SET007 Axioms: SET007+33.ax


%------------------------------------------------------------------------------
% File     : SET007+33 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Semilattice 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    : setwiseo [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  104 (  23 unit)
%            Number of atoms       :  792 ( 100 equality)
%            Maximal formula depth :   30 (   9 average)
%            Number of connectives :  803 ( 115 ~  ;  12  |; 313  &)
%                                         (  12 <=>; 351 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-3 arity)
%            Number of functors    :   36 (   6 constant; 0-6 arity)
%            Number of variables   :  385 (   0 singleton; 378 !;   7 ?)
%            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(rc1_setwiseo,axiom,(
    ! [A] :
    ? [B] :
      ( m1_subset_1(B,k5_finsub_1(A))
      & v1_xboole_0(B)
      & v1_finset_1(B) ) )).

fof(rc2_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) )).

fof(t1_setwiseo,axiom,(
    $true )).

fof(t2_setwiseo,axiom,(
    $true )).

fof(t3_setwiseo,axiom,(
    ! [A,B,C] : r1_tarski(k1_tarski(A),k1_enumset1(A,B,C)) )).

fof(t4_setwiseo,axiom,(
    ! [A,B,C] : r1_tarski(k2_tarski(A,B),k1_enumset1(A,B,C)) )).

fof(t5_setwiseo,axiom,(
    ! [A,B,C] :
      ~ ( r1_tarski(A,k2_xboole_0(B,k1_tarski(C)))
        & ~ r2_hidden(C,A)
        & ~ r1_tarski(A,B) ) )).

fof(t6_setwiseo,axiom,(
    ! [A,B,C] :
      ( r2_hidden(A,k2_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        | A = C ) ) )).

fof(t7_setwiseo,axiom,(
    $true )).

fof(t8_setwiseo,axiom,(
    ! [A,B,C] :
      ( r1_tarski(k2_xboole_0(A,k1_tarski(B)),C)
    <=> ( r2_hidden(B,C)
        & r1_tarski(A,C) ) ) )).

fof(t9_setwiseo,axiom,(
    $true )).

fof(t10_setwiseo,axiom,(
    $true )).

fof(t11_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => k9_relat_1(C,k4_xboole_0(B,k10_relat_1(C,A))) = k4_xboole_0(k9_relat_1(C,B),A) ) )).

fof(t12_setwiseo,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] :
                  ( m1_subset_1(D,B)
                 => r2_hidden(D,k3_funct_2(B,A,C,k1_tarski(k8_funct_2(B,A,C,D)))) ) ) ) ) )).

fof(t13_setwiseo,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] :
                  ( m1_subset_1(D,B)
                 => k2_funct_2(B,A,C,k1_tarski(D)) = k1_tarski(k8_funct_2(B,A,C,D)) ) ) ) ) )).

fof(t14_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ! [C] :
              ( r2_hidden(C,B)
             => m1_subset_1(C,A) ) ) ) )).

fof(t15_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_subset_1(C,k5_finsub_1(A))
             => ! [D,E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,A,B)
                    & m2_relset_1(E,A,B) )
                 => ( ! [F] :
                        ( m1_subset_1(F,A)
                       => ( r2_hidden(F,C)
                         => r2_hidden(k8_funct_2(A,B,E,F),D) ) )
                   => r1_tarski(k2_funct_2(A,B,E,C),D) ) ) ) ) ) )).

fof(t16_setwiseo,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k5_finsub_1(A))
     => ! [C] :
          ( r1_tarski(C,B)
         => m1_subset_1(C,k5_finsub_1(A)) ) ) )).

fof(t17_setwiseo,axiom,(
    $true )).

fof(t18_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => ~ ( B != k1_xboole_0
              & ! [C] :
                  ( m1_subset_1(C,A)
                 => ~ r2_hidden(C,B) ) ) ) ) )).

fof(t19_setwiseo,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] :
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ( k2_funct_2(B,A,C,D) = k1_xboole_0
                   => D = k1_xboole_0 ) ) ) ) ) )).

fof(d1_setwiseo,axiom,(
    ! [A] : k1_setwiseo(A) = k1_xboole_0 )).

fof(d2_setwiseo,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)
          <=> ? [C] :
                ( m1_subset_1(C,A)
                & r3_binop_1(A,C,B) ) ) ) ) )).

fof(t20_setwiseo,axiom,(
    $true )).

fof(t21_setwiseo,axiom,(
    $true )).

fof(t22_setwiseo,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)
          <=> r3_binop_1(A,k3_binop_1(A,B),B) ) ) ) )).

fof(t23_setwiseo,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)
           => ! [C] :
                ( m1_subset_1(C,A)
               => ( k2_binop_1(A,A,A,B,k3_binop_1(A,B),C) = C
                  & k2_binop_1(A,A,A,B,C,k3_binop_1(A,B)) = C ) ) ) ) ) )).

fof(d3_setwiseo,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] :
                  ( 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) )
                     => ( ( v1_binop_1(C,B)
                          & v2_binop_1(C,B) )
                       => ( ( D = k1_xboole_0
                            & ~ v1_setwiseo(C,B) )
                          | ! [F] :
                              ( m1_subset_1(F,B)
                             => ( F = k7_setwiseo(A,B,C,D,E)
                              <=> ? [G] :
                                    ( v1_funct_1(G)
                                    & v1_funct_2(G,k5_finsub_1(A),B)
                                    & m2_relset_1(G,k5_finsub_1(A),B)
                                    & F = k8_funct_2(k5_finsub_1(A),B,G,D)
                                    & ! [H] :
                                        ( m1_subset_1(H,B)
                                       => ( r3_binop_1(B,H,C)
                                         => k1_funct_1(G,k1_xboole_0) = H ) )
                                    & ! [H] :
                                        ( m1_subset_1(H,A)
                                       => k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H) )
                                    & ! [H] :
                                        ( m1_subset_1(H,k5_finsub_1(A))
                                       => ( r1_tarski(H,D)
                                         => ( H = k1_xboole_0
                                            | ! [I] :
                                                ( m1_subset_1(I,A)
                                               => ( r2_hidden(I,k6_setwiseo(A,D,H))
                                                 => k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t24_setwiseo,axiom,(
    $true )).

fof(t25_setwiseo,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] :
                  ( 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) )
                     => ( ( v3_binop_1(C,B)
                          & v1_binop_1(C,B)
                          & v2_binop_1(C,B) )
                       => ( ( D = k1_xboole_0
                            & ~ v1_setwiseo(C,B) )
                          | ! [F] :
                              ( m1_subset_1(F,B)
                             => ( F = k7_setwiseo(A,B,C,D,E)
                              <=> ? [G] :
                                    ( v1_funct_1(G)
                                    & v1_funct_2(G,k5_finsub_1(A),B)
                                    & m2_relset_1(G,k5_finsub_1(A),B)
                                    & F = k8_funct_2(k5_finsub_1(A),B,G,D)
                                    & ! [H] :
                                        ( m1_subset_1(H,B)
                                       => ( r3_binop_1(B,H,C)
                                         => k1_funct_1(G,k1_xboole_0) = H ) )
                                    & ! [H] :
                                        ( m1_subset_1(H,A)
                                       => k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H) )
                                    & ! [H] :
                                        ( m1_subset_1(H,k5_finsub_1(A))
                                       => ( r1_tarski(H,D)
                                         => ( H = k1_xboole_0
                                            | ! [I] :
                                                ( m1_subset_1(I,A)
                                               => ( r2_hidden(I,D)
                                                 => k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t26_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] :
                        ( m1_subset_1(E,B)
                       => k7_setwiseo(B,A,C,k2_setwiseo(B,E),D) = k8_funct_2(B,A,D,E) ) ) ) ) ) ) )).

fof(t27_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] :
                        ( m1_subset_1(E,B)
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)) ) ) ) ) ) ) ) )).

fof(t28_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] :
                        ( m1_subset_1(E,B)
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => ! [G] :
                                ( m1_subset_1(G,B)
                               => k7_setwiseo(B,A,C,k4_setwiseo(B,E,F,G),D) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)),k8_funct_2(B,A,D,G)) ) ) ) ) ) ) ) ) )).

fof(t29_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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] :
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ( ( v3_binop_1(C,A)
                          & v1_binop_1(C,A)
                          & v2_binop_1(C,A) )
                       => ( D = k1_xboole_0
                          | ! [F] :
                              ( m1_subset_1(F,B)
                             => k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) ) ) ) ) ) ) ) ) )).

fof(t30_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A) )
                   => ! [E] :
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ! [F] :
                            ( m1_subset_1(F,k5_finsub_1(B))
                           => ~ ( E != k1_xboole_0
                                & F != k1_xboole_0
                                & k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) != k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) ) ) ) ) ) ) ) ) )).

fof(t31_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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] :
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ( ( v1_binop_1(C,A)
                          & v2_binop_1(C,A)
                          & v3_binop_1(C,A) )
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => ( r2_hidden(F,D)
                             => k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)) = k7_setwiseo(B,A,C,D,E) ) ) ) ) ) ) ) ) )).

fof(t32_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v1_binop_1(C,A)
                      & v2_binop_1(C,A)
                      & v3_binop_1(C,A) )
                   => ! [E] :
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ! [F] :
                            ( m1_subset_1(F,k5_finsub_1(B))
                           => ( r1_tarski(E,F)
                             => ( E = k1_xboole_0
                                | k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) = k7_setwiseo(B,A,C,F,D) ) ) ) ) ) ) ) ) ) )).

fof(t33_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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] :
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ( ( v1_binop_1(C,A)
                          & v2_binop_1(C,A)
                          & v3_binop_1(C,A) )
                       => ( D = k1_xboole_0
                          | ! [F] :
                              ( m1_subset_1(F,A)
                             => ( ! [G] :
                                    ( m1_subset_1(G,B)
                                   => ( r2_hidden(G,D)
                                     => k8_funct_2(B,A,E,G) = F ) )
                               => k7_setwiseo(B,A,C,D,E) = F ) ) ) ) ) ) ) ) ) )).

fof(t34_setwiseo,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] :
                  ( 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) )
                     => ( ( v1_binop_1(C,B)
                          & v2_binop_1(C,B)
                          & v3_binop_1(C,B) )
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => ( k2_funct_2(A,B,E,D) = k2_setwiseo(B,F)
                             => k7_setwiseo(A,B,C,D,E) = F ) ) ) ) ) ) ) ) )).

fof(t35_setwiseo,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) )
             => ( ( v1_binop_1(C,B)
                  & v2_binop_1(C,B)
                  & v3_binop_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] :
                            ( m1_subset_1(F,k5_finsub_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,k5_finsub_1(A))
                               => ( k2_funct_2(A,B,D,F) = k2_funct_2(A,B,E,G)
                                 => ( F = k1_xboole_0
                                    | k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E) ) ) ) ) ) ) ) ) ) ) )).

fof(t36_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A)
                      & r6_binop_1(A,D,C) )
                   => ! [E] :
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ( E != k1_xboole_0
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,B,A)
                                & m2_relset_1(F,B,A) )
                             => ! [G] :
                                  ( m1_subset_1(G,A)
                                 => k2_binop_1(A,A,A,D,G,k7_setwiseo(B,A,C,E,F)) = k7_setwiseo(B,A,C,E,k8_funcop_1(A,B,D,G,F)) ) ) ) ) ) ) ) ) ) )).

fof(t37_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A)
                      & r6_binop_1(A,D,C) )
                   => ! [E] :
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ( E != k1_xboole_0
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,B,A)
                                & m2_relset_1(F,B,A) )
                             => ! [G] :
                                  ( m1_subset_1(G,A)
                                 => k2_binop_1(A,A,A,D,k7_setwiseo(B,A,C,E,F),G) = k7_setwiseo(B,A,C,E,k7_funcop_1(A,B,D,F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t38_setwiseo,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,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v3_binop_1(D,A)
                      & v1_binop_1(D,A)
                      & v2_binop_1(D,A) )
                   => ! [E] :
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ( E != k1_xboole_0
                         => ! [F] :
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,B,C)
                                & m2_relset_1(F,B,C) )
                             => ! [G] :
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,C,A)
                                    & m2_relset_1(G,C,A) )
                                 => k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t39_setwiseo,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) )
             => ( ( v1_binop_1(C,B)
                  & v2_binop_1(C,B)
                  & v3_binop_1(C,B) )
               => ! [D] :
                    ( ~ v1_xboole_0(D)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k2_zfmisc_1(D,D),D)
                          & m2_relset_1(E,k2_zfmisc_1(D,D),D) )
                       => ( ( v1_binop_1(E,D)
                            & v2_binop_1(E,D)
                            & v3_binop_1(E,D) )
                         => ! [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,B,D)
                                    & m2_relset_1(G,B,D) )
                                 => ( ! [H] :
                                        ( m1_subset_1(H,B)
                                       => ! [I] :
                                            ( m1_subset_1(I,B)
                                           => k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) ) )
                                   => ! [H] :
                                        ( m1_subset_1(H,k5_finsub_1(A))
                                       => ( H != k1_xboole_0
                                         => k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t40_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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(C,A)
                  & v2_binop_1(C,A)
                  & v1_setwiseo(C,A) )
               => ! [D] :
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,B,A)
                      & m2_relset_1(D,B,A) )
                   => k7_setwiseo(B,A,C,k1_setwiseo(B),D) = k3_binop_1(A,C) ) ) ) ) ) )).

fof(t41_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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] :
                  ( m1_subset_1(D,k5_finsub_1(B))
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,B,A)
                        & m2_relset_1(E,B,A) )
                     => ( ( v3_binop_1(C,A)
                          & v1_binop_1(C,A)
                          & v2_binop_1(C,A)
                          & v1_setwiseo(C,A) )
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) ) ) ) ) ) ) ) )).

fof(t42_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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,B,A)
                    & m2_relset_1(D,B,A) )
                 => ( ( v3_binop_1(C,A)
                      & v1_binop_1(C,A)
                      & v2_binop_1(C,A)
                      & v1_setwiseo(C,A) )
                   => ! [E] :
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ! [F] :
                            ( m1_subset_1(F,k5_finsub_1(B))
                           => k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) ) ) ) ) ) ) ) )).

fof(t43_setwiseo,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) )
             => ( ( v1_binop_1(C,B)
                  & v2_binop_1(C,B)
                  & v3_binop_1(C,B)
                  & v1_setwiseo(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] :
                            ( m1_subset_1(F,k5_finsub_1(A))
                           => ! [G] :
                                ( m1_subset_1(G,k5_finsub_1(A))
                               => ( k8_setwiseo(A,B,D,F) = k8_setwiseo(A,B,E,G)
                                 => k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E) ) ) ) ) ) ) ) ) ) )).

fof(t44_setwiseo,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,k2_zfmisc_1(A,A),A)
                    & m2_relset_1(D,k2_zfmisc_1(A,A),A) )
                 => ( ( v3_binop_1(D,A)
                      & v1_binop_1(D,A)
                      & v2_binop_1(D,A)
                      & v1_setwiseo(D,A) )
                   => ! [E] :
                        ( m1_subset_1(E,k5_finsub_1(B))
                       => ! [F] :
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,B,C)
                              & m2_relset_1(F,B,C) )
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,C,A)
                                  & m2_relset_1(G,C,A) )
                               => k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)) ) ) ) ) ) ) ) ) )).

fof(t45_setwiseo,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) )
             => ( ( v1_binop_1(C,B)
                  & v2_binop_1(C,B)
                  & v3_binop_1(C,B)
                  & v1_setwiseo(C,B) )
               => ! [D] :
                    ( ~ v1_xboole_0(D)
                   => ! [E] :
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,k2_zfmisc_1(D,D),D)
                          & m2_relset_1(E,k2_zfmisc_1(D,D),D) )
                       => ( ( v1_binop_1(E,D)
                            & v2_binop_1(E,D)
                            & v3_binop_1(E,D)
                            & v1_setwiseo(E,D) )
                         => ! [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,B,D)
                                    & m2_relset_1(G,B,D) )
                                 => ( ( k8_funct_2(B,D,G,k3_binop_1(B,C)) = k3_binop_1(D,E)
                                      & ! [H] :
                                          ( m1_subset_1(H,B)
                                         => ! [I] :
                                              ( m1_subset_1(I,B)
                                             => k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) ) ) )
                                   => ! [H] :
                                        ( m1_subset_1(H,k5_finsub_1(A))
                                       => k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_setwiseo,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A))
        & m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) )
     => ( B = k9_setwiseo(A)
      <=> ! [C] :
            ( m1_subset_1(C,k5_finsub_1(A))
           => ! [D] :
                ( m1_subset_1(D,k5_finsub_1(A))
               => k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D) = k5_setwiseo(A,C,D) ) ) ) ) )).

fof(t46_setwiseo,axiom,(
    $true )).

fof(t47_setwiseo,axiom,(
    $true )).

fof(t48_setwiseo,axiom,(
    $true )).

fof(t49_setwiseo,axiom,(
    ! [A] : v3_binop_1(k9_setwiseo(A),k5_finsub_1(A)) )).

fof(t50_setwiseo,axiom,(
    ! [A] : v1_binop_1(k9_setwiseo(A),k5_finsub_1(A)) )).

fof(t51_setwiseo,axiom,(
    ! [A] : v2_binop_1(k9_setwiseo(A),k5_finsub_1(A)) )).

fof(t52_setwiseo,axiom,(
    ! [A] : r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A)) )).

fof(t53_setwiseo,axiom,(
    ! [A] : v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A)) )).

fof(t54_setwiseo,axiom,(
    ! [A] : r3_binop_1(k5_finsub_1(A),k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)),k9_setwiseo(A)) )).

fof(t55_setwiseo,axiom,(
    ! [A] : k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)) = k1_xboole_0 )).

fof(d5_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( m1_subset_1(C,k5_finsub_1(A))
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,k5_finsub_1(B))
                & m2_relset_1(D,A,k5_finsub_1(B)) )
             => k10_setwiseo(A,B,C,D) = k7_setwiseo(A,k5_finsub_1(B),k9_setwiseo(B),C,D) ) ) ) )).

fof(t56_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] :
              ( m1_subset_1(D,A)
             => k10_setwiseo(A,B,k2_setwiseo(A,D),C) = k8_funct_2(A,k5_finsub_1(B),C,D) ) ) ) )).

fof(t57_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] :
              ( m1_subset_1(D,A)
             => ! [E] :
                  ( m1_subset_1(E,A)
                 => k10_setwiseo(A,B,k3_setwiseo(A,D,E),C) = k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)) ) ) ) ) )).

fof(t58_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] :
              ( m1_subset_1(D,A)
             => ! [E] :
                  ( m1_subset_1(E,A)
                 => ! [F] :
                      ( m1_subset_1(F,A)
                     => k10_setwiseo(A,B,k4_setwiseo(A,D,E,F),C) = k5_setwiseo(B,k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)),k8_funct_2(A,k5_finsub_1(B),C,F)) ) ) ) ) ) )).

fof(t59_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => k10_setwiseo(A,B,k1_setwiseo(A),C) = k1_xboole_0 ) ) )).

fof(t60_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] :
              ( m1_subset_1(D,A)
             => ! [E] :
                  ( m1_subset_1(E,k5_finsub_1(A))
                 => k10_setwiseo(A,B,k5_setwiseo(A,E,k2_setwiseo(A,D)),C) = k5_setwiseo(B,k10_setwiseo(A,B,E,C),k8_funct_2(A,k5_finsub_1(B),C,D)) ) ) ) ) )).

fof(t61_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(A))
             => k10_setwiseo(A,B,D,C) = k3_tarski(k8_setwiseo(A,k5_finsub_1(B),C,D)) ) ) ) )).

fof(t62_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(A))
             => ! [E] :
                  ( m1_subset_1(E,k5_finsub_1(A))
                 => k10_setwiseo(A,B,k5_setwiseo(A,D,E),C) = k5_setwiseo(B,k10_setwiseo(A,B,D,C),k10_setwiseo(A,B,E,C)) ) ) ) ) )).

fof(t63_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [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,B,k5_finsub_1(C))
                        & m2_relset_1(F,B,k5_finsub_1(C)) )
                     => k10_setwiseo(B,C,k8_setwiseo(A,B,E,D),F) = k10_setwiseo(A,C,D,k7_funct_2(A,B,k5_finsub_1(C),E,F)) ) ) ) ) ) )).

fof(t64_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C,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_binop_1(D,A)
                  & v2_binop_1(D,A)
                  & v3_binop_1(D,A) )
               => ! [E] :
                    ( m1_subset_1(E,k5_finsub_1(B))
                   => ( E != k1_xboole_0
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,B,k5_finsub_1(C))
                            & m2_relset_1(F,B,k5_finsub_1(C)) )
                         => ! [G] :
                              ( ( v1_funct_1(G)
                                & v1_funct_2(G,k5_finsub_1(C),A)
                                & m2_relset_1(G,k5_finsub_1(C),A) )
                             => ( ! [H] :
                                    ( m1_subset_1(H,k5_finsub_1(C))
                                   => ! [I] :
                                        ( m1_subset_1(I,k5_finsub_1(C))
                                       => k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)) = k2_binop_1(A,A,A,D,k8_funct_2(k5_finsub_1(C),A,G,H),k8_funct_2(k5_finsub_1(C),A,G,I)) ) )
                               => k8_funct_2(k5_finsub_1(C),A,G,k10_setwiseo(B,C,E,F)) = k7_setwiseo(B,A,D,E,k7_funct_2(B,k5_finsub_1(C),A,F,G)) ) ) ) ) ) ) ) ) ) )).

fof(t65_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C,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_binop_1(D,B)
                  & v2_binop_1(D,B)
                  & v3_binop_1(D,B)
                  & v1_setwiseo(D,B) )
               => ! [E] :
                    ( ( v1_funct_1(E)
                      & v1_funct_2(E,A,k5_finsub_1(C))
                      & m2_relset_1(E,A,k5_finsub_1(C)) )
                   => ! [F] :
                        ( ( v1_funct_1(F)
                          & v1_funct_2(F,k5_finsub_1(C),B)
                          & m2_relset_1(F,k5_finsub_1(C),B) )
                       => ( ( k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) = k3_binop_1(B,D)
                            & ! [G] :
                                ( m1_subset_1(G,k5_finsub_1(C))
                               => ! [H] :
                                    ( m1_subset_1(H,k5_finsub_1(C))
                                   => k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)) = k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)) ) ) )
                         => ! [G] :
                              ( m1_subset_1(G,k5_finsub_1(A))
                             => k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)) = k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)) ) ) ) ) ) ) ) ) )).

fof(d6_setwiseo,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,k5_finsub_1(A))
        & m2_relset_1(B,A,k5_finsub_1(A)) )
     => ( B = k11_setwiseo(A)
      <=> ! [C] :
            ( r2_hidden(C,A)
           => k1_funct_1(B,C) = k1_tarski(C) ) ) ) )).

fof(t66_setwiseo,axiom,(
    $true )).

fof(t67_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,k5_finsub_1(A))
            & m2_relset_1(B,A,k5_finsub_1(A)) )
         => ( B = k11_setwiseo(A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => k8_funct_2(A,k5_finsub_1(A),B,C) = k2_setwiseo(A,C) ) ) ) ) )).

fof(t68_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( m1_subset_1(C,A)
         => ( r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C))
          <=> B = C ) ) ) )).

fof(t69_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,A)
                 => ( ( r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D))
                      & r2_hidden(C,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) )
                   => B = C ) ) ) ) ) )).

fof(t70_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k5_finsub_1(B))
            & m2_relset_1(C,A,k5_finsub_1(B)) )
         => ! [D] :
              ( m1_subset_1(D,k5_finsub_1(A))
             => ! [E] :
                  ( r2_hidden(E,k10_setwiseo(A,B,D,C))
                <=> ? [F] :
                      ( m1_subset_1(F,A)
                      & r2_hidden(F,D)
                      & r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) ) ) ) ) ) )).

fof(t71_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(A))
         => k10_setwiseo(A,A,B,k11_setwiseo(A)) = B ) ) )).

fof(t72_setwiseo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B,C,D] :
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,k5_finsub_1(B))
            & m2_relset_1(D,A,k5_finsub_1(B)) )
         => ! [E] :
              ( ( v1_funct_1(E)
                & v1_funct_2(E,k5_finsub_1(B),k5_finsub_1(C))
                & m2_relset_1(E,k5_finsub_1(B),k5_finsub_1(C)) )
             => ( ( k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) = k1_setwiseo(C)
                  & ! [F] :
                      ( m1_subset_1(F,k5_finsub_1(B))
                     => ! [G] :
                          ( m1_subset_1(G,k5_finsub_1(B))
                         => k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k5_setwiseo(B,F,G)) = k5_setwiseo(C,k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,F),k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,G)) ) ) )
               => ! [F] :
                    ( m1_subset_1(F,k5_finsub_1(A))
                   => k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D)) = k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E)) ) ) ) ) ) )).

fof(s1_setwiseo,axiom,(
    ? [A] :
      ( v1_funct_1(A)
      & v1_funct_2(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo))
      & m2_relset_1(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo))
      & ! [B] :
          ( m1_subset_1(B,f1_s1_setwiseo)
         => ! [C] :
              ( m1_subset_1(C,f1_s1_setwiseo)
             => ( r2_hidden(C,k8_funct_2(f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo),A,B))
              <=> ( r2_hidden(C,f2_s1_setwiseo)
                  & p1_s1_setwiseo(C,B) ) ) ) ) ) )).

fof(s2_setwiseo,axiom,
    ( ( p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo))
      & ! [A] :
          ( m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo))
         => ! [B] :
              ( m1_subset_1(B,f1_s2_setwiseo)
             => ( p1_s2_setwiseo(A)
               => ( r2_hidden(B,A)
                  | p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B))) ) ) ) ) )
   => ! [A] :
        ( m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo))
       => p1_s2_setwiseo(A) ) )).

fof(s3_setwiseo,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s3_setwiseo)
         => p1_s3_setwiseo(k2_setwiseo(f1_s3_setwiseo,A)) )
      & ! [A] :
          ( m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo))
         => ! [B] :
              ( m1_subset_1(B,k5_finsub_1(f1_s3_setwiseo))
             => ( ( p1_s3_setwiseo(A)
                  & p1_s3_setwiseo(B) )
               => ( A = k1_xboole_0
                  | B = k1_xboole_0
                  | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,B)) ) ) ) ) )
   => ! [A] :
        ( m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo))
       => ( A != k1_xboole_0
         => p1_s3_setwiseo(A) ) ) )).

fof(s4_setwiseo,axiom,
    ( ( p1_s4_setwiseo(k1_setwiseo(f1_s4_setwiseo))
      & ! [A] :
          ( m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo))
         => ! [B] :
              ( m1_subset_1(B,f1_s4_setwiseo)
             => ( p1_s4_setwiseo(A)
               => p1_s4_setwiseo(k5_setwiseo(f1_s4_setwiseo,A,k2_setwiseo(f1_s4_setwiseo,B))) ) ) ) )
   => ! [A] :
        ( m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo))
       => p1_s4_setwiseo(A) ) )).

fof(dt_k1_setwiseo,axiom,(
    ! [A] :
      ( v1_xboole_0(k1_setwiseo(A))
      & m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)) ) )).

fof(dt_k2_setwiseo,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)) ) )).

fof(redefinition_k2_setwiseo,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k2_setwiseo(A,B) = k1_tarski(B) ) )).

fof(dt_k3_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)) ) )).

fof(commutativity_k3_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k3_setwiseo(A,B,C) = k3_setwiseo(A,C,B) ) )).

fof(redefinition_k3_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k3_setwiseo(A,B,C) = k2_tarski(B,C) ) )).

fof(dt_k4_setwiseo,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => m1_subset_1(k4_setwiseo(A,B,C,D),k5_finsub_1(A)) ) )).

fof(redefinition_k4_setwiseo,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A)
        & m1_subset_1(D,A) )
     => k4_setwiseo(A,B,C,D) = k1_enumset1(B,C,D) ) )).

fof(dt_k5_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)) ) )).

fof(commutativity_k5_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,C) = k5_setwiseo(A,C,B) ) )).

fof(idempotence_k5_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,B) = B ) )).

fof(redefinition_k5_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k5_setwiseo(A,B,C) = k2_xboole_0(B,C) ) )).

fof(dt_k6_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => m1_subset_1(k6_setwiseo(A,B,C),k5_finsub_1(A)) ) )).

fof(redefinition_k6_setwiseo,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(B,k5_finsub_1(A))
        & m1_subset_1(C,k5_finsub_1(A)) )
     => k6_setwiseo(A,B,C) = k4_xboole_0(B,C) ) )).

fof(dt_k7_setwiseo,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,k5_finsub_1(A))
        & v1_funct_1(E)
        & v1_funct_2(E,A,B)
        & m1_relset_1(E,A,B) )
     => m1_subset_1(k7_setwiseo(A,B,C,D,E),B) ) )).

fof(dt_k8_setwiseo,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,k5_finsub_1(A)) )
     => m1_subset_1(k8_setwiseo(A,B,C,D),k5_finsub_1(B)) ) )).

fof(redefinition_k8_setwiseo,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,k5_finsub_1(A)) )
     => k8_setwiseo(A,B,C,D) = k9_relat_1(C,D) ) )).

fof(dt_k9_setwiseo,axiom,(
    ! [A] :
      ( v1_funct_1(k9_setwiseo(A))
      & v1_funct_2(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A))
      & m2_relset_1(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) ) )).

fof(dt_k10_setwiseo,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(C,k5_finsub_1(A))
        & v1_funct_1(D)
        & v1_funct_2(D,A,k5_finsub_1(B))
        & m1_relset_1(D,A,k5_finsub_1(B)) )
     => m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)) ) )).

fof(dt_k11_setwiseo,axiom,(
    ! [A] :
      ( v1_funct_1(k11_setwiseo(A))
      & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A))
      & m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)) ) )).
%------------------------------------------------------------------------------