).

fof(t82_finseqop,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) )
             => ( r2_hidden(k4_tarski(A,B),k1_relat_1(k7_finseqop(C,D,E)))
               => k1_funct_1(k7_finseqop(C,D,E),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(k1_funct_1(D,A),k1_funct_1(E,B))) ) ) ) ) )).

fof(t83_finseqop,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) )
             => ( r2_hidden(k4_tarski(A,B),k1_relat_1(k7_finseqop(C,D,E)))
               => k1_binop_1(k7_finseqop(C,D,E),A,B) = k1_binop_1(C,k1_funct_1(D,A),k1_funct_1(E,B)) ) ) ) ) )).

fof(t84_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ~ v1_xboole_0(E)
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(A,B),C)
                            & m2_relset_1(F,k2_zfmisc_1(A,B),C) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,D,A)
                                & m2_relset_1(G,D,A) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,E,B)
                                    & m2_relset_1(H,E,B) )
                                 => ( v1_funct_1(k7_finseqop(F,G,H))
                                    & v1_funct_2(k7_finseqop(F,G,H),k2_zfmisc_1(D,E),C)
                                    & m2_relset_1(k7_finseqop(F,G,H),k2_zfmisc_1(D,E),C) ) ) ) ) ) ) ) ) ) )).

fof(t85_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => ( v1_funct_1(k7_finseqop(B,C,D))
                    & v1_funct_2(k7_finseqop(B,C,D),k2_zfmisc_1(A,A),A)
                    & m2_relset_1(k7_finseqop(B,C,D),k2_zfmisc_1(A,A),A) ) ) ) ) ) )).

fof(t86_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( ~ v1_xboole_0(D)
                 => ! [E] :
                      ( ~ v1_xboole_0(E)
                     => ! [F] :
                          ( m1_subset_1(F,D)
                         => ! [G] :
                              ( m1_subset_1(G,E)
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,k2_zfmisc_1(A,B),C)
                                    & m2_relset_1(H,k2_zfmisc_1(A,B),C) )
                                 => ! [I] :
                                      ( ( v1_funct_1(I)
                                        & v1_funct_2(I,D,A)
                                        & m2_relset_1(I,D,A) )
                                     => ! [J] :
                                          ( ( v1_funct_1(J)
                                            & v1_funct_2(J,E,B)
                                            & m2_relset_1(J,E,B) )
                                         => k1_binop_1(k7_finseqop(H,I,J),F,G) = k2_binop_1(A,B,C,H,k8_funct_2(D,A,I,F),k8_funct_2(E,B,J,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t87_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,A)
                        & m2_relset_1(E,A,A) )
                     => ( k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C) = k2_binop_1(A,A,A,D,B,k8_funct_2(A,A,E,C))
                        & k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C) = k2_binop_1(A,A,A,D,k8_funct_2(A,A,E,B),C) ) ) ) ) ) ) )).

fof(t88_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(B,B),B)
                        & m2_relset_1(E,k2_zfmisc_1(B,B),B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,B)
                            & m2_relset_1(F,B,B) )
                         => k6_funcop_1(B,A,k8_finseqop(B,E,k6_partfun1(B),F),C,D) = k6_funcop_1(B,A,E,C,k7_funct_2(A,B,B,D,F)) ) ) ) ) ) ) )).

fof(t89_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_2(C,A,k4_finseq_2(B,A))
             => ! [D] :
                  ( m2_finseq_2(D,A,k4_finseq_2(B,A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
                        & m2_relset_1(E,k2_zfmisc_1(A,A),A) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,A)
                            & m2_relset_1(F,A,A) )
                         => k1_finseqop(A,A,A,k8_finseqop(A,E,k6_partfun1(A),F),C,D) = k1_finseqop(A,A,A,E,C,k5_finseqop(A,A,D,F)) ) ) ) ) ) ) )).

fof(t90_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,A)
                        & m2_relset_1(E,A,A) )
                     => ( ( v2_binop_1(D,A)
                          & v1_setwiseo(D,A)
                          & v1_binop_1(D,A)
                          & v1_finseqop(D,A)
                          & E = k6_finseqop(A,D) )
                       => ( k8_funct_2(A,A,E,k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C)) = k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C)
                          & k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C) = k8_funct_2(A,A,E,k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C)) ) ) ) ) ) ) ) )).

fof(t91_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v2_binop_1(C,A)
                  & v1_setwiseo(C,A)
                  & v1_finseqop(C,A) )
               => k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),k6_finseqop(A,C)),B,B) = k3_binop_1(A,C) ) ) ) ) )).

fof(t92_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v2_binop_1(C,A)
                  & v1_setwiseo(C,A)
                  & v1_finseqop(C,A) )
               => k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),k6_finseqop(A,C)),B,k3_binop_1(A,C)) = B ) ) ) ) )).

fof(t93_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => ( ( v2_binop_1(C,A)
                      & v1_setwiseo(C,A)
                      & v1_finseqop(C,A)
                      & D = k6_finseqop(A,C) )
                   => k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),D),k3_binop_1(A,C),B) = k8_funct_2(A,A,D,B) ) ) ) ) ) )).

fof(t94_finseqop,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(A,A),A)
            & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),A)
                & m2_relset_1(C,k2_zfmisc_1(A,A),A) )
             => ( ( v1_binop_1(B,A)
                  & v2_binop_1(B,A)
                  & v1_setwiseo(B,A)
                  & v1_finseqop(B,A)
                  & C = k8_finseqop(A,B,k6_partfun1(A),k6_finseqop(A,B)) )
               => ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ! [G] :
                                ( m1_subset_1(G,A)
                               => k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,F,G)) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,G)) ) ) ) ) ) ) ) ) )).

fof(dt_k1_finseqop,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_finseq_1(E,A)
        & m1_finseq_1(F,B) )
     => m2_finseq_1(k1_finseqop(A,B,C,D,E,F),C) ) )).

fof(redefinition_k1_finseqop,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_finseq_1(E,A)
        & m1_finseq_1(F,B) )
     => k1_finseqop(A,B,C,D,E,F) = k3_funcop_1(D,E,F) ) )).

fof(dt_k2_finseqop,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_finseq_1(E,A)
        & m1_subset_1(F,B) )
     => m2_finseq_1(k2_finseqop(A,B,C,D,E,F),C) ) )).

fof(redefinition_k2_finseqop,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_finseq_1(E,A)
        & m1_subset_1(F,B) )
     => k2_finseqop(A,B,C,D,E,F) = k4_funcop_1(D,E,F) ) )).

fof(dt_k3_finseqop,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_finseq_1(F,B) )
     => m2_finseq_1(k3_finseqop(A,B,C,D,E,F),C) ) )).

fof(redefinition_k3_finseqop,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_finseq_1(F,B) )
     => k3_finseqop(A,B,C,D,E,F) = k5_funcop_1(D,E,F) ) )).

fof(dt_k4_finseqop,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => m2_finseq_2(k4_finseqop(A,B,C),A,k4_finseq_2(B,A)) ) )).

fof(redefinition_k4_finseqop,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => k4_finseqop(A,B,C) = k2_finseq_2(B,C) ) )).

fof(dt_k5_finseqop,axiom,(
    ! [A,B,C,D] :
      ( ( m1_finseq_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => m2_finseq_1(k5_finseqop(A,B,C,D),B) ) )).

fof(redefinition_k5_finseqop,axiom,(
    ! [A,B,C,D] :
      ( ( m1_finseq_1(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => k5_finseqop(A,B,C,D) = k5_relat_1(C,D) ) )).

fof(dt_k6_finseqop,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_funct_1(k6_finseqop(A,B))
        & v1_funct_2(k6_finseqop(A,B),A,A)
        & m2_relset_1(k6_finseqop(A,B),A,A) ) ) )).

fof(dt_k7_finseqop,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_relat_1(C)
        & v1_funct_1(C) )
     => ( v1_relat_1(k7_finseqop(A,B,C))
        & v1_funct_1(k7_finseqop(A,B,C)) ) ) )).

fof(dt_k8_finseqop,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,A)
        & m1_relset_1(D,A,A) )
     => ( v1_funct_1(k8_finseqop(A,B,C,D))
        & v1_funct_2(k8_finseqop(A,B,C,D),k2_zfmisc_1(A,A),A)
        & m2_relset_1(k8_finseqop(A,B,C,D),k2_zfmisc_1(A,A),A) ) ) )).

fof(redefinition_k8_finseqop,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,A)
        & m1_relset_1(D,A,A) )
     => k8_finseqop(A,B,C,D) = k7_finseqop(B,C,D) ) )).
%------------------------------------------------------------------------------