SET007 Axioms: SET007+99.ax


%------------------------------------------------------------------------------
% File     : SET007+99 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Semigroup Operations on Finite Subsets
% 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    : setwop_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   59 (  11 unit)
%            Number of atoms       :  680 (  89 equality)
%            Maximal formula depth :   31 (  13 average)
%            Number of connectives :  705 (  84 ~  ;  14  |; 306  &)
%                                         (   0 <=>; 301 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   23 (   1 propositional; 0-3 arity)
%            Number of functors    :   46 (   4 constant; 0-6 arity)
%            Number of variables   :  264 (   0 singleton; 264 !;   0 ?)
%            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_setwop_2,axiom,(
    $true )).

fof(t2_setwop_2,axiom,(
    $true )).

fof(t3_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [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,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ( v1_binop_1(E,B)
                              & v2_binop_1(E,B) )
                           => ( C = D
                              | k7_setwiseo(A,B,E,k3_setwiseo(A,C,D),F) = k2_binop_1(B,B,B,E,k8_funct_2(A,B,F,C),k8_funct_2(A,B,F,D)) ) ) ) ) ) ) ) ) )).

fof(t4_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => ! [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,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ( v1_binop_1(E,B)
                              & v2_binop_1(E,B) )
                           => ( ( D = k1_xboole_0
                                & ~ v1_setwiseo(E,B) )
                              | r2_hidden(C,D)
                              | k7_setwiseo(A,B,E,k5_setwiseo(A,D,k2_setwiseo(A,C)),F) = k2_binop_1(B,B,B,E,k7_setwiseo(A,B,E,D,F),k8_funct_2(A,B,F,C)) ) ) ) ) ) ) ) ) )).

fof(t5_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ! [E] :
                      ( m1_subset_1(E,A)
                     => ! [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,A,B)
                                & m2_relset_1(G,A,B) )
                             => ( ( v1_binop_1(F,B)
                                  & v2_binop_1(F,B) )
                               => ( C = D
                                  | C = E
                                  | D = E
                                  | k7_setwiseo(A,B,F,k4_setwiseo(A,C,D,E),G) = k2_binop_1(B,B,B,F,k2_binop_1(B,B,B,F,k8_funct_2(A,B,G,C),k8_funct_2(A,B,G,D)),k8_funct_2(A,B,G,E)) ) ) ) ) ) ) ) ) ) )).

fof(t6_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => ! [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,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ( v1_binop_1(E,B)
                              & v2_binop_1(E,B)
                              & r1_xboole_0(C,D) )
                           => ( ( ~ ( C != k1_xboole_0
                                    & D != k1_xboole_0 )
                                & ~ v1_setwiseo(E,B) )
                              | k7_setwiseo(A,B,E,k5_setwiseo(A,C,D),F) = k2_binop_1(B,B,B,E,k7_setwiseo(A,B,E,C,F),k7_setwiseo(A,B,E,D,F)) ) ) ) ) ) ) ) ) )).

fof(t7_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => ! [E] :
                      ( m1_subset_1(E,k5_finsub_1(B))
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,k2_zfmisc_1(C,C),C)
                            & m2_relset_1(F,k2_zfmisc_1(C,C),C) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,A,C)
                                & m2_relset_1(G,A,C) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,B,C)
                                    & m2_relset_1(H,B,C) )
                                 => ( ( v1_binop_1(F,C)
                                      & v2_binop_1(F,C) )
                                   => ( ( E = k1_xboole_0
                                        & ~ v1_setwiseo(F,C) )
                                      | ! [I] :
                                          ( ( v1_relat_1(I)
                                            & v1_funct_1(I) )
                                         => ~ ( k1_relat_1(I) = E
                                              & k2_relat_1(I) = D
                                              & v2_funct_1(I)
                                              & k2_partfun1(B,C,H,E) = k5_relat_1(I,G) ) )
                                      | k7_setwiseo(B,C,F,E,H) = k7_setwiseo(A,C,F,D,G) ) ) ) ) ) ) ) ) ) ) )).

fof(t8_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => ! [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(C,C),C)
                            & m2_relset_1(F,k2_zfmisc_1(C,C),C) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,B,C)
                                & m2_relset_1(G,B,C) )
                             => ( ( v1_binop_1(F,C)
                                  & v2_binop_1(F,C)
                                  & v2_funct_1(E) )
                               => ( ( D = k1_xboole_0
                                    & ~ v1_setwiseo(F,C) )
                                  | k7_setwiseo(B,C,F,k8_setwiseo(A,B,E,D),G) = k7_setwiseo(A,C,F,D,k7_funct_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) )).

fof(t9_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [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) )
                 => ! [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,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ( v1_binop_1(D,B)
                              & v2_binop_1(D,B)
                              & k2_partfun1(A,B,E,C) = k2_partfun1(A,B,F,C) )
                           => ( ( C = k1_xboole_0
                                & ~ v1_setwiseo(D,B) )
                              | k7_setwiseo(A,B,D,C,E) = k7_setwiseo(A,B,D,C,F) ) ) ) ) ) ) ) ) )).

fof(t10_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( m1_subset_1(D,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,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ( v1_binop_1(E,B)
                              & v2_binop_1(E,B)
                              & v1_setwiseo(E,B)
                              & D = k3_binop_1(B,E)
                              & k8_setwiseo(A,B,F,C) = k2_setwiseo(B,D) )
                           => k7_setwiseo(A,B,E,C,F) = D ) ) ) ) ) ) ) )).

fof(t11_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( m1_subset_1(D,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,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,A,B)
                                & m2_relset_1(G,A,B) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,A,B)
                                    & m2_relset_1(H,A,B) )
                                 => ( ( v1_binop_1(E,B)
                                      & v2_binop_1(E,B)
                                      & v1_setwiseo(E,B)
                                      & D = k3_binop_1(B,E)
                                      & k2_binop_1(B,B,B,F,D,D) = D
                                      & ! [I] :
                                          ( m1_subset_1(I,B)
                                         => ! [J] :
                                              ( m1_subset_1(J,B)
                                             => ! [K] :
                                                  ( m1_subset_1(K,B)
                                                 => ! [L] :
                                                      ( m1_subset_1(L,B)
                                                     => k2_binop_1(B,B,B,E,k2_binop_1(B,B,B,F,I,J),k2_binop_1(B,B,B,F,K,L)) = k2_binop_1(B,B,B,F,k2_binop_1(B,B,B,E,I,K),k2_binop_1(B,B,B,E,J,L)) ) ) ) ) )
                                   => k2_binop_1(B,B,B,F,k7_setwiseo(A,B,E,C,G),k7_setwiseo(A,B,E,C,H)) = k7_setwiseo(A,B,E,C,k6_funcop_1(B,A,F,G,H)) ) ) ) ) ) ) ) ) ) )).

fof(t12_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [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) )
                 => ! [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,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ( v1_binop_1(D,B)
                              & v2_binop_1(D,B)
                              & v1_setwiseo(D,B) )
                           => k2_binop_1(B,B,B,D,k7_setwiseo(A,B,D,C,E),k7_setwiseo(A,B,D,C,F)) = k7_setwiseo(A,B,D,C,k6_funcop_1(B,A,D,E,F)) ) ) ) ) ) ) ) )).

fof(t13_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [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) )
                 => ! [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,A,B)
                            & m2_relset_1(F,A,B) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,A,B)
                                & m2_relset_1(G,A,B) )
                             => ( ( v1_binop_1(D,B)
                                  & v2_binop_1(D,B)
                                  & v1_setwiseo(D,B)
                                  & v1_finseqop(D,B)
                                  & E = k8_finseqop(B,D,k6_partfun1(B),k6_finseqop(B,D)) )
                               => k2_binop_1(B,B,B,E,k7_setwiseo(A,B,D,C,F),k7_setwiseo(A,B,D,C,G)) = k7_setwiseo(A,B,D,C,k6_funcop_1(B,A,E,F,G)) ) ) ) ) ) ) ) ) )).

fof(t14_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( m1_subset_1(E,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) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,A,B)
                                    & m2_relset_1(H,A,B) )
                                 => ( ( v1_binop_1(F,B)
                                      & v2_binop_1(F,B)
                                      & v1_setwiseo(F,B)
                                      & D = k3_binop_1(B,F)
                                      & r6_binop_1(B,G,F)
                                      & k2_binop_1(B,B,B,G,E,D) = D )
                                   => k2_binop_1(B,B,B,G,E,k7_setwiseo(A,B,F,C,H)) = k7_setwiseo(A,B,F,C,k8_funcop_1(B,A,G,E,H)) ) ) ) ) ) ) ) ) ) )).

fof(t15_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( m1_subset_1(D,B)
                 => ! [E] :
                      ( m1_subset_1(E,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) )
                             => ! [H] :
                                  ( ( v1_funct_1(H)
                                    & v1_funct_2(H,A,B)
                                    & m2_relset_1(H,A,B) )
                                 => ( ( v1_binop_1(F,B)
                                      & v2_binop_1(F,B)
                                      & v1_setwiseo(F,B)
                                      & D = k3_binop_1(B,F)
                                      & r6_binop_1(B,G,F)
                                      & k2_binop_1(B,B,B,G,D,E) = D )
                                   => k2_binop_1(B,B,B,G,k7_setwiseo(A,B,F,C,H),E) = k7_setwiseo(A,B,F,C,k7_funcop_1(B,A,G,H,E)) ) ) ) ) ) ) ) ) ) )).

fof(t16_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( m1_subset_1(D,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,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,A,B)
                                & m2_relset_1(G,A,B) )
                             => ( ( v1_binop_1(E,B)
                                  & v2_binop_1(E,B)
                                  & v1_setwiseo(E,B)
                                  & v1_finseqop(E,B)
                                  & r6_binop_1(B,F,E) )
                               => k2_binop_1(B,B,B,F,D,k7_setwiseo(A,B,E,C,G)) = k7_setwiseo(A,B,E,C,k8_funcop_1(B,A,F,D,G)) ) ) ) ) ) ) ) ) )).

fof(t17_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( m1_subset_1(D,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,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,A,B)
                                & m2_relset_1(G,A,B) )
                             => ( ( v1_binop_1(E,B)
                                  & v2_binop_1(E,B)
                                  & v1_setwiseo(E,B)
                                  & v1_finseqop(E,B)
                                  & r6_binop_1(B,F,E) )
                               => k2_binop_1(B,B,B,F,k7_setwiseo(A,B,E,C,G),D) = k7_setwiseo(A,B,E,C,k7_funcop_1(B,A,F,G,D)) ) ) ) ) ) ) ) ) )).

fof(t18_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ~ v1_xboole_0(C)
             => ! [D] :
                  ( m1_subset_1(D,k5_finsub_1(A))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,k2_zfmisc_1(C,C),C)
                        & m2_relset_1(E,k2_zfmisc_1(C,C),C) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,C)
                            & m2_relset_1(F,A,C) )
                         => ! [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,C,B)
                                    & m2_relset_1(H,C,B) )
                                 => ( ( v1_binop_1(E,C)
                                      & v2_binop_1(E,C)
                                      & v1_setwiseo(E,C)
                                      & v1_binop_1(G,B)
                                      & v2_binop_1(G,B)
                                      & v1_setwiseo(G,B)
                                      & k8_funct_2(C,B,H,k3_binop_1(C,E)) = k3_binop_1(B,G)
                                      & ! [I] :
                                          ( m1_subset_1(I,C)
                                         => ! [J] :
                                              ( m1_subset_1(J,C)
                                             => k8_funct_2(C,B,H,k2_binop_1(C,C,C,E,I,J)) = k2_binop_1(B,B,B,G,k8_funct_2(C,B,H,I),k8_funct_2(C,B,H,J)) ) ) )
                                   => k8_funct_2(C,B,H,k7_setwiseo(A,C,E,D,F)) = k7_setwiseo(A,B,G,D,k7_funct_2(A,C,B,F,H)) ) ) ) ) ) ) ) ) ) )).

fof(t19_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [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) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,B)
                        & m2_relset_1(E,B,B) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,A,B)
                            & m2_relset_1(F,A,B) )
                         => ( ( v1_binop_1(D,B)
                              & v2_binop_1(D,B)
                              & v1_setwiseo(D,B)
                              & k8_funct_2(B,B,E,k3_binop_1(B,D)) = k3_binop_1(B,D)
                              & r7_binop_1(B,E,D) )
                           => k8_funct_2(B,B,E,k7_setwiseo(A,B,D,C,F)) = k7_setwiseo(A,B,D,C,k7_funct_2(A,B,B,F,E)) ) ) ) ) ) ) ) )).

fof(t20_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D] :
                  ( m1_subset_1(D,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,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,A,B)
                                & m2_relset_1(G,A,B) )
                             => ( ( v1_binop_1(E,B)
                                  & v2_binop_1(E,B)
                                  & v1_setwiseo(E,B)
                                  & v1_finseqop(E,B)
                                  & r6_binop_1(B,F,E) )
                               => k8_funct_2(B,B,k8_funcop_1(B,B,F,D,k6_partfun1(B)),k7_setwiseo(A,B,E,C,G)) = k7_setwiseo(A,B,E,C,k7_funct_2(A,B,B,G,k8_funcop_1(B,B,F,D,k6_partfun1(B)))) ) ) ) ) ) ) ) ) )).

fof(t21_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [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) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( ( v1_binop_1(D,B)
                          & v2_binop_1(D,B)
                          & v1_setwiseo(D,B)
                          & v1_finseqop(D,B) )
                       => k8_funct_2(B,B,k6_finseqop(B,D),k7_setwiseo(A,B,D,C,E)) = k7_setwiseo(A,B,D,C,k7_funct_2(A,B,B,E,k6_finseqop(B,D))) ) ) ) ) ) ) )).

fof(d1_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => k1_setwop_2(A,B,C) = k4_finsop_1(A,k3_finsop_1(A,k5_numbers,C),B) ) ) ) )).

fof(t22_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ( ( r2_hidden(C,k5_finsop_1(D))
                     => k8_funct_2(k5_numbers,A,k1_setwop_2(A,D,B),C) = k1_funct_1(D,C) )
                    & ( ~ r2_hidden(C,k5_finsop_1(D))
                     => k8_funct_2(k5_numbers,A,k1_setwop_2(A,D,B),C) = B ) ) ) ) ) ) )).

fof(t23_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => k2_partfun1(k5_numbers,A,k1_setwop_2(A,C,B),k5_finsop_1(C)) = C ) ) ) )).

fof(t24_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => k2_partfun1(k5_numbers,A,k1_setwop_2(A,k8_finseq_1(A,C,D),B),k5_finsop_1(C)) = C ) ) ) ) )).

fof(t25_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => k2_relat_1(k1_setwop_2(A,C,B)) = k2_xboole_0(k2_relat_1(C),k2_setwiseo(A,B)) ) ) ) )).

fof(t26_setwop_2,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,B,A)
                    & m2_relset_1(D,B,A) )
                 => ! [E] :
                      ( m2_finseq_1(E,B)
                     => k7_funct_2(k5_numbers,B,A,k1_setwop_2(B,E,C),D) = k1_setwop_2(A,k5_finseqop(B,A,E,D),k8_funct_2(B,A,D,C)) ) ) ) ) ) )).

fof(d2_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_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_binop_1(C,A) )
               => ( ( ~ v1_setwiseo(C,A)
                    & ~ r1_xreal_0(np__1,k3_finseq_1(B)) )
                  | k2_finsop_1(A,B,C) = k7_setwiseo(k5_numbers,A,C,k3_setwop_2(B),k1_setwop_2(A,B,k3_binop_1(A,C))) ) ) ) ) ) )).

fof(t27_setwop_2,axiom,(
    $true )).

fof(t28_setwop_2,axiom,(
    $true )).

fof(t29_setwop_2,axiom,(
    $true )).

fof(t30_setwop_2,axiom,(
    $true )).

fof(t31_setwop_2,axiom,(
    $true )).

fof(t32_setwop_2,axiom,(
    $true )).

fof(t33_setwop_2,axiom,(
    $true )).

fof(t34_setwop_2,axiom,(
    $true )).

fof(t35_setwop_2,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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( v1_setwiseo(B,A)
               => k2_finsop_1(A,k1_finsop_1(A,C,k3_binop_1(A,B)),B) = k3_binop_1(A,B) ) ) ) ) )).

fof(t36_setwop_2,axiom,(
    $true )).

fof(t37_setwop_2,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] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( v2_binop_1(C,A)
                       => ( ( ~ ( r1_xreal_0(np__1,D)
                                & r1_xreal_0(np__1,E) )
                            & ~ v1_setwiseo(C,A) )
                          | k2_finsop_1(A,k1_finsop_1(A,k1_nat_1(D,E),B),C) = k2_binop_1(A,A,A,C,k2_finsop_1(A,k1_finsop_1(A,D,B),C),k2_finsop_1(A,k1_finsop_1(A,E,B),C)) ) ) ) ) ) ) ) )).

fof(t38_setwop_2,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] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( v1_binop_1(C,A)
                          & v2_binop_1(C,A) )
                       => ( ( ~ ( r1_xreal_0(np__1,D)
                                & r1_xreal_0(np__1,E) )
                            & ~ v1_setwiseo(C,A) )
                          | k2_finsop_1(A,k1_finsop_1(A,k2_nat_1(D,E),B),C) = k2_finsop_1(A,k1_finsop_1(A,E,k2_finsop_1(A,k1_finsop_1(A,D,B),C)),C) ) ) ) ) ) ) ) )).

fof(t39_setwop_2,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(B,B),B)
                & m2_relset_1(C,k2_zfmisc_1(B,B),B) )
             => ! [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,B,A)
                        & m2_relset_1(E,B,A) )
                     => ! [F] :
                          ( m2_finseq_1(F,B)
                         => ( ( v1_setwiseo(C,B)
                              & v1_setwiseo(D,A)
                              & k8_funct_2(B,A,E,k3_binop_1(B,C)) = k3_binop_1(A,D)
                              & ! [G] :
                                  ( m1_subset_1(G,B)
                                 => ! [H] :
                                      ( m1_subset_1(H,B)
                                     => k8_funct_2(B,A,E,k2_binop_1(B,B,B,C,G,H)) = k2_binop_1(A,A,A,D,k8_funct_2(B,A,E,G),k8_funct_2(B,A,E,H)) ) ) )
                           => k8_funct_2(B,A,E,k2_finsop_1(B,F,C)) = k2_finsop_1(A,k5_finseqop(B,A,F,E),D) ) ) ) ) ) ) ) )).

fof(t40_setwop_2,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] :
                  ( m2_finseq_1(D,A)
                 => ( ( v1_setwiseo(B,A)
                      & k8_funct_2(A,A,C,k3_binop_1(A,B)) = k3_binop_1(A,B)
                      & r7_binop_1(A,C,B) )
                   => k8_funct_2(A,A,C,k2_finsop_1(A,D,B)) = k2_finsop_1(A,k5_finseqop(A,A,D,C),B) ) ) ) ) ) )).

fof(t41_setwop_2,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] :
                      ( m2_finseq_1(E,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)),k2_finsop_1(A,E,C)) = k2_finsop_1(A,k5_finseqop(A,A,E,k8_funcop_1(A,A,D,B,k6_partfun1(A))),C) ) ) ) ) ) ) )).

fof(t42_setwop_2,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] :
              ( m2_finseq_1(C,A)
             => ( ( v1_binop_1(B,A)
                  & v2_binop_1(B,A)
                  & v1_setwiseo(B,A)
                  & v1_finseqop(B,A) )
               => k8_funct_2(A,A,k6_finseqop(A,B),k2_finsop_1(A,C,B)) = k2_finsop_1(A,k5_finseqop(A,A,C,k6_finseqop(A,B)),B) ) ) ) ) )).

fof(t43_setwop_2,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] :
                      ( m2_finseq_1(E,A)
                     => ! [F] :
                          ( m2_finseq_1(F,A)
                         => ( ( v1_binop_1(C,A)
                              & v2_binop_1(C,A)
                              & v1_setwiseo(C,A)
                              & B = k3_binop_1(A,C)
                              & k2_binop_1(A,A,A,D,B,B) = B
                              & ! [G] :
                                  ( m1_subset_1(G,A)
                                 => ! [H] :
                                      ( m1_subset_1(H,A)
                                     => ! [I] :
                                          ( m1_subset_1(I,A)
                                         => ! [J] :
                                              ( m1_subset_1(J,A)
                                             => k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,D,G,H),k2_binop_1(A,A,A,D,I,J)) = k2_binop_1(A,A,A,D,k2_binop_1(A,A,A,C,G,I),k2_binop_1(A,A,A,C,H,J)) ) ) ) )
                              & k3_finseq_1(E) = k3_finseq_1(F) )
                           => k2_binop_1(A,A,A,D,k2_finsop_1(A,E,C),k2_finsop_1(A,F,C)) = k2_finsop_1(A,k1_finseqop(A,A,A,D,E,F),C) ) ) ) ) ) ) ) )).

fof(t44_setwop_2,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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_finseq_2(F,A,k4_finseq_2(E,A))
                         => ! [G] :
                              ( m2_finseq_2(G,A,k4_finseq_2(E,A))
                             => ( ( v1_binop_1(C,A)
                                  & v2_binop_1(C,A)
                                  & v1_setwiseo(C,A)
                                  & B = k3_binop_1(A,C)
                                  & k2_binop_1(A,A,A,D,B,B) = B
                                  & ! [H] :
                                      ( m1_subset_1(H,A)
                                     => ! [I] :
                                          ( m1_subset_1(I,A)
                                         => ! [J] :
                                              ( m1_subset_1(J,A)
                                             => ! [K] :
                                                  ( m1_subset_1(K,A)
                                                 => k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,D,H,I),k2_binop_1(A,A,A,D,J,K)) = k2_binop_1(A,A,A,D,k2_binop_1(A,A,A,C,H,J),k2_binop_1(A,A,A,C,I,K)) ) ) ) ) )
                               => k2_binop_1(A,A,A,D,k2_finsop_1(A,F,C),k2_finsop_1(A,G,C)) = k2_finsop_1(A,k1_finseqop(A,A,A,D,F,G),C) ) ) ) ) ) ) ) ) )).

fof(t45_setwop_2,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] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ( ( v1_binop_1(B,A)
                      & v2_binop_1(B,A)
                      & v1_setwiseo(B,A)
                      & k3_finseq_1(C) = k3_finseq_1(D) )
                   => k2_binop_1(A,A,A,B,k2_finsop_1(A,C,B),k2_finsop_1(A,D,B)) = k2_finsop_1(A,k1_finseqop(A,A,A,B,C,D),B) ) ) ) ) ) )).

fof(t46_setwop_2,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] :
              ( 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))
                     => ( ( v1_binop_1(B,A)
                          & v2_binop_1(B,A)
                          & v1_setwiseo(B,A) )
                       => k2_binop_1(A,A,A,B,k2_finsop_1(A,D,B),k2_finsop_1(A,E,B)) = k2_finsop_1(A,k1_finseqop(A,A,A,B,D,E),B) ) ) ) ) ) ) )).

fof(t47_setwop_2,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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( v1_binop_1(D,A)
                          & v2_binop_1(D,A)
                          & v1_setwiseo(D,A) )
                       => k2_finsop_1(A,k1_finsop_1(A,E,k2_binop_1(A,A,A,D,B,C)),D) = k2_binop_1(A,A,A,D,k2_finsop_1(A,k1_finsop_1(A,E,B),D),k2_finsop_1(A,k1_finsop_1(A,E,C),D)) ) ) ) ) ) ) )).

fof(t48_setwop_2,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] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_finseq_2(E,A,k4_finseq_2(D,A))
                     => ! [F] :
                          ( m2_finseq_2(F,A,k4_finseq_2(D,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)) )
                           => k2_binop_1(A,A,A,C,k2_finsop_1(A,E,B),k2_finsop_1(A,F,B)) = k2_finsop_1(A,k1_finseqop(A,A,A,C,E,F),B) ) ) ) ) ) ) ) )).

fof(t49_setwop_2,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] :
                          ( m2_finseq_1(F,A)
                         => ( ( v1_binop_1(D,A)
                              & v2_binop_1(D,A)
                              & v1_setwiseo(D,A)
                              & B = k3_binop_1(A,D)
                              & r6_binop_1(A,E,D)
                              & k2_binop_1(A,A,A,E,C,B) = B )
                           => k2_binop_1(A,A,A,E,C,k2_finsop_1(A,F,D)) = k2_finsop_1(A,k3_finseqop(A,A,A,E,C,F),D) ) ) ) ) ) ) ) )).

fof(t50_setwop_2,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] :
                          ( m2_finseq_1(F,A)
                         => ( ( v1_binop_1(D,A)
                              & v2_binop_1(D,A)
                              & v1_setwiseo(D,A)
                              & B = k3_binop_1(A,D)
                              & r6_binop_1(A,E,D)
                              & k2_binop_1(A,A,A,E,B,C) = B )
                           => k2_binop_1(A,A,A,E,k2_finsop_1(A,F,D),C) = k2_finsop_1(A,k2_finseqop(A,A,A,E,F,C),D) ) ) ) ) ) ) ) )).

fof(t51_setwop_2,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] :
                      ( m2_finseq_1(E,A)
                     => ( ( v1_binop_1(C,A)
                          & v2_binop_1(C,A)
                          & v1_setwiseo(C,A)
                          & v1_finseqop(C,A)
                          & r6_binop_1(A,D,C) )
                       => k2_binop_1(A,A,A,D,B,k2_finsop_1(A,E,C)) = k2_finsop_1(A,k3_finseqop(A,A,A,D,B,E),C) ) ) ) ) ) ) )).

fof(t52_setwop_2,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] :
                      ( m2_finseq_1(E,A)
                     => ( ( v1_binop_1(C,A)
                          & v2_binop_1(C,A)
                          & v1_setwiseo(C,A)
                          & v1_finseqop(C,A)
                          & r6_binop_1(A,D,C) )
                       => k2_binop_1(A,A,A,D,k2_finsop_1(A,E,C),B) = k2_finsop_1(A,k2_finseqop(A,A,A,D,E,B),C) ) ) ) ) ) ) )).

fof(dt_k1_setwop_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_finseq_1(B,A)
        & m1_subset_1(C,A) )
     => ( v1_funct_1(k1_setwop_2(A,B,C))
        & v1_funct_2(k1_setwop_2(A,B,C),k5_numbers,A)
        & m2_relset_1(k1_setwop_2(A,B,C),k5_numbers,A) ) ) )).

fof(dt_k2_setwop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k2_setwop_2(A),k5_finsub_1(k5_numbers)) ) )).

fof(redefinition_k2_setwop_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => k2_setwop_2(A) = k1_finseq_1(A) ) )).

fof(dt_k3_setwop_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k3_setwop_2(A),k5_finsub_1(k5_numbers)) ) )).

fof(redefinition_k3_setwop_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_setwop_2(A) = k1_relat_1(A) ) )).
%------------------------------------------------------------------------------